Probability and statistics Books

Book SynopsisMultilevel Modeling Methods with Introductory and Advanced Applications provides a cogent and comprehensive introduction to the area of multilevel modeling for methodological and applied researchers as well as advanced graduate students. The book is designed to be able to serve as a textbook for a one or two semester course in multilevel modeling. The topics of the seventeen chapters range from basic to advanced, yet each chapter is designed to be able to stand alone as an instructional unit on its respective topic, with an emphasis on application and interpretation.In addition to covering foundational topics on the use of multilevel models for organizational and longitudinal research, the book includes chapters on more advanced extensions and applications, such as cross-classified random effects models, non-linear growth models, mixed effects location scale models, logistic, ordinal, and Poisson models, and multilevel mediation. In addition, the volume includes chapters addressing some of the most important design and analytic issues including missing data, power analyses, causal inference, model fit, and measurement issues. Finally, the volume includes chapters addressing special topics such as using large-scale complex sample datasets, and reporting the results of multilevel designs.Each chapter contains a section called Try This!, which poses a structured data problem for the reader. We have linked our book to a website (http://modeling.uconn.edu) containing data for the Try This! section, creating an opportunity for readers to learn by doing. The inclusion of the Try This! problems, data, and sample code eases the burden for instructors, who must continually search for class examples and homework problems. In addition, each chapter provides recommendations for additional methodological and applied readings.

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Book SynopsisMultilevel Modeling Methods with Introductory and Advanced Applications provides a cogent and comprehensive introduction to the area of multilevel modeling for methodological and applied researchers as well as advanced graduate students. The book is designed to be able to serve as a textbook for a one or two semester course in multilevel modeling. The topics of the seventeen chapters range from basic to advanced, yet each chapter is designed to be able to stand alone as an instructional unit on its respective topic, with an emphasis on application and interpretation.In addition to covering foundational topics on the use of multilevel models for organizational and longitudinal research, the book includes chapters on more advanced extensions and applications, such as cross-classified random effects models, non-linear growth models, mixed effects location scale models, logistic, ordinal, and Poisson models, and multilevel mediation. In addition, the volume includes chapters addressing some of the most important design and analytic issues including missing data, power analyses, causal inference, model fit, and measurement issues. Finally, the volume includes chapters addressing special topics such as using large-scale complex sample datasets, and reporting the results of multilevel designs.Each chapter contains a section called Try This!, which poses a structured data problem for the reader. We have linked our book to a website (http://modeling.uconn.edu) containing data for the Try This! section, creating an opportunity for readers to learn by doing. The inclusion of the Try This! problems, data, and sample code eases the burden for instructors, who must continually search for class examples and homework problems. In addition, each chapter provides recommendations for additional methodological and applied readings.

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Book SynopsisThis book covers the use of R programming language for data visualization. The large real-world datasets can be quickly visualized to gain several insights from it using R. Whether the data is already clean or needs some preliminary steps before data visualization like data cleaning and wrangling, all these can be done using R to produce elegant, publication-ready, and exciting plots. This book covers different plot types from simple ones like univariate and bivariate plots (histograms, box plots, violin plots, scatter plots, density plots, bar graphs, pie charts, tree maps, beeswarm plots, Cleveland dot charts, line plots, etc) to more complex ones like mapping and visualizing patterns of missing data (upset plots, different Stamen map types with different zoom levels). All these were shown using free real-world data sets to illustrate the diverse capability of R for data visualization.Table of Contents Volume 1 Chapter 1 Installing R and RStudio Chapter 2 Getting Started with R and RStudio Chapter 3 Univariate Plots for Continuous Data Chapter 4 Univariate Plots for Categorical Data Chapter 5 Bivariate Plots for Continuous DataVolume 2 Chapter 6 Bivariate Plots for Continuous Categorical Data Chapter 7 Bivariate Plots for Categorical Data Chapter 8 More Than 2 Dimensions Chapter 9 Visualizing Missing Data Chapter 10 Mapping

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Book SynopsisThis book is devoted to the problems of construction and application of chi-squared goodness-of-fit tests for complete and censored data. Classical chi-squared tests assume that unknown distribution parameters are estimated using grouped data, but in practice this assumption is often forgotten. In this book, we consider modified chi-squared tests, which do not suffer from such a drawback. The authors provide examples of chi-squared tests for various distributions widely used in practice, and also consider chi-squared tests for the parametric proportional hazards model and accelerated failure time model, which are widely used in reliability and survival analysis. Particular attention is paid to the choice of grouping intervals and simulations. This book covers recent innovations in the field as well as important results previously only published in Russian. Chi-squared tests are compared with other goodness-of-fit tests (such as the Cramer-von Mises-Smirnov, Anderson-Darling and Zhang tests) in terms of power when testing close competing hypotheses.Table of ContentsIntroduction ix Chapter 1. Chi-squared Goodness-of-fit Tests for Complete Data 1 1.1. Classical Pearson’s chi-squared test 1 1.2. Joint distribution of Xn(θ∗n)and√n(θ∗n−θ) 3 1.3. Parameter estimation based on complete data Lemma of Chernoff and Lehmann 5 1.4. Parameter estimation based on grouped data. Theorem of Fisher 10 1.5. Nikulin-Rao-Robson chi-squared test 12 1.6. Other modifications 18 1.7. The choice of grouping intervals 20 Chapter 2. Chi-squared Test for Censored Data 31 2.1. Generalized Pearson-Fisher chi-squared test 32 2.2. Maximum likelihood estimators for censored data 34 2.3. Nikulin-Rao-Robson chi-squared test for censored data 38 2.4. The choice of grouping intervals 45 2.4.1. Equifrequent grouping (EFG) 45 2.4.2. Intervals with equal expected numbers of failures (EENFG) 46 2.4.3. Optimal grouping (OptG) 48 2.5. Chi-squared tests for specific families of distributions 51 2.5.1. Exponential distribution 51 2.5.2. Weibull distribution 55 2.5.3. Lognormal distribution 60 2.5.4. Loglogistic distribution 63 2.5.5. Gompertz distribution 67 Chapter 3. Comparison of the Chi-squared Goodness-of-fit Test with Other Tests 71 3.1. Tests based on the difference between non-parametric and parametric estimators 71 3.2. Comparison of goodness-of-fit tests for complete data 76 3.3. Comparison of goodness-of-fit tests for censored data 79 3.3.1. Lognormal-generalized Weibull pair of competing hypotheses 80 3.3.2. Exponential-Weibull pair of competing hypotheses 82 3.3.3. Weibull-generalized Weibull pairs of competing hypotheses 84 Chapter 4. Chi-squared Goodness-of-fit Tests for Regression Models 87 4.1. Data and the idea of chi-squared test construction 89 4.2. Asymptotic distribution of the random vector Z 91 4.3. Test statistic 96 4.4. Choice of random grouping intervals 97 4.4.1. Test for the exponential AFT model 99 4.4.2. Tests for the scale-shape AFT models with constant covariates 101 4.4.3. Test for the Weibull AFT model with step-stresses 108 Appendices 111 Appendix 1 113 Appendix 2 125 Bibliography 131 Index 141

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Book SynopsisThe purpose of this book is to provide a comprehensive discussion of the available results for discrete time branching processes with random control functions. The independence of individuals’ reproduction is a fundamental assumption in the classical branching processes. Alternatively, the controlled branching processes (CBPs) allow the number of reproductive individuals in one generation to decrease or increase depending on the size of the previous generation. Generating a wide range of behaviors, the CBPs have been successfully used as modeling tools in diverse areas of applications.Table of ContentsForeword ix Preface xi Chapter 1 Classical Branching Models 1 1.1 Bienaymé–Galton–Watson process 1 1.1.1 Moments and probability of extinction 4 1.1.2 Limit theorems 9 1.2 Processes with unrestricted immigration 17 1.2.1 Limit theorems 21 1.2.2 Critical process with decreasing to zero immigration 25 1.3 Processes with immigration after empty generation only 29 1.3.1 Limit theorems 31 1.3.2 Critical process with decreasing to zero immigration 36 1.4 Background and bibliographical notes 40 Chapter 2 Branching Processes with Migration 43 2.1 Galton–Watson process with migration 43 2.2 Limit theorems 47 2.2.1 Non-critical processes 47 2.2.2 Critical processes with non-negative migration mean 49 2.2.3 Critical processes with negative migration mean 52 2.3 Regeneration and migration 55 2.3.1 Alternating regenerative processes 56 2.3.2 An extension of Galton–Watson processes with migration 58 2.4 Background and bibliographical notes 62 Chapter 3 CB Processes: Extinction 65 3.1 Definition of processes and basic properties 65 3.1.1 Basic properties 69 3.1.2 Probability generating functions and moments 73 3.2 Extinction probability 75 3.2.1 Subcritical processes 76 3.2.2 Supercritical processes 78 3.2.3 Critical processes 84 3.3 Background and bibliographical notes 91 Chapter 4 CB Processes: Limit Theorems 95 4.1 Subcritical processes 95 4.2 Critical processes 100 4.2.1 Extinction is not certain 101 4.2.2 Extinction is certain 109 4.2.3 Feller diffusion approximation 110 4.3 Supercritical processes 115 4.3.1 Almost sure convergence 117 4.3.2 L1–convergence 118 4.3.3 L2–convergence 121 4.4 Background and bibliographical notes 125 Chapter 5 Statistics of CB Processes 127 5.1 Maximum likelihood estimation 127 5.1.1 MLE based on entire family tree up to nth generation 130 5.1.2 EM algorithms for incomplete data 146 5.1.3 Simulated example 152 5.2 Conditional weighted least squares estimation 158 5.2.1 Subcritical processes 159 5.2.2 Critical processes 161 5.2.3 Supercritical processes 166 5.3 Minimum disparity estimation 169 5.4 Bayesian inference 171 5.4.1 Estimation based on entire family tree up to nth generation 172 5.4.2 MCMC algorithms for incomplete data 173 5.5 Background and bibliographical notes 176 Appendices 179 Appendix 1 181 Appendix 2 185 Appendix 3 191 Appendix 4 195 Bibliography 197 Index 209

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Book Synopsis Piecewise-deterministic Markov processes form a class of stochastic models with a sizeable scope of applications: biology, insurance, neuroscience, networks, finance... Such processes are defined by a deterministic motion punctuated by random jumps at random times, and offer simple yet challenging models to study. Nevertheless, the issue of statistical estimation of the parameters ruling the jump mechanism is far from trivial. Responding to new developments in the field as well as to current research interests and needs, Statistical inference for piecewise-deterministic Markov processes offers a detailed and comprehensive survey of state-of-the-art results. It covers a wide range of general processes as well as applied models. The present book also dwells on statistics in the context of Markov chains, since piecewise-deterministic Markov processes are characterized by an embedded Markov chain corresponding to the position of the process right after the jumps. Table of ContentsPreface xiRomain AZAÏS and Florian BOUGUET List of Acronyms xiii Introduction xvRomain AZAÏS and Florian BOUGUET Chapter 1. Statistical Analysis for Structured Models on Trees 1Marc HOFFMANN and Adelaide OLIVIER 1.1. Introduction 1 1.1.1. Motivation 1 1.1.2. Genealogical versus temporal data 2 1.2. Size-dependent division rate 4 1.2.1. From partial differential equation to stochastic models 4 1.2.2. Non-parametric estimation: the Markov tree approach 6 1.2.3. Sketch of proof of Theorem 1.1 10 1.3. Estimating the age-dependent division rate 16 1.3.1. Heuristics and convergence of empirical measures 17 1.3.2. Estimation results 20 1.3.3. Sketch of proof of Theorem 1.4 24 1.4. Bibliography 37 Chapter 2. Regularity of the Invariant Measure and Non-parametric Estimation of the Jump Rate 39Pierre HODARA, Nathalie KRELL and Eva LOCHERBACH 2.1. Introduction 39 2.2. Absolute continuity of the invariant measure 43 2.2.1. The dynamics 43 2.2.2. An associated Markov chain and its invariant measure 45 2.2.3. Smoothness of the invariant density of a single particle 47 2.2.4. Lebesgue density in dimension N 50 2.3. Estimation of the spiking rate in systems of interacting neurons 51 2.3.1. Harris recurrence 55 2.3.2. Properties of the estimator 56 2.3.3. Simulation results 58 2.4. Bibliography 61 Chapter 3. Level Crossings and Absorption of an Insurance Model 65Romain AZAÏS and Alexandre GENADOT 3.1. An insurance model 65 3.2. Some results about the crossing and absorption features 70 3.2.1. Transition density of the post-jump locations 70 3.2.2. Absorption time and probability 71 3.2.3. Kac–Rice formula 74 3.3. Inference for the absorption features of the process 77 3.3.1. Semi-parametric framework 77 3.3.2. Estimators and convergence results 79 3.3.3. Numerical illustration 81 3.4. Inference for the average number of crossings 89 3.4.1. Estimation procedures 89 3.4.2. Numerical application 90 3.5. Some additional proofs 92 3.5.1. Technical lemmas 92 3.5.2. Proof of Proposition 3.3 97 3.5.3. Proof of Corollary 3.2 98 3.5.4. Proof of Theorem 3.5 100 3.5.5. Proof of Theorem 3.6 102 3.5.6. Discussion on the condition (C2G) 103 3.6. Bibliography 104 Chapter 4. Robust Estimation for Markov Chains with Applications to Piecewise-deterministic Markov Processes 107Patrice BERTAIL, Gabriela CIOŁEK and Charles TILLIER 4.1. Introduction 107 4.2. (Pseudo)-regenerative Markov chains 109 4.2.1. General Harris Markov chains and the splitting technique 110 4.2.2. Regenerative blocks for dominated families 111 4.2.3. Construction of regeneration blocks 112 4.3. Robust functional parameter estimation for Markov chains 114 4.3.1. The influence function on the torus 115 4.3.2. Example 1: sample means 116 4.3.3. Example 2: M-estimators 117 4.3.4. Example 3: quantiles 118 4.4. Central limit theorem for functionals of Markov chains and robustness 118 4.5. A Markov view for estimators in PDMPs 121 4.5.1. Example 1: Sparre Andersen model with barrier 122 4.5.2. Example 2: kinetic dietary exposure model 125 4.6. Robustness for risk PDMP models 127 4.6.1. Stationary measure 127 4.6.2. Ruin probability 132 4.6.3. Extremal index 136 4.6.4. Expected shortfall 138 4.7. Simulations 140 4.8. Bibliography 144 Chapter 5. Numerical Method for Control of Piecewise-deterministic Markov Processes . 147Benoite DE SAPORTA and Francois DUFOUR 5.1. Introduction 147 5.2. Simulation of piecewise-deterministic Markov processes 149 5.3. Optimal stopping 150 5.3.1. Assumptions and notations 150 5.3.2. Dynamic programming 153 5.3.3. Quantized approximation 154 5.4. Exit time 158 5.4.1. Problem setting and assumptions 158 5.4.2. Recursive formulation 159 5.4.3. Numerical approximation 161 5.5. Numerical example 162 5.5.1. Piecewise-deterministic Markov model 162 5.5.2. Deterministic time to reach the boundary 164 5.5.3. Quantization 166 5.5.4. Optimal stopping 167 5.5.5. Exit time 169 5.6. Conclusion 170 5.7. Bibliography 171 Chapter 6. Rupture Detection in Fatigue Crack Propagation 173Romain AZAIS, Anne GEGOUT-PETIT and Florine GRECIET 6.1. Phenomenon of crack propagation 173 6.1.1. Virkler’s data 174 6.2. Modeling crack propagation 175 6.2.1. Deterministic models 175 6.2.2. Sources of uncertainties 177 6.2.3. Stochastic models 178 6.3. PDMP models of propagation 183 6.3.1. Relevance of PDMP models 183 6.3.2. Multiplicative model 185 6.3.3. One-jump models 186 6.4. Rupture detection 193 6.4.1. Length at versus time t . 193 6.4.2. Growth rate dat /dt versus ΔKt in log scale 194 6.5. Conclusion and perspectives 203 6.6. Bibliography 204 Chapter 7. Piecewise-deterministic Markov Processes for Spatio-temporal Population Dynamics . 209Candy ABBOUD, Rachid SENOUSSI and Samuel SOUBEYRAND 7.1. Introduction 209 7.1.1. Models of population dynamics 209 7.1.2. Spatio-temporal PDMP for population dynamics 210 7.1.3. Chapter contents 212 7.2. Stratified dispersal models 212 7.2.1. Reaction–diffusion equations for modeling short-distance dispersal 212 7.2.2. Stratified diffusion 215 7.2.3. Coalescing colony model with Allee effect 216 7.2.4. A PDMP based on reaction–diffusion for modeling invasions with multiple introductions 221 7.3. Metapopulation epidemic model 223 7.3.1. Spatially realistic Levins model 223 7.3.2. A colonization PDMP 224 7.3.3. Bayesian inference approach 229 7.3.4. Markov chain Monte Carlo algorithm 235 7.3.5. Examples of results 236 7.4. Stochastic approaches for modeling spatial trajectories 237 7.4.1. Conditioning a Brownian motion by punctual observations 239 7.4.2. Movements with jumps 242 7.4.3. The Doléans–Dade exponential semi-martingales 247 7.4.4. Statistical issues 249 7.5. Conclusion 252 7.6. Bibliography 252 List of Authors 257 Index 259

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Book SynopsisData science unifies statistics, data analysis and machine learning to achieve a better understanding of the masses of data which are produced today, and to improve prediction. Special kinds of data (symbolic, network, complex, compositional) are increasingly frequent in data science. These data require specific methodologies, but there is a lack of reference work in this field. Advances in Data Science fills this gap. It presents a collection of up-to-date contributions by eminent scholars following two international workshops held in Beijing and Paris. The 10 chapters are organized into four parts: Symbolic Data, Complex Data, Network Data and Clustering. They include fundamental contributions, as well as applications to several domains, including business and the social sciences. Table of ContentsPreface xi Part 1. Symbolic Data 1 Chapter 1. Explanatory Tools for Machine Learning in the Symbolic Data Analysis Framework 3Edwin DIDAY 1.1. Introduction 4 1.2. Introduction to Symbolic Data Analysis 6 1.2.1. What are complex data? 6 1.2.2. What are “classes” and “class of complex data”? 7 1.2.3. Which kind of class variability? 7 1.2.4. What are “symbolic variables” and “symbolic data tables”? 7 1.2.5. Symbolic Data Analysis (SDA) 9 1.3. Symbolic data tables from Dynamic Clustering Method and EM 10 1.3.1. The “dynamical clustering method” (DCM) 10 1.3.2. Examples of DCM applications 10 1.3.3. Clustering methods by mixture decomposition 12 1.3.4. Symbolic data tables from clustering 13 1.3.5. A general way to compare results of clustering methods by the “explanatory power” of their associated symbolic data table 15 1.3.6. Quality criteria of classes and variables based on the cells of the symbolic data table containing intervals or inferred distributions 15 1.4. Criteria for ranking individuals, classes and their bar chart descriptive symbolic variables 16 1.4.1. A theoretical framework for SDA 16 1.4.2. Characterization of a category and a class by a measure of discordance 18 1.4.3. Link between a characterization by the criteria W and the standard Tf-Idf 19 1.4.4. Ranking the individuals, the symbolic variables and the classes of a bar chart symbolic data table 21 1.5. Two directions of research 23 1.5.1. Parametrization of concordance and discordance criteria 23 1.5.2. Improving the explanatory power of any machine learning tool by a filtering process 25 1.6. Conclusion 27 1.7. References 28 Chapter 2. Likelihood in the Symbolic Context 31Richard EMILION and Edwin DIDAY 2.1. Introduction 31 2.2. Probabilistic setting 32 2.2.1. Description variable and class variable 32 2.2.2. Conditional distributions 33 2.2.3. Symbolic variables 33 2.2.4. Examples 35 2.2.5. Probability measures on (ℂ, C), likelihood 37 2.3. Parametric models for p = 1 38 2.3.1. LDA model 38 2.3.2. BLS method 41 2.3.3. Interval-valued variables 42 2.3.4. Probability vectors and histogram-valued variables 42 2.4. Nonparametric estimation for p = 1 45 2.4.1. Multihistograms and multivariate polygons 45 2.4.2. Dirichlet kernel mixtures 45 2.4.3. Dirichlet Process Mixture (DPM) 45 2.5. Density models for p ≥ 2 46 2.6. Conclusion 46 2.7. References 47 Chapter 3. Dimension Reduction and Visualization of Symbolic Interval-Valued Data Using Sliced Inverse Regression 49Han-Ming WU, Chiun-How KAO and Chun-houh CHEN 3.1. Introduction 49 3.2. PCA for interval-valued data and the sliced inverse regression 51 3.2.1. PCA for interval-valued data 51 3.2.2. Classic SIR 52 3.3. SIR for interval-valued data 53 3.3.1. Quantification approaches 54 3.3.2. Distributional approaches 56 3.4. Projections and visualization in DR subspace 58 3.4.1. Linear combinations of intervals 58 3.4.2. The graphical representation of the projected intervals in the 2D DR subspace 59 3.5. Some computational issues 61 3.5.1. Standardization of interval-valued data 61 3.5.2. The slicing schemes for iSIR 62 3.5.3. The evaluation of DR components 62 3.6. Simulation studies 63 3.6.1. Scenario 1: aggregated data 63 3.6.2. Scenario 2: data based on interval arithmetic 63 3.6.3. Results 64 3.7. A real data example: face recognition data 65 3.8. Conclusion and discussion 73 3.9. References 74 Chapter 4. On the “Complexity” of Social Reality. Some Reflections About the Use of Symbolic Data Analysis in Social Sciences 79Frédéric LEBARON 4.1. Introduction 79 4.2. Social sciences facing “complexity” 80 4.2.1. The total social fact, a designation of “complexity” in social sciences 80 4.2.2. Two families of answers 80 4.2.3. The contemporary deepening of the two approaches, “reductionist” and “encompassing” 81 4.2.4. Issues of scale and heterogeneity 82 4.3. Symbolic data analysis in the social sciences: an example 83 4.3.1. Symbolic data analysis 83 4.3.2. An exploratory case study on European data 83 4.3.3. A sociological interpretation 94 4.4. Conclusion 95 4.5. References 96 Part 2. Complex Data 99 Chapter 5. A Spatial Dependence Measure and Prediction of Georeferenced Data Streams Summarized by Histograms 101Rosanna VERDE and Antonio BALZANELLA 5.1. Introduction 101 5.2. Processing setup 103 5.3. Main definitions 104 5.4. Online summarization of a data stream through CluStream for Histogram data 106 5.5. Spatial dependence monitoring: a variogram for histogram data 107 5.6. Ordinary kriging for histogram data 110 5.7. Experimental results on real data 112 5.8. Conclusion 116 5.9. References 116 Chapter 6. Incremental Calculation Framework for Complex Data 119Huiwen WANG, Yuan WEI and Siyang WANG 6.1. Introduction 119 6.2. Basic data 122 6.2.1. The basic data space 122 6.2.2. Sample covariance matrix 123 6.3. Incremental calculation of complex data 124 6.3.1. Transformation of complex data 124 6.3.2. Online decomposition of covariance matrix 125 6.3.3. Adopted algorithms 128 6.4. Simulation studies 131 6.4.1. Functional linear regression 131 6.4.2. Compositional PCA 133 6.5. Conclusion 135 6.6. Acknowledgment 135 6.7. References 135 Part 3. Network Data 139 Chapter 7. Recommender Systems and Attributed Networks 141Françoise FOGELMAN-SOULIÉ, Lanxiang MEI, Jianyu ZHANG, Yiming LI, Wen GE, Yinglan LI and Qiaofei YE 7.1. Introduction 141 7.2. Recommender systems 142 7.2.1. Data used 143 7.2.2. Model-based collaborative filtering 145 7.2.3. Neighborhood-based collaborative filtering 145 7.2.4. Hybrid models 148 7.3. Social networks 150 7.3.1. Non-independence 150 7.3.2. Definition of a social network 150 7.3.3. Properties of social networks 151 7.3.4. Bipartite networks 152 7.3.5. Multilayer networks 153 7.4. Using social networks for recommendation 154 7.4.1. Social filtering 154 7.4.2. Extension to use attributes 155 7.4.3. Remarks 156 7.5. Experiments 156 7.5.1. Performance evaluation 156 7.5.2. Datasets 157 7.5.3. Analysis of one-mode projected networks 158 7.5.4. Models evaluated 160 7.5.5. Results 160 7.6. Perspectives 163 7.7. References 163 Chapter 8. Attributed Networks Partitioning Based on Modularity Optimization 169David COMBE, Christine LARGERON, Baptiste JEUDY, Françoise FOGELMAN-SOULIÉ and Jing WANG 8.1. Introduction 169 8.2. Related work 171 8.3. Inertia based modularity 172 8.4. I-Louvain 174 8.5. Incremental computation of the modularity gain 176 8.6. Evaluation of I-Louvain method 179 8.6.1. Performance of I-Louvain on artificial datasets 179 8.6.2. Run-time of I-Louvain 180 8.7. Conclusion 181 8.8. References 182 Part 4. Clustering 187 Chapter 9. A Novel Clustering Method with Automatic Weighting of Tables and Variables 189Rodrigo C. DE ARAÚJO, Francisco DE ASSIS TENORIO DE CARVALHO and Yves LECHEVALLIER 9.1. Introduction 189 9.2. Related Work 190 9.3. Definitions, notations and objective 191 9.3.1. Choice of distances 192 9.3.2. Criterion W measures the homogeneity of the partition P on the set of tables 193 9.3.3. Optimization of the criterion W 195 9.4. Hard clustering with automated weighting of tables and variables 196 9.4.1. Clustering algorithms MND–W and MND–WT 196 9.5. Applications: UCI data sets 201 9.5.1. Application I: Iris plant 201 9.5.2. Application II: multi-features dataset 204 9.6. Conclusion 206 9.7. References 206 Chapter 10. Clustering and Generalized ANOVA for Symbolic Data Constructed from Open Data 209Simona KORENJAK-ČERNE, Nataša KEJŽAR and Vladimir BATAGELJ 10.1. Introduction 209 10.2. Data description based on discrete (membership) distributions 210 10.3. Clustering 212 10.3.1. TIMSS – study of teaching approaches 215 10.3.2. Clustering countries based on age–sex distributions of their populations 217 10.4. Generalized ANOVA 221 10.5. Conclusion 225 10.6. References 226 List of Authors 229 Index 233

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Book SynopsisData analysis as an area of importance has grown exponentially, especially during the past couple of decades. This can be attributed to a rapidly growing computer industry and the wide applicability of computational techniques, in conjunction with new advances of analytic tools. This being the case, the need for literature that addresses this is self-evident. New publications are appearing, covering the need for information from all fields of science and engineering, thanks to the universal relevance of data analysis and statistics packages. This book is a collective work by a number of leading scientists, analysts, engineers, mathematicians and statisticians who have been working at the forefront of data analysis. The chapters included in this volume represent a cross-section of current concerns and research interests in these scientific areas. The material is divided into three parts: Financial Data Analysis and Methods, Statistics and Stochastic Data Analysis and Methods, and Demographic Methods and Data Analysis- providing the reader with both theoretical and applied information on data analysis methods, models and techniques and appropriate applications.Table of ContentsPart 1. Financial Data Analysis and Methods 1. Forecasting Methods in Extreme Scenarios and Advanced Data Analytics for Improved Risk Estimation, George-Jason Siouris, Despoina Skilogianni and Alex Karagrigoriou. 2. Credit Portfolio Risk Evaluation with Non-Gaussian One-factor Merton Models and its Application to CDO Pricing, Takuya Fujii and Takayuki Shiohama. 3. Towards an Improved Credit Scoring System with Alternative Data: the Greek Case, Panagiota Giannouli and Christos E. Kountzakis. 4. EM Algorithm for Estimating the Parameters of the Multivariate Stable Distribution, Leonidas Sakalauskas and Ingrida Vaiciulyte. Part 2. Statistics and Stochastic Data Analysis and Methods 5. Methods for Assessing Critical States of Complex Systems, Valery Antonov. 6. Resampling Procedures for a More Reliable Extremal Index Estimation, Dora Prata Gomes and M. Manuela Neves. 7. Generalizations of Poisson Process in the Modeling of Random Processes Related to Road Accidents, Franciszek Grabski. 8. Dependability and Performance Analysis for a Two Unit Multi-state System with Imperfect Switch, Vasilis P. Koutras, Sonia Malefaki and Agapios N. Platis. 9. Models for Time Series Whose Trend Has Local Maximum and Minimum Values, Norio Watanabe. 10. How to Model the Covariance Structure in a Spatial Framework: Variogram or Correlation Function?, Giovanni Pistone and Grazia Vicario. 11. Comparison of Stochastic Processes, Jesús Enrique García, Ramin Gholizadeh and Verónica Andrea González-López. Part 3 . Demographic Methods and Data Analysis 12. Conjoint Analysis of Gross Annual Salary Re-evaluation: Evidence from Lombardy ELECTUS Data, Paolo Mariani, Andrea Marletta and Mariangela Zenga. 13. Methodology for an Optimum Health Expenditure Allocation, George Matalliotakis. 14. Probabilistic Models for Clinical Pathways: The Case of Chronic Patients, Stergiani Spyrou, Anatoli Kazektsidou and Panagiotis Bamidis. 15. On Clustering Techniques for Multivariate Demographic Health Data, Achilleas Anastasiou, George Mavridoglou, Petros Hatzopoulos and Alex Karagrigoriou. 16. Tobacco-related Mortality in Greece: The Effect of Malignant Neoplasms, Circulatory and Respiratory Diseases,1994–2016, Konstantinos N. Zafeiris.

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Book SynopsisMarkov chains are a fundamental class of stochastic processes. They are widely used to solve problems in a large number of domains such as operational research, computer science, communication networks and manufacturing systems. The success of Markov chains is mainly due to their simplicity of use, the large number of available theoretical results and the quality of algorithms developed for the numerical evaluation of many metrics of interest. The author presents the theory of both discrete-time and continuous-time homogeneous Markov chains. He carefully examines the explosion phenomenon, the Kolmogorov equations, the convergence to equilibrium and the passage time distributions to a state and to a subset of states. These results are applied to birth-and-death processes. He then proposes a detailed study of the uniformization technique by means of Banach algebra. This technique is used for the transient analysis of several queuing systems. Contents 1. Discrete-Time Markov Chains 2. Continuous-Time Markov Chains 3. Birth-and-Death Processes 4. Uniformization 5. Queues About the Authors Bruno Sericola is a Senior Research Scientist at Inria Rennes – Bretagne Atlantique in France. His main research activity is in performance evaluation of computer and communication systems, dependability analysis of fault-tolerant systems and stochastic models.Table of ContentsPreface ix Chapter 1. Discrete-Time Markov Chains 1 1.1. Definitions and properties 1 1.2. Strong Markov property 5 1.3. Recurrent and transient states 8 1.4. State classification 12 1.5. Visits to a state 14 1.6. State space decomposition 18 1.7. Irreducible and recurrent Markov chains 22 1.8. Aperiodic Markov chains 30 1.9. Convergence to equilibrium 34 1.10. Ergodic theorem 41 1.11. First passage times and number of visits 53 1.12. Finite Markov chains 68 1.13. Absorbing Markov chains 70 1.14. Examples 76 1.15. Bibliographical notes 87 Chapter 2. Continuous-Time Markov Chains 89 2.1. Definitions and properties 92 2.2. Transition functions and infinitesimal generator 93 2.3. Kolmogorov’s backward equation 108 2.4. Kolmogorov’s forward equation 114 2.5. Existence and uniqueness of the solutions 127 2.6. Recurrent and transient states 130 2.7. State classification 137 2.8. Explosion 141 2.9. Irreducible and recurrent Markov chains 148 2.10. Convergence to equilibrium 162 2.11. Ergodic theorem 166 2.12. First passage times 172 2.13. Absorbing Markov chains 184 2.14. Bibliographical notes 190 Chapter 3. Birth-and-Death Processes 191 3.1. Discrete-time birth-and-death processes 191 3.2. Absorbing discrete-time birth-and-death processes 200 3.3. Periodic discrete-time birth-and-death processes 208 3.4. Continuous-time pure birth processes 209 3.5. Continuous-time birth-and-death processes 213 3.6. Absorbing continuous-time birth-and-death processes 228 3.7. Bibliographical notes 233 Chapter 4. Uniformization 235 4.1. Introduction 235 4.2. Banach spaces and algebra 237 4.3. Infinite matrices and vectors 243 4.4. Poisson process 249 4.5. Uniformizable Markov chains 263 4.6. First passage time to a subset of states 273 4.7. Finite Markov chains 275 4.8. Transient regime 276 4.9. Bibliographical notes 286 Chapter 5. Queues 287 5.1. The M/M/1 queue 288 5.2. The M/M/c queue 315 5.3. The M/M/∞ queue 318 5.4. Phase-type distributions 323 5.5. Markovian arrival processes 326 5.6. Batch Markovian arrival process 342 5.7. Block-structured Markov chains 352 5.8. Applications 370 5.9. Bibliographical notes 380 Appendix 1 Basic Results 381 Bibliography 387 Index 395

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Book SynopsisStatistical Models and Methods for Reliability and Survival Analysis brings together contributions by specialists in statistical theory as they discuss their applications providing up-to-date developments in methods used in survival analysis, statistical goodness of fit, stochastic processes for system reliability, amongst others. Many of these are related to the work of Professor M. Nikulin in statistics over the past 30 years. The authors gather together various contributions with a broad array of techniques and results, divided into three parts - Statistical Models and Methods, Statistical Models and Methods in Survival Analysis, and Reliability and Maintenance. The book is intended for researchers interested in statistical methodology and models useful in survival analysis, system reliability and statistical testing for censored and non-censored data.Table of ContentsPreface xv Biography of Mikhail Stepanovitch Nikouline xvii Vincent COUALLIER, Léo GERVILLE-RÉACHE, Catherine HUBER-CAROL, Nikolaos LIMNIOS and Mounir MESBAH Part 1. Statistical Models and Methods 1 Chapter 1. Unidimensionality, Agreement and Concordance Probability 3 Zhezhen JIN and Mounir MESBAH 1.1. Introduction 3 1.2. From reliability to unidimensionality: CAC and curve 4 1.2.1. Classical unidimensional models for measurement 4 1.2.2. Reliability of an instrument: CAC 6 1.2.3. Unidimensionality of an instrument: BRC 9 1.3. Agreement between binary outcomes: the kappa coefficient 10 1.3.1. The kappa model 10 1.3.2. The kappa coefficient 10 1.3.3. Estimation of the kappa coefficient 10 1.4. Concordance probability 11 1.4.1. Relationship with Kendall’s τ measure 12 1.4.2. Relationship with Somer’s D measure 12 1.4.3. Relationship with ROC curve 13 1.5. Estimation and inference 14 1.6. Measure of agreement 14 1.7. Extension to survival data 15 1.7.1. Harrell’s c-index 15 1.7.2. Measure of discriminatory power 16 1.8. Discussion 17 1.9. Bibliography 18 Chapter 2. A Universal Goodness-of-Fit Test Based on Regression Techniques 21 Florence GEORGE and Sneh GULATI 2.1. Introduction 21 2.2. The Brain and Shapiro procedure for the exponential distribution 22 2.3. Applications of the Brain and Shapiro test 24 2.4. Small sample null distribution of the test statistic for specific distributions 25 2.5. Power studies 28 2.6. Some real examples 28 2.7. Conclusions 31 2.8. Acknowledgment 32 2.9. Bibliography 32 Chapter 3. Entropy-type Goodness-of-Fit Tests for Heavy-Tailed Distributions 33 Andreas MAKRIDES, Alex KARAGRIGORIOU and Filia VONTA 3.1. Introduction 33 3.2. The entropy test for heavy-tailed distributions 35 3.2.1. Development and asymptotic theory 35 3.2.2. Discussion 39 3.3. Simulation study 40 3.4. Conclusions 42 3.5. Bibliography 42 Chapter 4. Penalized Likelihood Methodology and Frailty Models 45 Emmanouil ANDROULAKIS, Christos KOUKOUVINOS and Filia VONTA 4.1. Introduction 45 4.2. Penalized likelihood in frailty models for clustered data 48 4.2.1. Gamma distributed frailty 52 4.2.2. Inverse Gaussian distributed frailty 52 4.2.3. Uniform distributed frailty 54 4.3. Simulation results 55 4.4. Concluding remarks 57 4.5. Bibliography 57 Chapter 5. Interactive Investigation of Statistical Regularities in Testing Composite Hypotheses of Goodness of Fit 61 Boris LEMESHKO, Stanislav LEMESHKO and Andrey ROGOZHNIKOV 5.1. Introduction 61 5.2. Distributions of the test statistics in the case of testing composite hypotheses 63 5.3. Testing composite hypotheses in “real-time” 68 5.4. Conclusions 73 5.5. Acknowledgment 73 5.6. Bibliography 73 Chapter 6. Modeling of Categorical Data 77 Henning LÄUTER 6.1. Introduction 77 6.2. Continuous conditional distributions 78 6.2.1. Conditional normal distribution 78 6.2.1.1. Estimation of parameters 78 6.2.2. More general continuous conditional distributions 81 6.2.2.1. Conditional distribution 82 6.2.2.2. Normal copula 83 6.3. Discrete conditional distributions 84 6.3.1. Parametric conditional distributions 84 6.3.2. Estimation of parameters 86 6.4. Goodness of fit 86 6.4.1. Distribution of ˆX2 87 6.5. Modeling of categorical data 88 6.5.1. Contingency tables 89 6.5.1.1. General tables 89 6.5.1.2. Further examples 93 6.6. Bibliography 93 Chapter 7. Within the Sample Comparison of Prediction Performance of Models and Submodels: Application to Alzheimer’s Disease 95 Catherine HUBER-CAROL, Shulamith T. GROSS and Annick ALPÉROVITCH 7.1. Introduction 95 7.2. Framework 96 7.2.1. General description of the data set and the models to be compared 96 7.2.2. Definition of the performance prediction criteria: IDI and BRI 96 7.3. Estimation of IDI and BRI 97 7.3.1. General estimating equations for IDI and BRI 98 7.3.2. Estimation of IDI and BRI in the logistic case 98 7.3.2.1. Asymptotics of IDI2/1 for logistic predictors 99 7.3.2.2. Asymptotics of BRI2/1 for logistic predictors 100 7.4. Simulation studies 102 7.4.1. First simulation 102 7.4.2. Second simulation: Gu and Pepe’s example 104 7.5. The three city study of Alzheimer’s disease 106 7.6. Conclusion 108 7.7. Bibliography 109 Chapter 8. Durbin–Knott Components and Transformations of the Cramér-von Mises Test 111 Gennady MARTYNOV 8.1. Introduction 111 8.2. Weighted Cramér-von Mises statistic 111 8.3. Examples of the Cramér-von Mises statistics 113 8.3.1. Classical Cramér-von Mises statistic 113 8.3.2. Anderson–Darling statistic 113 8.3.3. Cramér-von Mises statistic with the power weight function 114 8.4. Weighted parametric Cramér-von Mises statistic 114 8.4.1. Covariance functions of weighted parametric empirical process 114 8.4.2. Eigenvalues and eigenfunctions for weighted parametric Cramérvon Mises statistic 116 8.5. Transformations of the Cramér-von Mises statistic 117 8.5.1. Preliminary notes 117 8.5.2. Replacement of eigenvalues 118 8.5.3. Transformed statistics 119 8.6. Bibliography 122 Chapter 9. Conditional Inference in Parametric Models 125 Michel BRONIATOWSKI and Virgile CARON 9.1. Introduction and context 125 9.2. The approximate conditional density of the sample 127 9.2.1. Approximation of conditional densities 127 9.2.2. The proxy of the conditional density of the sample 129 9.2.3. Comments on implementation 131 9.3. Sufficient statistics and approximated conditional density 131 9.3.1. Keeping sufficiency under the proxy density 131 9.3.2. Rao–Blackwellization 132 9.4. Exponential models with nuisance parameters 135 9.4.1. Conditional inference in exponential families 135 9.4.2. Application of conditional sampling to MC tests 137 9.4.2.1. Context 137 9.4.2.2. Bimodal likelihood: testing the mean of a normal distribution in dimension 2 139 9.4.3. Estimation through conditional likelihood 140 9.5. Bibliography 142 Chapter 10. On Testing Stochastic Dominance by Exceedance, Precedence and Other Distribution-Free Tests, with Applications 145 Paul DEHEUVELS 10.1. Introduction 145 10.2. Results 148 10.2.1. The experimental data set 148 10.2.2. An application of the Wilcoxon–Mann–Whitney statistics 149 10.2.3. One-sided Kolmogorov-Smirnov tests 150 10.2.4. Precedence and Exceedance Tests. 152 10.3. Negative binomial limit laws 155 10.4. Conclusion 159 10.5. Bibliography 159 Chapter 11. Asymptotically Parameter-Free Tests for Ergodic Diffusion Processes 161 Yury A. KUTOYANTS and Li ZHOU 11.1. Introduction 161 11.2. Ergodic diffusion process and some limits 165 11.3. Shift parameter 168 11.4. Shift and scale parameters 172 11.5. Bibliography 175 Chapter 12. A Comparison of Homogeneity Tests for Different Alternative Hypotheses 177 Sergey POSTOVALOV and Petr PHILONENKO 12.1. Homogeneity tests 178 12.1.1. Tests for data without censoring 179 12.1.2. Tests for data with censoring 180 12.2. Alternative hypotheses 184 12.3. Power simulation 185 12.3.1. Power of tests without censoring 187 12.3.2. Power of tests with censoring 189 12.3.2.1. How does the distribution of censoring time affect the power of the test? 189 12.3.2.2. How does the censoring rate affect the power of the test? 191 12.4. Statistical inference 191 12.5. Acknowledgment 192 12.6. Bibliography 193 Chapter 13. Some Asymptotic Results for Exchangeably Weighted Bootstraps of the Empirical Estimator of a Semi-Markov Kernel with Applications 195 Salim BOUZEBDA and Nikolaos LIMNIOS 13.1. Introduction 195 13.2. Semi-Markov setting 197 13.3. Main results 201 13.4. Bootstrap for a multidimensional empirical estimator of a continuous-time semi-Markov kernel 205 13.5. Confidence intervals 208 13.6. Bibliography 210 Chapter 14. On Chi-Squared Goodness-of-Fit Test for Normality 213 Mikhail NIKULIN, Léo GERVILLE-RÉACHE and Xuan Quang TRAN 14.1. Chi–squared test for normality 213 14.2. Simulation study 221 14.3. Bibliography 226 Part 2. Statistical Models and Methods in Survival Analysis 229 Chapter 15. Estimation/Imputation Strategies for Missing Data in Survival Analysis 231 Elodie BRUNEL, Fabienne COMTE and Agathe GUILLOUX 15.1. Introduction 231 15.2. Model and strategies 233 15.2.1. Model assumptions 233 15.2.2. Strategy involving knowledge of ζ 234 15.2.3. Strategy involving knowledge of π 235 15.2.4. Estimation of ζ or π: logit or non-parametric regression 236 15.2.5. Computing the hazard estimators 236 15.2.6. Theoretical results 239 15.3. Imputation-based strategy 241 15.4. Numerical comparison 242 15.5. Proofs 244 15.6. Bibliography 251 Chapter 16. Non-Parametric Estimation of Linear Functionals of a Multivariate Distribution Under Multivariate Censoring with Applications 253 Olivier LOPEZ and Philippe SAINT-PIERRE 16.1. Introduction 253 16.2. Non-parametric estimation of the distribution 255 16.3. Asymptotic properties 257 16.4. Statistical applications of functionals 260 16.4.1. Dependence measures 260 16.4.2. Bootstrap 261 16.4.3. Linear regression 262 16.5. Illustration 263 16.6. Conclusion 264 16.7. Acknowledgment 264 16.8. Bibliography 264 Chapter 17. Kernel Estimation of Density from Indirect Observation 267 Valentin SOLEV 17.1. Introduction 267 17.1.1. Random partition 267 17.1.2. Indirect observation 268 17.1.3. Kernel density estimator 269 17.2. Density of random vector Λ(X) 271 17.3. Pseudo-kernel density estimator 273 17.3.1. Pointwise density estimation based on indirect data 273 17.3.2. Bias of the kernel estimator 274 17.3.3. Estimate of variance 276 17.4. Bibliography 279 Chapter 18. A Comparative Analysis of Some Chi-Square Goodness-of-Fit Tests for Censored Data 281 Ekaterina CHIMITOVA and Boris LEMESHKO 18.1. Introduction 281 18.2. Chi-square goodness-of-fit tests for censored data 283 18.2.1. NRR χ2 test 283 18.2.2. GPF χ2 test 284 18.3. The choice of grouping intervals 285 18.3.1. Equifrequent grouping (EFG) 289 18.3.2. Intervals with equal expected numbers of failures (EENFG) 289 18.3.3. Optimal grouping (OptG) 289 18.4. Empirical power study 290 18.5. Conclusions 293 18.6. Acknowledgment 294 18.7. Bibliography 294 Chapter 19. A Non-parametric Test for Comparing Treatments with Missing Data and Dependent Censoring 297 Amel MEZAOUER, Kamal BOUKHETALA and Jean-François DUPUY 19.1. Introduction 297 19.2. The proposed test statistic 299 19.3. Asymptotic distribution of the proposed test statistic 301 19.4. Acknowledgment 305 19.5. Appendix 306 19.6. Bibliography 309 Chapter 20. Group Sequential Tests for Treatment Effect with Covariates Adjustment through Simple Cross-Effect Models 311 Isaac Wu HONG-DAR 20.1. Introduction 311 20.2. Notations and models 313 20.3. Group sequential test 316 20.4. Discussion 318 20.5. Acknowledgment 318 20.6. Bibliography 318 Part 3. Reliability and Maintenance 321 Chapter 21. Optimal Maintenance in Degradation Processes 323 Waltraud KAHLE 21.1. Introduction 323 21.2. The degradation model 324 21.3. Optimal replacement after an inspection 326 21.4. The simulation of degradation processes 327 21.5. Shape of cost functions and optimal δ and a 329 21.6. Incomplete preventive maintenance 330 21.7. Bibliography 333 Chapter 22. Planning Accelerated Destructive Degradation Tests with Competing Risks 335 Ying SHI and William Q. MEEKER 22.1. Introduction 336 22.1.1. Background 336 22.1.2. Motivation: adhesive bond C 336 22.1.3. Related literature 337 22.1.4. Overview 338 22.2. Degradation models with competing risks 338 22.2.1. Accelerated degradation model for the primary response 338 22.2.2. Accelerated degradation model for the competing response 339 22.2.3. Degradation models for adhesive bond C 339 22.2.4. Degradation distribution and quantiles 340 22.3. Failure-time distribution with competing risks 341 22.3.1. Relationship between degradation and failure 341 22.3.2. Failure-time distribution and quantiles 342 22.4. Test planning with competing risks 342 22.4.1. ADDT planning information 342 22.4.2. Criterion for ADDT planning with competing risks 343 22.5. ADDT plans with competing risks 344 22.5.1. Initial optimum ADDT plan with competing risks 344 22.5.2. Constrained optimum ADDT plan with competing risks 348 22.5.3. General equivalence theorem 348 22.5.4. Compromise ADDT plan with competing risks 350 22.6. Monte Carlo simulation to evaluate test plans 352 22.7. Conclusions and extensions 353 22.8. Appendix: technical details 354 22.8.1. The Fisher information matrix for ADDT with competing risks 354 22.8.2. Large-sample approximate variance of ht (tp) and tp 355 22.9. Bibliography 355 Chapter 23. A New Goodness-of-Fit Test for Shape-Scale Families 357 Vilijandas BAGDONAVIČIUS 23.1. Introduction 357 23.2. The test statistic 358 23.3. The asymptotic distribution of the test statistic 359 23.4. The test 364 23.5. Weibull distribution 364 23.6. Loglogistic distribution 365 23.7. Lognormal distribution 366 23.8. Bibliography 367 Chapter 24. Time-to-Failure of Markov-Modulated Gamma Process with Application to Replacement Policies 369 Christian PAROISSIN and Landy RABEHASAINA 24.1. Introduction 369 24.2. Degradation model 370 24.2.1. Covariate process 370 24.2.2. Degradation process 371 24.3. Time-to-failure distribution 371 24.3.1. Case of a non-modulated gamma process 372 24.3.2. Case of a Markov-modulated gamma process 373 24.3.3. Stochastic comparison 374 24.4. Replacement policies 376 24.4.1. Block replacement policy 377 24.4.2. Age replacement policy 379 24.5. Conclusion 381 24.6. Acknowledgment 381 24.7. Bibliography 382 Chapter 25. Calculation of the Redundant Structure Reliability for Agingtype Elements 383 Alexandr ANTONOV, Alexandr PLYASKIN and Khizri TATAEV 25.1. Introduction 383 25.2. The operation process of the renewal and repaired products 384 25.3. The model of the geometric process 386 25.4. Task solution 387 25.5. Conclusion 389 25.6. Bibliography 390 Chapter 26. On Engineering Risks of Complex Hierarchical Systems Analysis 391 Vladimir RYKOV 26.1. Introduction 391 26.2. Risk definition and measurement 392 26.3. Engineering risk 393 26.4. Risk characteristics for general model calculation 395 26.4.1. Lifelength and appropriate loss size CDF 395 26.4.2. Probability of risk event evolution 396 26.4.3. Lifelength and loss moments 397 26.4.4. Mostly dangerous paths of risk event evolution and sensitivity analysis 399 26.5. Risk analysis for short-time risk models 400 26.6. Conclusion 402 26.7. Bibliography 402 List of Authors 405 Index 409

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Book SynopsisThis book is the first of a series which focuses on the interpolation and extrapolation of optimal designs, an area with significant applications in engineering, physics, chemistry and most experimental fields. In this volume, the authors emphasize the importance of problems associated with the construction of design. After a brief introduction on how the theory of optimal designs meets the theory of the uniform approximation of functions, the authors introduce the basic elements to design planning and link the statistical theory of optimal design and the theory of the uniform approximation of functions. The appendices provide the reader with material to accompany the proofs discussed throughout the book.Trade Review"it seems that the book deserves more attention than a typical textbook, due to its particular features. Firstly, the authors are active researchers in the eld. Secondly, they concentrate mainly on characterizing optimal designs analytically. Both in the book and in their research, they put emphasis on optimal experiment design for function approximation or interpolation from observations with random errors"...."The book is rigorously written and it will be useful not only for advanced teaching, but also as a good starting point for further research" Ewaryst Rafaj lowicz, Mathematical Reviews, Sept 2017Table of ContentsPreface ix Introduction xi Part 1 Elements from Approximation Theory 1 Chapter 1 Uniform Approximation 3 1.1. Canonical polynomials and uniform approximation 3 1.2. Existence of the best approximation 4 1.3. Characterization and uniqueness of the best approximation 5 1.3.1. Proof of the Borel–Chebyshev theorem 7 1.3.2. Example 13 Chapter 2 Convergence Rates for the Uniform Approximation and Algorithms 15 2.1. Introduction 15 2.2. The Borel–Chebyshev theorem and standard functions 15 2.3. Convergence of the minimax approximation 20 2.3.1. Rate of convergence of the minimax approximation 21 2.4. Proof of the de la Vallée Poussin theorem 24 2.5. The Yevgeny Yakovlevich Remez algorithm 28 2.5.1. The Remez algorithm 29 2.5.2. Convergence of the Remez algorithm 33 Chapter 3 Constrained Polynomial Approximation 43 3.1. Introduction and examples 43 3.2. Lagrange polynomial interpolation 47 3.3. The interpolation error 50 3.3.1. A qualitative result 50 3.3.2. A quantitative result 52 3.4. The role of the nodes and the minimization of the interpolation error 54 3.5. Convergence of the interpolation approximation 56 3.6. Runge phenomenon and lack of convergence 57 3.7. Uniform approximation for C (∞) ([a, b]) functions 62 3.8. Numerical instability 63 3.9. Convergence, choice of the distribution of the nodes, Lagrange interpolation and splines 67 Part 2 Optimal Designs for Polynomial Models 69 Chapter 4 Interpolation and Extrapolation Designs for the Polynomial Regression 71 4.1. Definition of the model and of the estimators 71 4.2. Optimal extrapolation designs: Hoel–Levine or Chebyshev designs 75 4.2.1. Uniform optimal interpolation designs (according to Guest) 85 4.2.2. The interplay between the Hoel–Levine and the Guest designs 95 4.2.3. Confidence bound for interpolation/extrapolation designs 98 4.3. An application of the Hoel–Levine design 100 4.4. Multivariate optimal designs: a special case 103 Chapter 5 An Introduction to Extrapolation Problems Based on Observations on a Collection of Intervals 113 5.1. Introduction 113 5.2. The model, the estimator and the criterion for the choice of the design 119 5.2.1. Criterion for the optimal design 121 5.3. A constrained Borel–Chebyshev theorem 122 5.3.1. Existence of solutions to the Pg−1 (0, 1) problem 122 5.3.2. A qualitative discussion on some constrained Borel–Chebyshev theorem 123 5.3.3 Borel–Chebyshev theorem on [a, b] ∪ [d, e] 125 5.3.4. From the constrained Borel–Chebyshev theorem to the support of the optimal design 126 5.4. Qualitative properties of the polynomial which determines the optimal nodes 127 5.4.1. The linear case 127 5.4.2. The general polynomial case 128 5.5. Identification of the polynomial which characterizes the optimal nodes 130 5.5.1. The differential equation 130 5.5.2. Example 132 5.6. The optimal design in favorable cases 134 5.6.1. Some explicit optimal designs 136 5.7. The optimal design in the general case 137 5.7.1. The extreme points of a linear functional 138 5.7.2. Some results on the representation of the extreme points 138 5.7.3 The specific case of the Dirac functional at point 0 142 5.7.4. Remez algorithm for the extreme polynomial: the optimal design in general cases 145 5.8. Spruill theorem: the optimal design 146 Chapter 6 Instability of the Lagrange Interpolation Scheme With Respect to Measurement Errors 147 6.1. Introduction 147 6.2. The errors that cannot be avoided 147 6.2.1. The role of the errors: interpolation designs with minimal propagation of the errors 150 6.2.2. Optimizing on the nodes 153 6.3. Control of the relative errors 157 6.3.1. Implementation of the Remez algorithm for the relative errors 162 6.4. Randomness 166 6.5. Some inequalities for the derivatives of polynomials 167 6.6. Concentration inequalities 168 6.7. Upper bounds of the extrapolation error due to randomness, and the resulting size of the design for real analytic regression functions 172 6.7.1. Case 1: the range of the observations is bounded 177 6.7.2. Case 2: the range of the observations is unbounded 183 Part 3 Mathematical Material 185 Appendix 1 Normed Linear Spaces 187 Appendix 2 Chebyshev Polynomials 217 Appendix 3 Some Useful Inequalities for Polynomials 221 Bibliography 243 Index 251

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Book SynopsisLluís Barbé has recreated the background and life of Francis Ysidro Edgeworth through a fascinating reconstruction that succeeds in shaping the first detailed biography ever published of this major economist and statistician.Originating from previously unexplored letters and documents stored in archives and registers in Ireland, England and Catalonia, Edgeworth?’s relationships with his academic fellows ?- including Sully, Jevons, Marshall, Galton, Pearson, Walras, Pantaleoni, Fisher, Pareto, Keynes ?- are meticulously depicted. Stemming from undiscovered primary sources, this book also reveals a detailed insight into the academic world of the period 1875?1925 in the fields of economics and statistics.With a descriptive survey of Edgeworth?’s work, this book will prove a captivating read for academics and postgraduate students in economic analysis, the history of economic thought and the history of statistics. Anyone with an interest in Francis Ysidro Edgeworth?’s life should also read this book.Trade Review‘Barbé’s work is a well-done, almost unique study and it is a pleasure to recommend it to historians of economic theory in particular.’ -- Warren J. Samuels, EH.NET‘Barbé’s aim was to provide a “portrait” of Edgeworth, and in that it succeeds admirably. . . a trove of new personal information, all presented with an unfailingly intelligent commentary and a very high level of scholarship. . . this book surpasses all previous biographical accounts to such a degree as to be in a class of its own.’ -- Stephen M. Stigler, History of Political Economy‘This is a welcome biography of Edgeworth.’ -- Peter Groenewegen, Economic History Review‘Barbè’s book is bound to become the bibliographical reference on Edgeworth.’ -- Alberto Baccini, Storia del Pensiero EconomicoTable of ContentsContents: Preface by John Creedy Introduction F.Y. Edgeworth’s Relatives 1. Edgeworth’s Background 2. The Making of Francis Ysidro Edgeworth 3. Professor F.Y. Edgeworth 4. The Esquire of Edgeworthstown Appendices Bibliography Index

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Book SynopsisThis important three volume set is a collection of Edgeworth's published writings in the areas of statistics and probability. There is a newly-emerging interest in probability theory as a basis for economic thought and this collection makes the writings of Edgeworth more accessible.A new introduction written by the editor covers the biographical details, a brief abstract of each of the articles and the basis of their selection is also included.Trade Review'The editor and the publisher have done well, I believe, in bringing so much of Edgeworth's work to renewed notice. Some of this work was originally published in very out-of-the-way locations. The editor deserves the thanks of the scholarly community for the thoroughness of his searches.'Table of ContentsContents: Volume I: Acknowledgements Introduction Part I: Probability Part II: The Law of Error Name Index • Volume II: The Theory of Statistics Name Index • Volume III: Part I: Applications of Probability and Statistical Theory to Economics and the Social Sciences Part II: Applications of Probability and Statistical Theory to Physics, Chemistry and Biology Part III: Applications of Probability and Statistical Theory to Education Part IV: Applications of Probability and Statistical Theory to Psychical Research Index

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Book SynopsisThis is the first volume in a ten-volume set designed for publication in 1997. It reprints in book form a selection of the most important and influential articles on probability, econometrics and economic games which cumulatively have had a major impact on the development of modern economics. There are 242 articles, dating from 1936 to 1996. Many of them were originally published in relatively inaccessible journals and may not, therefore, be available in the archives of many university libraries. The volumes are available separately and also as a complete ten-volume set. The contributors include D. Ellsberg, R.M. Hogart, J.B. Kadane, B.O. Koopmans, E.L. Lehman, D.F. Nicholls, H. Rubin, T.J. Sarjent, L.H. Summers and C.R. Wymer. This particular volume deals with the foundations of probability, econometrics and economic games.Table of ContentsContents: Series Introduction by Omar F. Hamouda and J.C.R. Rowley Introduction: ‘Expected Utility, Fair Gambles and Rational Choice’ by Omar F. Hamouda and J.C.R. Rowley Part I: Ordinal and Cardinal Utility Part II: Fair Gambles and the St Petersburg Paradox Part III: Expected Utility – Axioms and Rationality Part IV: Risk Aversion and Increasing Risk Name Index

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Book SynopsisThis is the second volume in a ten-volume set designed for publication in 1997. It reprints in book form a selection of the most important and influential articles on probability, econometrics and economic games which cumulatively have had a major impact on the development of modern economics. There are 242 articles, dating from 1936 to 1996. Many of them were originally published in relatively inaccessible journals and may not, therefore, be available in the archives of many university libraries. The volumes are available separately and also as a complete ten-volume set. The contributors include D. Ellsberg, R.M. Hogart, J.B. Kadane, B.O. Koopmans, E.L. Lehman, D.F. Nicholls, H. Rubin, T.J. Sarjent, L.H. Summers and C.R. Wymer. This particular volume deals with paradox and ambiguity.Table of ContentsContents: Series Introduction by Omar F. Hamouda and J.C.R. Rowley Introduction: ‘Paradoxes, Ambiguity and Rationality’ by Omar F. Hamouda and J.C.R. Rowley Part I: Ambiguity and Rationality Part II: Alternative Views of Rationality Part III: Behavioural and Psychological Perspectives Part IV: Generalized Expected Utility Part V: Regret, Prospects and Disappointment Name Index

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Book SynopsisThis is the third volume in a ten-volume set designed for publication in 1997. It reprints in book form a selection of the most important and influential articles on probability, econometrics and economic games which cumulatively have had a major impact on the development of modern economics. There are 242 articles, dating from 1936 to 1996. Many of them were originally published in relatively inaccessible journals and may not, therefore, be available in the archives of many university libraries. The volumes are available separately and also as a complete ten-volume set. The contributors include D. Ellsberg, R.M. Hogart, J.B. Kadane, B.O. Koopmans, E.L. Lehman, D.F. Nicholls, H. Rubin, T.J. Sarjent, L.H. Summers and C.R. Wymer. This particular volume deals with economic games and the functions of bargaining and solutions.Table of ContentsContents: Series introduction by Omar F. Hamouda and J.C.R. Rowley Introduction: ‘Economic Games, Bargaining and Solutions’ by Omar F. Hamouda and J.C.R. Rowley Part I: Bargaining and the Emergence of Games Part II: The Core Part III: Non-Cooperative Games and Bargaining Part IV: Empirical Aspects of Games Part V: Solution Concepts and Theories Part VI: Probability and Other Issues Name Index

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Book SynopsisThis is the fourth volume in a ten-volume set designed for publication in 1997. It reprints in book form a selection of the most important and influential articles on probability, econometrics and economic games which cumulatively have had a major impact on the development of modern economics. There are 242 articles, dating from 1936 to 1996. Many of them were originally published in relatively inaccessible journals and may not, therefore, be available in the archives of many university libraries. The volumes are available separately and also as a complete ten-volume set. The contributors include D. Ellsberg, R.M. Hogart, J.B. Kadane, B.O. Koopmans, E.L. Lehman, D.F. Nicholls, H. Rubin, T.J. Sarjent, L.H. Summers and C.R. Wymer. This particular volume deals with the dialogues and beliefs that underpin probability concepts.Table of ContentsContents: Series Introduction by Omar F. Hamouda and J.C.R. Rowley Introduction: ‘Probability Concepts, Dialogue and Beliefs’ by Omar F. Hamouda and J.C.R. Rowley Part I: Concepts of Probability and Statistics Part II: Elucidation and Calibration Part III: Bayesian Dialogue and Group Decisions Part IV: Beliefs – Support and Reliability Part V: Possibilities and Fuzziness Name Index

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Book SynopsisThis is the fifth volume in a ten-volume set designed for publication in 1997. It reprints in book form a selection of the most important and influential articles on probability, econometrics and economic games which cumulatively have had a major impact on the development of modern economics. There are 242 articles, dating from 1936 to 1996. Many of them were originally published in relatively inaccessible journals and may not, therefore, be available in the archives of many university libraries. The volumes are available separately and also as a complete ten-volume set. The contributors include D. Ellsberg, R.M. Hogart, J.B. Kadane, B.O. Koopmans, E.L. Lehman, D.F. Nicholls, H. Rubin, T.J. Sarjent, L.H. Summers and C.R. Wymer. This particular volume deals with the statistical theory that underlies the science of econometrics.Table of ContentsContents: Series introduction by Omar F. Hamouda and J.C.R. Rowley Introduction: ‘Statistical Foundations for Econometrics’ by Omar F. Hamouda and J.C.R. Rowley Part I: Statistical Inference Part II: Errors, Hypotheses and Tests: Criticisms and Discussion Part III: Conventional Treatments of Estimation Part IV: Alternative Approaches to Estimation Name Index

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Book SynopsisThis is the sixth volume in a ten-volume set designed for publication in 1997. It reprints in book form a selection of the most important and influential articles on probability, econometrics and economic games which cumulatively have had a major impact on the development of modern economics. There are 242 articles, dating from 1936 to 1996. Many of them were originally published in relatively inaccessible journals and may not, therefore, be available in the archives of many university libraries. The volumes are available separately and also as a complete ten-volume set. The contributors include D. Ellsberg, R.M. Hogart, J.B. Kadane, B.O. Koopmans, E.L. Lehman, D.F. Nicholls, H. Rubin, T.J. Sarjent, L.H. Summers and C.R. Wymer. This particular volume deals with the econometric exploration and diagnosis.Table of ContentsPart A - Autocorrelation, hetroscedasticity and multicollinearity. Part B - Daignosis, specification tests and wider concerns. Part C - Sequential analysis and pre-test complications. Part D - Robustness. Part E - Langrange multipliers and conflicting test criteria.

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Book SynopsisThis is the seventh volume in a ten-volume set designed for publication in 1997. It reprints in book form a selection of the most important and influential articles on probability, econometrics and economic games which cumulatively have had a major impact on the development of modern economics. There are 242 articles, dating from 1936 to 1996. Many of them were originally published in relatively inaccessible journals and may not, therefore, be available in the archives of many university libraries. The volumes are available separately and also as a complete ten-volume set. The contributors include D. Ellsberg, R.M. Hogart, J.B. Kadane, B.O. Koopmans, E.L. Lehman, D.F. Nicholls, H. Rubin, T.J. Sarjent, L.H. Summers and C.R. Wymer. This particular volume deals with the probability approach to simultaneous equations.Table of ContentsContents: Series introduction by Omar F. Hamouda and J.C.R. Rowley Introduction: ‘The Probability Approach to Simultaneous Equations’ by Omar F. Hamouda and J.C.R. Rowley Part I: Preliminaries Part II: The Probability Approach and Related Matters Part III: The Probability Approach in Retrospect Part IV: Resistance Part V: Positive Appraisals of Simultaneous-Equations Models Index

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Book SynopsisThis is the eighth volume in a ten-volume set designed for publication in 1997. It reprints in book form a selection of the most important and influential articles on probability, econometrics and economic games which cumulatively have had a major impact on the development of modern economics. There are 242 articles, dating from 1936 to 1996. Many of them were originally published in relatively inaccessible journals and may not, therefore, be available in the archives of many university libraries. The volumes are available separately and also as a complete ten-volume set. The contributors include D. Ellsberg, R.M. Hogart, J.B. Kadane, B.O. Koopmans, E.L. Lehman, D.F. Nicholls, H. Rubin, T.J. Sarjent, L.H. Summers and C.R. Wymer. This particular volume deals with the time series models.Table of ContentsContents: Series introduction by Omar F. Hamouda and J.C.R. Rowley Introduction: ‘Time Series Models, Causality and Exogeneity’ by Omar F. Hamouda and J.C.R. Rowley Part I: Mimic Cycles and Simulation Part II: Calibration Part III: Time Series Models: Estimation, Identification and Intervention Part IV: Causality and Exogeneity Part V: Spectral Approaches Name Index

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Book SynopsisThis is the ninth volume in a ten-volume set designed for publication in 1997. It reprints in book form a selection of the most important and influential articles on probability, econometrics and economic games which cumulatively have had a major impact on the development of modern economics. There are 242 articles, dating from 1936 to 1996. Many of them were originally published in relatively inaccessible journals and may not, therefore, be available in the archives of many university libraries. The volumes are available separately and also as a complete ten-volume set. The contributors include D. Ellsberg, R.M. Hogart, J.B. Kadane, B.O. Koopmans, E.L. Lehman, D.F. Nicholls, H. Rubin, T.J. Sarjent, L.H. Summers and C.R. Wymer. This particular volume deals with a reappraisal of econometrics.Table of ContentsContents: Series introduction by Omar F. Hamouda and J.C.R. Rowley Introduction: ‘The Reappraisal of Econometrics’ by Omar F. Hamouda and J.C.R. Rowley Part I: Rational Expectations Part II: Robustness and Interactive Criticism Part III: Specification Search Part IV: Encompassing and Testing Part V: Dismissal Part VI: The Keynes–Tinbergen Exchange Revisited Part VII: Time Series Connection Index

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Book SynopsisThis is the tenth volume in a ten-volume set designed for publication in 1997. It reprints in book form a selection of the most important and influential articles on probability, econometrics and economic games which cumulatively have had a major impact on the development of modern economics. There are 242 articles, dating from 1936 to 1996. Many of them were originally published in relatively inaccessible journals and may not, therefore, be available in the archives of many university libraries. The volumes are available separately and also as a complete ten-volume set. The contributors include D. Ellsberg, R.M. Hogart, J.B. Kadane, B.O. Koopmans, E.L. Lehman, D.F. Nicholls, H. Rubin, T.J. Sarjent, L.H. Summers and C.R. Wymer. This particular volume deals with discrete and coontinuous systems.Table of ContentsContents: Series Introduction by Omar F. Hamouda and J.C.R. Rowley Introduction: ‘Discrete and Continuous Systems, Cointegration and Chaos’ by Omar F. Hamouda and J.C.R. Rowley Part I: System Theory and General Considerations Part II: Nonlinearities Part III: Chaos Part Iv Cointegration Part V: Continuous Models Part VI: Long Memory Index

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Book SynopsisElementary Bayesian Statistics is a thorough and easily accessible introduction to the theory and practical application of Bayesian statistics. It presents methods to assist in the collection, summary and presentation of numerical data.Bayesian statistics are becoming an increasingly important and more frequently used method for analysing statistical data. The author defines concepts and methods with a variety of examples and uses a stage-by-stage approach to coach the reader through the applied examples. Also included are a wide range of problems to challenge the reader and the book makes extensive use of Minitab to apply computational techniques to statistical problems. Issues covered include probability, Bayes's Theorem and categorical states, frequency, the Bernoulli process and Poisson process, estimation, testing hypotheses and the normal process with known parameters and uncertain parameters.Elementary Bayesian Statistics will be an essential resource for students as a supplementary text in traditional statistics courses. It will also be welcomed by academics, researchers and econometricians wishing to know more about Bayesian statistics.Trade Review'A thorough and easily accessible introduction to the theory and practical application of Bayesian statistics.'Table of ContentsContents: Foreword 1. Introduction: Statistics and Probability 2. Some Basic Probability 3. More Basic Probability 4. Bayes’ Theorem, Categorical States 5. Bernoulli Process, Parameter Known 6. Bernoulli and Bayes 7. Poisson Process, Parameter Known 8. Poisson and Bayes 9. Normal Process, Known Parameters 10. Normal Process, Uncertain Parameters 11. Estimation 12. Testing Hypotheses Appendix References Index

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Book SynopsisTeaching Statistics Using Baseball is a collection of case studies and exercises applying statistical and probabilistic thinking to the game of baseball. Baseball is the most statistical of all sports, since players are identified and evaluated by their corresponding hitting and pitching statistics. There is an active effort by people in the baseball community to learn more about baseball performance and strategy by the use of statistics. This book illustrates basic methods of data analysis and probability models by means of baseball statistics collected on players and teams. Students often have difficulty learning statistics ideas since they are explained using examples that are foreign to the students. The idea of the book is to describe statistical thinking in a context (that is, baseball) that will be familiar and interesting to students.The book is organized using a same structure as most introductory statistics texts. There are chapters on the analysis on a single batch of data, followed with chapters on comparing batches of data and relationships. There are chapters on probability models and on statistical inference. The book can be used as the framework for a one-semester introductory statistics class focused on baseball or sports. This type of class has been taught at Bowling Green State University. It may be very suitable for a statistics class for students with sports-related majors, such as sports management or sports medicine. Alternately, the book can be used as a resource for instructors who wish to infuse their present course in probability or statistics with applications from baseball.The second edition of Teaching Statistics follows the same structure as the first edition, where the case studies and exercises have been replaced by modern players and teams, and the new types of baseball data from the PitchFX system and fangraphs.com are incorporated into the text.

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Book SynopsisThis book provides a comprehensive presentation of classical and advanced topics in estimation and control of dynamical systems with an emphasis on stochastic control. Many aspects which are not easily found in a single text are provided, such as connections between control theory and mathematical finance, as well as differential games.The book is self-contained and prioritizes concepts rather than full rigor, targeting scientists who want to use control theory in their research in applied mathematics, engineering, economics, and management science. Examples and exercises are included throughout, which will be useful for PhD courses and graduate courses in general.Dr. Alain Bensoussan is Lars Magnus Ericsson Chair at UT Dallas and Director of the International Center for Decision and Risk Analysis which develops risk management research as it pertains to large-investment industrial projects that involve new technologies, applications and markets. He is also Chair Professor at City University Hong Kong.Trade Review“This book is a great resource for graduate students and those who want to learn and understand stochastic control theory. It is also a great read for experts who want to gain a broader overview of the subject and wish to see connections between different techniques. … this is an excellent book and a great complement to the current offering in stochastic control.” (Jan Palczewski, SIAM Review, Vol. 62 (1), 2020)Table of ContentsIntroduction.- State Representation of Linear Dynamical Systems.- Optimal Control of Linear Dynamical Systems.- Estimation Theory.- Further Techniques of Estimation.- Compliments on Probability Theory.- Filtering Theory in Continuous Time.- Stochastic Control of Linear Dynamic Systems with Full Information.- Stochastic Control of Linear Dynamical Systems with Partial Information.- Deterministic Optimal Control.- Stochastic Optimal Control.- Additional Results for BSDE.- Stochastic Control Problems in Finance.- Stochastic Control for Non-Markov Processes.- Principal Agent Control Problems.- Differential Games.- Stackelberg Differential Games.- Target Problems.

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Book SynopsisThis book introduces readers to the fundamentals of creating presentation graphics using R, based on 111 detailed and complete scripts. It shows how bar and column charts, population pyramids, Lorenz curves, box plots, scatter plots, time series, radial polygons, Gantt charts, heat maps, bump charts, mosaic and balloon charts, and a series of different thematic map types can be created using R’s Base Graphics System. Every example uses real data and includes step-by-step explanations of the figures and their programming. This second edition contains additional examples for cartograms, chord-diagrams and networks, and interactive visualizations with Javascript.The open source software R is an established standard and a powerful tool for various visualizing applications, integrating nearly all technologies relevant for data visualization. The basic software, enhanced by more than 14000 extension packs currently freely available, is intensively used by organizations including Google, Facebook and the CIA. The book serves as a comprehensive reference guide to a broad variety of applications in various fields.This book is intended for all kinds of R users, ranging from experts, for whom especially the example codes are particularly useful, to beginners, who will find the finished graphics most helpful in learning what R can actually deliver.Trade Review“The book can be one of the favourites of a wide range of users from beginners with basic R knowledge to experts. It is especially recommended for students and researchers from social, environmental, and economic fields requiring a consistent and thorough reference always within reach.” (Márta Ladányi, ISCB News, iscb.info, Issue 69, July, 2020)Table of ContentsData for Everybody.- Structure and Technical Requirements.- Implementation in R.- Beyond R.- Regarding the Examples.- Categorical Data.- Distributions.- Time Series.- Scatter Plots.- Maps.- Illustrative Examples.- Interactive Visualisation with JavaScript: Highcharts and Mapael.- Appendix

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Book SynopsisThis book is dedicated to the systematization and development of models, methods, and algorithms for queuing systems with correlated arrivals. After first setting up the basic tools needed for the study of queuing theory, the authors concentrate on complicated systems: multi-server systems with phase type distribution of service time or single-server queues with arbitrary distribution of service time or semi-Markovian service. They pay special attention to practically important retrial queues, tandem queues, and queues with unreliable servers. Mathematical models of networks and queuing systems are widely used for the study and optimization of various technical, physical, economic, industrial, and administrative systems, and this book will be valuable for researchers, graduate students, and practitioners in these domains.Trade Review“The book fills a unique void and is a welcome addition to the queueing literature. The writing style is friendly and accessible, and the authors are to be congratulated on their accomplishment.” (Myron Hlynka, Mathematical Reviews, April, 2021)Table of ContentsMathematical Methods to Study Classical Queuing Systems.- Methods to Study Queuing Systems with Correlated Arrivals.- Queuing Systems with Waiting Space and Correlated Arrivals and Their Application to Evaluation of Network Structure Performance.- Retrial Queuing Systems with Correlated Input Flows and Their Application for Network Structures Performance Evaluation.- Mathematical Models and Methods of Investigation of Hybrid Communication Networks Based on Laser and Radio Technologies.- Tandem Queues with Correlated Arrivals and Their Application to System Structure Performance Evaluation.- App. A, Some Information from the Theory of Matrices and Functions of Matrices.

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Book SynopsisAufbauend auf dem ersten Band, werden in diesem Buch weiterführende Konzepte der Wahrscheinlichkeitstheorie ausführlich und verständlich diskutiert. Mit vielen exemplarisch durchgerechneten Aufgaben, einer Vielzahl weiterer Problemstellungen und ausführlichen Lösungen bietet es dem Leser die Möglichkeit, die eigenen Fähigkeiten ständig zu erweitern und kritisch zu überprüfen und ein tieferes Verständnis der Materie zu erlangen. Realitätsnahe Anwendungen ermöglichen einen Ausblick in die breite Verwendbarkeit dieser Theorie.Auch in diesem Band wird auf die Entwicklung der Begriffsbildung und der mathematischen Konzepte besonderer Wert gelegt, sodass man ihre Bedeutung bei der Erzeugung wie auch ständige Verbesserung von Forschungsinstrumenten für die Untersuchung unserer Welt erleben kann. Gerichtet ist das Buch an Gymnasiasten, Studienanfänger an Hochschulen, Lehrer und Interessierte, die sich mit diesem Gebiet vertraut machen möchten. Table of ContentsEinleitung.- Standardabweichung.- Wahrscheinlichkeiten von Wertebereichen.- Das Gesetz der grossen Zahlen.- Stetige Zufallsvariablen.- Erwartungswert und Standardabweichung von stetigen Zufallsvariablen.- Modellieren von Umfragen.- Hypothesentests.- Lineare Regression.

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Book SynopsisThis book introduces the open source R software language that can be implemented in biostatistics for data organization, statistical analysis, and graphical presentation. In the years since the authors’ 2014 work Introduction to Data Analysis and Graphical Presentation in Biostatistics with R, the R user community has grown exponentially and the R language has increased in maturity and functionality. This updated volume expands upon skill-sets useful for students and practitioners in the biological sciences by describing how to work with data in an efficient manner, how to engage in meaningful statistical analyses from multiple perspectives, and how to generate high-quality graphics for professional publication of their research. A common theme for research in the diverse biological sciences is that decision-making depends on the empirical use of data. Beginning with a focus on data from a parametric perspective, the authors address topics such as Student t-Tests for independent samples and matched pairs; oneway and twoway analyses of variance; and correlation and linear regression. The authors also demonstrate the importance of a nonparametric perspective for quality assurance through chapters on the Mann-Whitney U Test, Wilcoxon Matched-Pairs Signed-Ranks test, Kruskal-Wallis H-Test for Oneway Analysis of Variance, and the Friedman Twoway Analysis of Variance. To address the element of data presentation, the book also provides an extensive review of the many graphical functions available with R. There are now perhaps more than 15,000 external packages available to the R community. The authors place special emphasis on graphics using the lattice package and the ggplot2 package, as well as less common, but equally useful, figures such as bean plots, strip charts, and violin plots. A robust package of supplementary material, as well as an introduction of the development of both R and the discipline of biostatistics, makes this ideal for novice learners as well as more experienced practitioners.Trade Review“The strengths include the ideal analysis containing both graphical and statistical output as well as a variety of datasets … . the authors provide a number of R packages for obtaining the same results, such as graphics or statistics output. … Each chapter is so complete that it can be read in any order; learned readers will probably jump back and forth between the chapters. This book can be used for self-learning or teaching purpose on the subject.” (Shu-Hui Wen, Biometrics, Vol. 78 (2), July, 2022)Table of Contents1 Introduction: Biostatistics and R.- 1.1 Purpose of this Text.- 1.2 Development of Biostatistics.- 1.3 Development of R.- 1.4 How R is Used in this Text.- 1.5 Import Data into R.- 1.6 Addendum1: Efficient Programming with R, Project Workflow, and Good Programming Practices (gpp).- 1.7 Addendum2: Preview of Descriptive Statistics and Graphics Using R.- 1.8 Addendum3: R and Beautiful Graphics.- 1.9 Addendum4: Research Designs Used in Biostatistics.- 1.10 Prepare to Exit, Save, and Later Retrieve this R Session.- 1.11 External Data and/or Data Resources Used in this Lesson.- 2 Data Exploration, Descriptive Statistics, and Measures of Central Tendency.- 2.1 Background.- 2.2 Import Data in Comma-Separated Values (.csv) File Format and/or Self Generate the Data Using R-Based Functions.- 2.3 Organize the Data and Display the Code Book.- 2.4 Conduct a Visual Data Check Using Graphics (e.g., Figures).- 2.5 Descriptive Statistics for Initial Analysis of the Data.- 2.6 Quality Assurance, Data Distribution, and Tests for Normality.- 2.7 Statistical Test(s).- 2.8 Summary.- 2.9 Addendum1: Specialized External Packages and Functions.- 2.10 Addendum2: Parametric v Nonparametric.- 2.11 Addendum3: Additional Practice Datasets for Data with Normal Distribution Patterns and Data That Do Not Exhibit Normal Distribution Patterns.- 2.12 Prepare to Exit, Save, and Later Retrieve this R Session.- 2.13 External Data and/or Data Resources Used in this Lesson.- 3 Student's t-Test for Independent Samples.- 3.1 Background.- 3.2 Import Data in Comma-Separated Values (.csv) File Format and/or Self Generate the Data Using R-Based Functions.- 3.3 Organize the Data and Display the Code Book.- 3.4 Conduct a Visual Data Check Using Graphics (e.g., Figures).- 3.5 Descriptive Statistics for Initial Analysis of the Data.- 3.6 Quality Assurance, Data Distribution, and Tests for Normality.- 3.7 Statistical Test(s).- 3.8 Summary of Outcomes.- 3.9 Addendum1: t-Statistic v z-Statistic.- 3.10 Addendum2: Parametric v Nonparametric.- 3.11 Addendum3: Additional Practice Datasets for Data with Normal Distribution Patterns and Data That Do Not Exhibit Normal Distribution Patterns.- 3.12 Prepare to Exit, Save, and Later Retrieve This R Session.- 3.13 External Data and/or Data Resources Used in this Lesson.- 4 Student's t-Test for Matched Pairs.- 4.1 Background.- 4.2 Import Data in Comma-Separated Values (.csv) File Format and/or Self Generate the Data Using R-Based Functions.- 4.3 Organize the Data and Display the Code Book.- 4.4 Conduct a Visual Data Check Using Graphics(e.g., Figures).- 4.5 Descriptive Statistics for Initial Analysis of the Data.- 4.6 Quality Assurance, Data Distribution, and Tests for Normality.- 4.7 Statistical Test(s).- 4.8 Summary of Outcomes.- 4.9 Addendum1: R-Based Tools for Unstacked (e.g. Wide) Data.- 4.10 Addendum2: Stacked Data and Student's t-Test for Matched Pairs.- 4.11 Addendum 3: The Impact of N on Student's t-Test.- 4.12 Addendum 4: Parametric v Nonparametric.- 4.13 Addendum5: Additional Practice Datasets for Data with Normal Distribution Patterns and Data That Do Not Exhibit Normal Distribution Patterns.- 4.14 Prepare to Exit, Save, and Later Retrieve This R Session.- 4.15 External Data and/or Data Resources Used in this Lesson.- 5 Oneway Analysis of Variance (ANOVA).- 5.1 Background.- 5.2 Import Data in Comma-Separated Values (.csv) File Format and/or Self Generate the Data Using R-Based Functions.- 5.3 Organize the Data and Display the Code Book.- 5.4 Conduct a Visual Data Check Using Graphics(e.g., Figures).- 5.5 Descriptive Statistics for Initial Analysis of the Data.- 5.6 Quality Assurance, Data Distribution, and Tests for Normality.- 5.7 Statistical Test(s).- 5.8 Summary of Outcomes.- 5.9 Addendum1: Other Packages for Display of Oneway ANOVA.- 5.10 Addendum2: Parametric v Nonparametric.- 5.11 Addendum3: Additional Practice Data Sets.- 5.12 Prepare to Exit, Save, and Later Retrieve This R Session.- 5.13 External Data and/or Data Resources Used in this Lesson.- 6 Twoway Analysis of Variance (ANOVA).- 6.1 Background.- 6.2 Import Data in Comma-Separated Values (.csv) File Format and/or Self Generate the Data Using R-Based Functions.- 6.3 Organize the Data and Display the Code Book.- 6.4 Conduct a Visual Data Check Using Graphics (e.g., Figures).- 6.5 Descriptive Statistics for Initial Analysis of the Data.- 6.6 Quality Assurance, Data Distribution, and Tests for Normality.- 6.7 Statistical Test(s).- 6.8 Summary of Outcomes.- 6.9 Addendum 1: Other Packages for Display of Twoway ANOVA.- 6.10 Addendum 2: Parametric v Nonparametric.- 6.11 Addendum 3: Additional Practice Data Sets.- 6.12 Prepare to Exit, Save, and Later Retrieve This R Session.- 6.13 External Data and/or Data Resources Used in this Lesson.- 7 Correlation, Association, Regression, Likelihood, and Prediction.- 7.1 Background.- 7.2 Import Data in Comma-Separated Values (.csv) File Format and/or Self Generate the Data Using R-Based Functions.- 7.3 Organize the Data and Display the Code Book.- 7.4 Quality Assurance, Data Distribution, and Tests for Normality.- 7.5 Statistical Test(s).- 7.6 Summary of Outcomes.- 7.7 Addendum 1: Multiple Regression.- 7.8 Addendum 2: Likelihood and Odds Ratio.- 7.9 Addendum 3:Parametric v Nonparametric.- 7.10 Addendum 4: Additional Practice Data Sets.- 7.11 Prepare to Exit, Save, and Later Retrieve This R Session.- 7.12 External Data and/or Data Resources Used in this Lesson.- 8 Working with Large and Complex Datasets.- 8.1 Background.- 8.2 Import Data in Comma-Separated Values (.csv) File Format and/or Self Generate the Data Using R-Based Functions.- 8.3 Organize the Data and Display the Code Book.- 8.4 Conduct a Visual Data Check Using Graphics (e.g., Figures).- 8.5 Descriptive Statistics for Initial Analysis of the Data.- 8.6 Quality Assurance, Data Distribution, and Tests for Normality.- 8.7 Statistical Test(s).- 8.8 Summary of Outcomes.- 8.9 Addendum1: Additional Graphics, to Show Relationships Between and Among Data.- 8.10 Addendum2: Graphics Using the lattice Package.- 8.11 Addendum3: Graphics Using the ggplot2 Package.- 8.12 Addendum 4: Beyond an Introduction to R - Use the tidyverse to Create Subsets of Original Datasets.- 8.13 Prepare to Exit, Save, and Later Retrieve This R Session.- 8.14 External Data and/or Data Resources Used in this Lesson.- 9 Future Actions and Next Steps.- 9.1 Use of This Text.- 9.2 R and Beautiful Reporting with R Markdown.- 9.3 Future Use of R for Biostatistics.- 9.4 Big Data and Bio Informatics.- 9.5 External Resources.- 9.6 Contact the Authors.

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Book SynopsisThis book shows the capabilities of Microsoft Excel in teaching marketing statistics effectively. It is a step-by-step, exercise-driven guide for students and practitioners who need to master Excel to solve practical marketing problems. If understanding statistics isn’t your strongest suit, you are not especially mathematically inclined, or if you are wary of computers, this is the right book for you.Excel, a widely available computer program for students and managers, is also an effective teaching and learning tool for quantitative analyses in marketing courses. Its powerful computational ability and graphical functions make learning statistics much easier than in years past. Excel 2019 for Marketing Statistics: A Guide to Solving Practical Problems capitalizes on these improvements by teaching students and managers how to apply Excel to statistical techniques necessary in their courses and work.In this new edition, each chapter explains statistical formulas and directs the reader to use Excel commands to solve specific, easy-to-understand marketing problems. Practice problems are provided at the end of each chapter with their solutions in an appendix. Separately, there is a full practice test (with answers in an appendix) that allows readers to test what they have learned.Table of ContentsPreface.- Acknowledgements.- 1 Sample Size, Mean, Standard Deviation, and Standard Error of the Mean.- 2 Random Number Generator.- 3 Confidence Interval About the Mean Using the TINV Function and Hypothesis Testing.- 4 One-Group t-Test for the Mean.- 5 Two-Group t-Test of the Difference of the Means for Independent Groups.- 6 Correlation and Simple Linear Regression.- 7 Multiple Correlation and Multiple Regression.- 8 One-Way Analysis of Variance (ANOVA).- Appendix A: Answers to End-of-Chapter Practice Problems.- Appendix B: Practice Test.- Appendix C: Answers to Practice Test.- Appendix D: Statistical Formulas.- Appendix E: t-table.- Index.

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Book SynopsisThis book constitutes an up-to-date account of principles, methods, and tools for mathematical and statistical modelling in a wide range of research fields, including medicine, health sciences, biology, environmental science, engineering, physics, chemistry, computation, finance, economics, and social sciences. It presents original solutions to real-world problems, emphasizes the coordinated development of theories and applications, and promotes interdisciplinary collaboration among mathematicians, statisticians, and researchers in other disciplines.Based on a highly successful meeting, the International Conference on Applied Mathematics, Modeling and Computational Science, AMMCS 2019, held from August 18 to 23, 2019, on the main campus of Wilfrid Laurier University, Waterloo, Canada, the contributions are the results of submissions from the conference participants. They provide readers with a broader view of the methods, ideas and tools used in mathematical, statistical and computational sciences.Table of ContentsS. M. Dastjerdi, A. HormoziNejad, K. Gharali and J. Nathwani, Numerical investigation of VAWT airfoil shapes on power extraction and self-starting purposes.- O. Abu and I. I. Ayogu, An Optimal Control Strategy for a Malaria Model.- L. Feng and X. Wang, Automate Obstructive Sleep Apnea Diagnosis Using Convolutional Neural Networks.- M. Rezaeian, M. Soltani and F. M. Kashkooli, On the modeling of drug delivery to solid tumors; computational viewpoint.- A. F. Ivanov and Z. A. Dzalilov, Oscillations and Periodic Solutions in a Two-Dimensional Differential Delay Model.- K. R. Green and R. J. Spiteri, Solving cardiac bidomain problems with B-spline adaptive collocation.- A. Sowa, Toral diffeomorphisms induce quantum superoperators via TAQS.- N. Mudalige, BOLD.R: A software package to interface with BOLD through R.- E. I. Verriest, Properties of the Zeros of the Scale-Delay Equation and Its Time-Variant ODE Realization .- M. Ashrafizaadeh, A. Ghavaminia, Development of a lattice Boltzmann model for the solution of partial differential equations, A performance comparison study with that of the finite difference method.- M. Ashrafizaadeh, F. Gharibi and S. M. Khatoonabadi, An extended pseudo potential multiphase lattice Boltzmann model with variable viscosity ratio.- M. Ahmed and S. A. Campbell, Effect of genetic defects in a cortical circuit model associated with childhood absence epilepsy.- P. C. Jentsch and C. L. Nehaniv, Exploring Tetris as a Transformation Semigroup.- W. M. Abdullah, S. Hossain and M. A. Khan, Covering Large Complex Networks by Cliques - A Sparse Matrix Approach.- T. Migot and Monica-G. Cojocaru, Revisiting Path-Following to Solve the Generalized Nash Equilibrium Problem.- H. Shaheen, R. Melnik and S. Singh, Analysis of Cortical Spreading Depression in Brian with Multiscale Mathematical Models.- M. Syed Usama and N. A. Malik, A Comparison of Turbulence Generated by 3DS Sparse Grids With Different Blockage Ratios and Different Co-Frame Arrangements.- R. Fallahpour and R. Melnik, Numerical Analysis of Nanowire Resonators for Ultra-High Resolution Mass Sensing in Biomedical Applications.- I. Farahbakhsh and C. L. Nehaniv, Spatial Iterated Prisoner’s Dilemma as a Transformation Semigroup.- L. Graham, M. Demers, Applying Neural Networks to a Fractal Inverse Problem.- D. St Jean, H. Kunze and D. Gillis.- Evaluating a logistic k-mer based model for classifying CO1 sequences of C. clupeaformis.- A. Egri-Nagy and C. L. Nehaniv, A Bestiary of Transformation Semigroups for the Holonomy Decomposition.- R. Xu and R. N. Makarov, High-Frequency Statistical Modelling for Jump-Diffusion Multi-Asset Price Processes with a Systemic Component.- M. M. Mukhopadhyay and R. N. Makarov, Calibration and Analysis of Structural Credit Risk Models with Occupation Time.- N. Mattia Marazzi, V. H. Huxley, R. Sacco and G. Guidoboni, Quantitative study of the coupling among cardiovascular system, lymphatic system and interstitial space.

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Book SynopsisMicrobiome research has focused on microorganisms that live within the human body and their effects on health. During the last few years, the quantification of microbiome composition in different environments has been facilitated by the advent of high throughput sequencing technologies. The statistical challenges include computational difficulties due to the high volume of data; normalization and quantification of metabolic abundances, relative taxa and bacterial genes; high-dimensionality; multivariate analysis; the inherently compositional nature of the data; and the proper utilization of complementary phylogenetic information. This has resulted in an explosion of statistical approaches aimed at tackling the unique opportunities and challenges presented by microbiome data. This book provides a comprehensive overview of the state of the art in statistical and informatics technologies for microbiome research. In addition to reviewing demonstrably successful cutting-edge methods, particular emphasis is placed on examples in R that rely on available statistical packages for microbiome data. With its wide-ranging approach, the book benefits not only trained statisticians in academia and industry involved in microbiome research, but also other scientists working in microbiomics and in related fields.Table of Contents1. Tree-guided regression and multivariate analysis of microbiome data - Hongu Zhao and Tao Wang.- 2. Computational methods for metagenomic assemblies and strain identification - Hongzhe Li.- 3. Graphical models for microbiome data - Ali Shojaie.- 4. Bayesian models for understanding the modulating factors of microbiome data - Francesco Denti, Matthew D. Koslovsky, Michele Guindani, Marina Vannucci, and Katrine L. Whiteson.- 5. Use of variable importance in microbiome studies - Hemant Ishwaran.- 6. Log-linear models for microbiome data - Glen Satten.- 7. Quantification of amplicon sequences in microbiome samples using statistical methods - Karin Dorman.- 8. TBD - Jeanine Houwing Duistermaat.- 9. Analyzing microbiome data by employing the power of abundance ratios - Zhigang Li.- 10. Beta diversity analysis - Michael Wu.- 11. MicroPro: using metagenomic unmapped reads to provide insights into human microbiota and disease associations - Fengzhu Sun.- 12. Statistical methods for feature selection in microbiome studies - Peng Liu.- 13. A Bayesian restoration of the duality between principal components of a distance matrix and operational taxonomic units in microbiome analyses - Somnath Datta and Subharup Guha.

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Book SynopsisThis book takes a unique approach to explaining permutation statistics by integrating permutation statistical methods with a wide range of classical statistical methods and associated R programs. It opens by comparing and contrasting two models of statistical inference: the classical population model espoused by J. Neyman and E.S. Pearson and the permutation model first introduced by R.A. Fisher and E.J.G. Pitman. Numerous comparisons of permutation and classical statistical methods are presented, supplemented with a variety of R scripts for ease of computation. The text follows the general outline of an introductory textbook in statistics with chapters on central tendency and variability, one-sample tests, two-sample tests, matched-pairs tests, completely-randomized analysis of variance, randomized-blocks analysis of variance, simple linear regression and correlation, and the analysis of goodness of fit and contingency. Unlike classical statistical methods, permutation statistical methods do not rely on theoretical distributions, avoid the usual assumptions of normality and homogeneity, depend only on the observed data, and do not require random sampling. The methods are relatively new in that it took modern computing power to make them available to those working in mainstream research. Designed for an audience with a limited statistical background, the book can easily serve as a textbook for undergraduate or graduate courses in statistics, psychology, economics, political science or biology. No statistical training beyond a first course in statistics is required, but some knowledge of, or some interest in, the R programming language is assumed. Trade Review“This book is a real gem for statistics lovers for several reasons (novelty and depth of the topics covered, facilities to understand them for newcomers to statistics, to name just a few).” (Oscar Bustos, zbMATH 1480.62001, 2022)Table of ContentsPreface.- 1 Introduction.- 2 The R Programming Language.- 3 Permutation Statistical Methods.- 4 Central Tendency and Variability.- 5 One-sample Tests.- 6 Two-sample Tests.- 7 Matched-pairs Tests.- 8 Completely-randomized Designs.- 9 Randomized-blocks Designs.- 10 Correlation and Association.- 11 Chi-squared and Related Measures.- References.- Index.

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Book SynopsisThis volume gathers peer-reviewed contributions that address a wide range of recent developments in the methodology and applications of data analysis and classification tools in micro and macroeconomic problems. The papers were originally presented at the 29th Conference of the Section on Classification and Data Analysis of the Polish Statistical Association, SKAD 2020, held in Sopot, Poland, September 7–9, 2020. Providing a balance between methodological contributions and empirical papers, the book is divided into five parts focusing on methodology, finance, economics, social issues and applications dealing with COVID-19 data. It is aimed at a wide audience, including researchers at universities and research institutions, graduate and doctoral students, practitioners, data scientists and employees in public statistical institutions.Table of ContentsPart 1: Methodology Chapter 1 - Evaluation of Two-Step Spectral Clustering Algorithm for Large Untypical Data Sets (Andrzej Dudek) Chapter 2 - Determining the Number of Groups in Cluster Analysis Using Classical Indexes and Stability Measures – Comparison of Results (Dorota Rozmus)Chapter 3 - Identification of the Words Most Frequently Used by Different Generations of Twitter Users (Agata Majkowska, Kamila Migdał-Najman, Krzysztof Najman and Katarzyna Raca)Chapter 4 - Classification Algorithms Applications for Information Security on the Internet: a Review (Michał Bryś)Chapter 5 - Outlier Detection with the Use of Isolation Forests (Krzysztof Najman and Krystian Zieliński)Part 2: Application in FinanceChapter 6 - Propositions of Transformations of Asymmetrical Nominants into Stimulants on the Example of Chosen Financial Ratios ( Barbara Batóg and Katarzyna Wawrzyniak)Chapter 7 - Gini Regression in The Capital Investment Risk Assessment – Sensitivity Risk Measures in Portfolio Analysis (Grażyna Trzpiot).- Part 3: Application in EconomicsChapter 8 - Enterprise Dark Data (Katarzyna Raca)Chapter 9 - The Significance of Medical Science Issues in Research Papers Published in the Field of Economics (Urszula Cieraszewska, Monika Hamerska, Paweł Lula and Marcela Zembura)Chapter 10 - Application of Duration Analysis Methods in the Study of the Exit of a Real Estate Sale Offer from the Offer Database System (Ewa Putek-Szeląg, Anna Gdakowicz)Chapter 11 - Is Society Ready for Long-Term Investments? – Profiles of Electricity Users in Silesia (Sylwia Słupik and Joanna Trzęsiok) Chapter 12 - The Use of the Spatial Taxonomic Measure of Development to Assess the Tourist Attractiveness of Districts of the Lesser Poland Province(Jacek Wolak).- Part 4: Application in Social Issues Chapter 13 - Models of Competing Events in Assessing the Effects of the Transition of Unemployed People Between the States of Registration and De-registration (Beata Bieszk-Stolorz).- Chapter 14 - Direct Adjusted Survival Probabilities in the Analysis of Finding a Job by the Unemployed Depending on Their Individual Characteristics(Wioletta Grzenda)Chapter 15 - Europe 2020 Strategy – Objective Evaluation of Realization and Subjective Assessment by Seniors as Beneficiaries of Social Assumptions (Klaudia Przybysz, Agnieszka Stanimir and Marta Wasiak)Chapter 16 - Do Seniors Get to the Disco by Bike or in a Taxi? – Classification of Seniors According to Their Preferred Means of Transport (Joanna Kos-Łabędowicz and Joanna Trzęsiok)Part 5: Application with COVID-19 Data Chapter 17 - The Impact of the COVID-19 Pandemic on the Economies of European Countries in the Period January-September 2020 Based on Economic Indicators (Ewelina Nojszewska and Agata Sielska)Chapter 18 - Modelling the Risk of Foreign Divestment in the Visegrad Group Countries During the COVID-19 Pandemic (Marcin Salamaga) Chapter 19 - Analysis of COVID-19 Dynamics in EU Countries Using the Dynamic Time Warping Method and ARIMA Models (Joanna Landmesser).

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Book SynopsisThe main focus of this book is on presenting advances in fuzzy statistics, and on proposing a methodology for testing hypotheses in the fuzzy environment based on the estimation of fuzzy confidence intervals, a context in which not only the data but also the hypotheses are considered to be fuzzy. The proposed method for estimating these intervals is based on the likelihood method and employs the bootstrap technique. A new metric generalizing the signed distance measure is also developed. In turn, the book presents two conceptually diverse applications in which defended intervals play a role: one is a novel methodology for evaluating linguistic questionnaires developed at the global and individual levels; the other is an extension of the multi-ways analysis of variance to the space of fuzzy sets. To illustrate these approaches, the book presents several empirical and simulation-based studies with synthetic and real data sets. In closing, it presents a coherent R package called “FuzzySTs” which covers all the previously mentioned concepts with full documentation and selected use cases. Given its scope, the book will be of interest to all researchers whose work involves advanced fuzzy statistical methods.Table of Contents- 1. Introduction. - Part I Theoretical Part. - 2. Fundamental Concepts on Fuzzy Sets. - 3. Fuzzy Rule-Based Systems. - 4. Distances Between Fuzzy Sets. - 5. Fuzzy Random Variables and Fuzzy Distributions. - 6. Fuzzy Statistical Inference. - Conclusion Part I. - Part II Applications. - 7. Evaluation of Linguistic Questionnaire. - 8. Fuzzy Analysis of Variance. - Part III An R Package for Fuzzy Statistical Analysis: A DetailedDescription. - 9. FuzzySTs: Fuzzy Statistical Tools: A Detailed Description. - Conclusion.

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Book SynopsisThis book provides empirical evidence and statistical analyses to uncover answers to some of the most debated questions in the NBA. The sports world lives and breathes off of debates on who deserves an MVP award, and which athletes should be considered all-stars. This book provides some statistics-backed perspectives to some of these debates that are specific to the NBA. Was LeBron snubbed of an MVP in the 2010-2011 season? Why has the G.O.A.T. debate turned into LeBron vs. Jordan….Did Kobe get overlooked? How come Klay Thompson didn’t get All-NBA honors in the 2018-2019 season? This book explores these questions and many more with empirical evidence. This book is invaluable for any undergraduate or masters level course in sport analytics, sports marketing, or sports management. It will also be incredibly useful for scouts, recruiters, and general managers in the NBA who would like to use analytics in their work.Table of ContentsIntroduction.- 1. Da Real MVP.- 2. A Tribe of Goats.- 3. The Myth of the Superteam.- 4. Hey Now, You're an All-Star...But Are You All-NBA?- 5. Small Ball in a Big Man's Game.- 6.Is the Clutch Gene Real.- 7. Offense Wins Games, But Does Defense Win Championships? - 8. Strategic Implications of the Findings in This Book.- 9. Debates the Future Work Should Consider.

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Book SynopsisThis textbook teaches some of the basic econometric methods and the underlying assumptions behind them. It also includes a simple and concise treatment of more advanced topics in spatial correlation, panel data, limited dependent variables, regression diagnostics, specification testing and time series analysis. Each chapter has a set of theoretical exercises as well as empirical illustrations using real economic applications. These empirical exercises usually replicate a published article using Stata, Eviews as well as SAS.This new sixth edition has been fully revised and updated, and includes new material on limited dependent variables and panel data as well as revision of basic topics like heteroskedasticity, endogeneity, over-identification and specification testing. The author also provides more exercises and empirical examples based on published economic applications.Table of ContentsPart 1: What Is Econometrics?.- Basic Statistical Concepts.- Simple Linear Regression.- Multiple Regression Analysis.- Violations of the Classical Assumptions.- Distributed Lags and Dynamic Models.- Part 2: The General Linear Model: The Basics.- Regression Diagnostics and Specification Tests.- Generalized Least Squares.- Seemingly Unrelated Regressions.- Simultaneous Equations Model.- Pooling Time-Series of Cross-Section Data.- Limited Dependent Variables.- Time-Series Analysis.

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Book SynopsisThis book provides a unified exposition of some fundamental theoretical problems in high-dimensional statistics. It specifically considers the canonical problems of detection and support estimation for sparse signals observed with noise. Novel phase-transition results are obtained for the signal support estimation problem under a variety of statistical risks. Based on a surprising connection to a concentration of maxima probabilistic phenomenon, the authors obtain a complete characterization of the exact support recovery problem for thresholding estimators under dependent errors. Table of Contents

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Book SynopsisThis book is devoted to the development of optimal control theory for finite dimensional systems governed by deterministic and stochastic differential equations driven by vector measures. The book deals with a broad class of controls, including regular controls (vector-valued measurable functions), relaxed controls (measure-valued functions) and controls determined by vector measures, where both fully and partially observed control problems are considered. In the past few decades, there have been remarkable advances in the field of systems and control theory thanks to the unprecedented interaction between mathematics and the physical and engineering sciences. Recently, optimal control theory for dynamic systems driven by vector measures has attracted increasing interest. This book presents this theory for dynamic systems governed by both ordinary and stochastic differential equations, including extensive results on the existence of optimal controls and necessary conditions for optimality. Computational algorithms are developed based on the optimality conditions, with numerical results presented to demonstrate the applicability of the theoretical results developed in the book. This book will be of interest to researchers in optimal control or applied functional analysis interested in applications of vector measures to control theory, stochastic systems driven by vector measures, and related topics. In particular, this self-contained account can be a starting point for further advances in the theory and applications of dynamic systems driven and controlled by vector measures.Trade Review“This book is a masterpiece of mathematical work where the authors joyfully stroll with the reader through the pleasant universe of control theory and its many applications. … I think the authors did a very good job. Their contribution is surely going to be particularly helpful to applied mathematicians. It’s a must read!” (Calvin Tadmon, SIAM Review, Vol. 64 (4), December, 2022)Table of Contents1 Mathematical Preliminaries.- 2 Linear Systems.- 3 Nonlinear Systems.- 4 Optimal Control: Existence Theory.- Optimal Control: Necessary Conditions of Optimality.- 6 Stochastic Systems Controlled by Vector Measures.- 7 Applications to Physical Examples.- Bibliography.- Index.

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Book SynopsisThis book deals with selected problems of machine perception, using various 2D and 3D imaging sensors. It proposes several new original methods, and also provides a detailed state-of-the-art overview of existing techniques for automated, multi-level interpretation of the observed static or dynamic environment. To ensure a sound theoretical basis of the new models, the surveys and algorithmic developments are performed in well-established Bayesian frameworks. Low level scene understanding functions are formulated as various image segmentation problems, where the advantages of probabilistic inference techniques such as Markov Random Fields (MRF) or Mixed Markov Models are considered. For the object level scene analysis, the book mainly relies on the literature of Marked Point Process (MPP) approaches, which consider strong geometric and prior interaction constraints in object population modeling. In particular, key developments are introduced in the spatial hierarchical decomposition of the observed scenarios, and in the temporal extension of complex MRF and MPP models. Apart from utilizing conventional optical sensors, case studies are provided on passive radar (ISAR) and Lidar-based Bayesian environment perception tasks. It is shown, via several experiments, that the proposed contributions embedded into a strict mathematical toolkit can significantly improve the results in real world 2D/3D test images and videos, for applications in video surveillance, smart city monitoring, autonomous driving, remote sensing, and optical industrial inspection.Table of ContentsIntroduction.- Fundamentals. - Bayesian models for Dynamic Scene Analysis.- Multi-layer label fusion models.- Multitemporal data analysis with Marked Point Processes. - Multi-level object population analysis with an EMPP model.- Concluding Remarks.- References.- Index.

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Book SynopsisDedicated to one of the most outstanding researchers in the field of statistics, this volume in honor of C.R. Rao, on the occasion of his 100th birthday, provides a bird’s-eye view of a broad spectrum of research topics, paralleling C.R. Rao’s wide-ranging research interests. The book’s contributors comprise a representative sample of the countless number of researchers whose careers have been influenced by C.R. Rao, through his work or his personal aid and advice. As such, written by experts from more than 15 countries, the book’s original and review contributions address topics including statistical inference, distribution theory, estimation theory, multivariate analysis, hypothesis testing, statistical modeling, design and sampling, shape and circular analysis, and applications. The book will appeal to statistics researchers, theoretical and applied alike, and PhD students. Happy Birthday, C.R. Rao!Table of ContentsPreface.- Dedication.- Part I – Inference.- Robust Statistical Inference for One-shot Devices Based on Density Power Divergences: An Overview (N. Balakrishnan, E. Castilla, L. Pardo).- Statistical Meaning of Mean Functions: A Novel Matrix Mean Derived from Fisher Information, authors: A.M. Kagan, P.J. Smith).- The Legend of the Equality of OLSE and BLUE: highlighted by C.R. Rao in 1967 (A. Markiewicz, S. Puntanen, G.P.H. Styan).- Comparison of Local Powers of Some Exact Tests for a Common Normal Mean with Unequal Variances (Y.G. Kifle, A.M. Moluh, B.K. Sinha).- Quantile Function: Overview of Collaboration with Professor C. R. Rao (G.J. Babu).- Part II – Distribution Theory.- Some Bivariate and Multivariate Models Involving Independent Gamma Distributed Components (B.C. Arnold).- An Absolute Continuous Bivariate Inverse Generalized Exponential Distribution: Properties, Inference and Extensions (D. Kundu).- Part III – Multivariate Analysis.- The Likelihood Ratio Test of Equality of Mean Vectors with a Doubly Exchangeable Covariance Matrix (C.A. Coelho, J. Pielaszkiewicz).- Bilinear Regression with Rank Restrictions on the Mean and the Dispersion Matrix (D. von Rosen).- Limiting Canonical Distribution of Two Large Dimensional Random Vectors (Z. Bai, Z. Hou, J. Hu, D. Jiang, X. Zhang).- Some Contributions to Multivariate Analysis due to C. R. Rao and Associated Developments (Y. Fujikoshi).- On Testing Structures of the Covariance Matrix: A Non-normal Approach (T. Kollo, M. Valge).- Part IV – Design and Sampling.- The Existence of Perpendicular Multi-arrays (K. Matsubara, S. Kageyama).- Statistical Design Issues for fMRI Studies: A Beginner’s Training Manual (B.K. Sinha, N.K. Mandal, M. Pal).- A Review of Rigorous Randomized Response Methods for Protecting Respondent's Privacy and Data Confidentiality (T. Nayak).- Part V – Shape and Circular Analysis.- A Statistical Analysis of the Cardioid Radial Growth Model (J.T. Kent, K.V. Mardia, L. Ippoliti, P. Valentini).- A Flexible Family of Mixed Distributions for Discrete Linear and Continuous Circular Random Variables (A. SenGupta, K. Shimizu, S.H. Ong, R. Das).- Goodness of Fit for Wrapped Stable Distributions Based on the Characteristic Function (S.G. Meintanis, S.R. Jammalamadaka, Q. Jin).- Part VI – Applications.- Partial Differential Equations Models and Riemann-Stieltjes Integrals in Measuring Sustainability (A.S.R.S. Rao, S. Saride).- Extreme Point Methodology in Power Calculations – The Case of Hardy-Weinberg Equilibrium (S. Venkatesan, M.B. Rao, H.-I. Hsiao).- Part VII – General.- On the Association of Professor C. R. Rao with the Poznan School of Mathematical Statistics and Biometry (T.Calinski).

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Book SynopsisThis book is designed to train graduate students across disciplines within the fields of public health and medicine, with the goal of guiding them in the transition to independent researchers. It focuses on theories, principles, techniques, and methods essential for data processing and quantitative analysis to address medical, health, and behavioral challenges. Students will learn to access to existing data and process their own data, quantify the distribution of a medical or health problem to inform decision making; to identify influential factors of a disease/behavioral problem; and to support health promotion and disease prevention. Concepts, principles, methods and skills are demonstrated with SAS programs, figures and tables generated from real, publicly available data. In addition to various methods for introductory analysis, the following are featured, including 4-dimensional measurement of distribution and geographic mapping, multiple linear and logistic regression, Poisson regression, Cox regression, missing data imputing, and statistical power analysis. Table of Contents1. Introduction to Quantitative Epidemiology.- 2. Characters, Variables, Data, and Information.- 3. Quantitative Descriptive Epidemiology.- 4. Causal Exploration with Bivariate Analysis.- 5. Confirmation with Multiple Linear Regression.- 6. Multivariate Analyses of Categorical and Counting Data.- 7. Multivariate Analysis of Time to Event Data.- 8. Simultaneous Analysis of Two Correlated Predictors.- 9. Special Issues with Quantitative Epidemiology.- 10. Power Analysis.

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Book SynopsisThis book is designed to train graduate students across disciplines within the fields of public health and medicine, with the goal of guiding them in the transition to independent researchers. It focuses on theories, principles, techniques, and methods essential for data processing and quantitative analysis to address medical, health, and behavioral challenges. Students will learn to access to existing data and process their own data, quantify the distribution of a medical or health problem to inform decision making; to identify influential factors of a disease/behavioral problem; and to support health promotion and disease prevention. Concepts, principles, methods and skills are demonstrated with SAS programs, figures and tables generated from real, publicly available data. In addition to various methods for introductory analysis, the following are featured, including 4-dimensional measurement of distribution and geographic mapping, multiple linear and logistic regression, Poisson regression, Cox regression, missing data imputing, and statistical power analysis. Table of Contents1. Introduction to Quantitative Epidemiology.- 2. Characters, Variables, Data, and Information.- 3. Quantitative Descriptive Epidemiology.- 4. Causal Exploration with Bivariate Analysis.- 5. Confirmation with Multiple Linear Regression.- 6. Multivariate Analyses of Categorical and Counting Data.- 7. Multivariate Analysis of Time to Event Data.- 8. Simultaneous Analysis of Two Correlated Predictors.- 9. Special Issues with Quantitative Epidemiology.- 10. Power Analysis.

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Book SynopsisThis proceedings volume gathers together original articles and survey works that originate from presentations given at the conference Transient Transcendence in Transylvania, held in Brașov, Romania, from May 13th to 17th, 2019. The conference gathered international experts from various fields of mathematics and computer science, with diverse interests and viewpoints on transcendence. The covered topics are related to algebraic and transcendental aspects of special functions and special numbers arising in algebra, combinatorics, geometry and number theory. Besides contributions on key topics from invited speakers, this volume also brings selected papers from attendees.Table of ContentsFrobenius action on a hypergeometric curve and an algorithm for computing values of Dwork’s p-adic hypergeometric functions (Asakura).- A Matrix version of Dwork’s Congruences (Beukers).- On the kernel curves associated with walks in the quarter plane (Singer).- A survey on the hypertranscendence of the solutions of the Schröder's, Böttcher's and Abel's equations (Fernandes).- Hodge structures and differential operators (Vlasenko).- Beck-type identities for Euler pairs of order (Welch et al.).- Quarter-plane lattice paths with interacting boundaries: the Kreweras and reverse Kreweras models (Xu et al.).- Infinite product formulae for generating functions for sequences of squares (Radu et al.).- A theta identity of Gauss connecting functions from additive and multiplicative number theory (Merca).- Combinatorial quantum field theory and the Jacobian conjecture (Tanasa).- How regular are regular singularities? (Hauser).- Néron desingularization of extensions of valuation rings with an appendix by kęstutis česnavičius (Popescu).- Diagonal Representation of Algebraic Power Series: A Glimpse Behind the Scenes (Yurkevich).- Proof of chudnovskys’ hypergeometric series for 1/π using weber modular polynomials (Guillera).-Computing an order-complete basis for m∞(n) and applications (Radu et al.).- An algorithm to prove holonomic differential equations for modular forms (Radu et al.).- A case study for ζ(4) (zudilin et al.).- Support of an algebraic series as the range of a recursive sequence (bell).- X-coordinates of pell equations in various sequences (luca).- A conditional proof of the leopoldt conjecture for cm fields (mihailescu).- Siegel’s problem for e-functions of order 2 (Roques et al.).- Irrationality and Transcendence of Alternating Series Via Continued Fractions (Snowdow).- On the transcendence of critical hecke l-values (sprang).

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Book SynopsisThis volume contains papers which were presented at the XV Latin American Congress of Probability and Mathematical Statistics (CLAPEM) in December 2019 in Mérida-Yucatán, México. They represent well the wide set of topics on probability and statistics that was covered at this congress, and their high quality and variety illustrates the rich academic program of the conference.

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Book SynopsisThis textbook provides the tools, techniques, and industry examples needed for the successful implementation of design of experiments (DoE) in engineering and manufacturing applications. It contains a high-level engineering analysis of key issues in the design, development, and successful analysis of industrial DoE, focusing on the design aspect of the experiment and then on interpreting the results. Statistical analysis is shown without formula derivation, and readers are directed as to the meaning of each term in the statistical analysis. Industrial Design of Experiments: A Case Study Approach for Design and Process Optimization is designed for graduate-level DoE, engineering design, and general statistical courses, as well as professional education and certification classes. Practicing engineers and managers working in multidisciplinary product development will find it to be an invaluable reference that provides all the information needed to accomplish a successful DoE. Table of Contents1) Presentations, Statistical Distributions, Quality Tools and Relationship to DoE2) Samples and Populations: Statistical Tests for Significance of Mean and Variability3) Regression, Treatments, DoE Design and Modelling Tools. 4) Two-Level Factorial Design and Analysis Techniques5) Three-Level Factorial Design and Analysis Techniques 6) DoE Error Handling, Significance and Goal Setting 7) DoE Reduction Using Confounding and Professional Experience 8) Multiple Level Factorial Design and DoE Sequencing Techniques9) Variability Reduction Techniques and Combining with Mean Analysis 10) Strategies for Multiple Outcome Analysis and Summary of DoE Case Studies and Techniques

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Book SynopsisThis essential book details intermediate-level statistical methods and frameworks for the clinician and medical researcher with an elementary grasp of health statistics and focuses on selecting the appropriate statistical method for many scenarios. Detailed evaluation of various methodologies familiarizes readers with the available techniques and equips them with the tools to select the best from a range of options. The inclusion of a hypothetical case study between a clinician and statistician charting the conception of the research idea through to results dissemination enables the reader to understand how to apply the concepts covered into their day-to-day clinical practice.Applied Statistical Considerations for Clinical Researchers focuses on how clinicians can approach statistical issues when confronted with a medical research problem by considering the data structure, how this relates to their study's aims and any potential knock-on effects relating to the evidence required to make correct clinical decisions. It covers the application of intermediate-level techniques in health statistics making it an ideal resource for the clinician seeking an up-to-date resource on the topic.Table of ContentsIntroduction.- Preliminaries.- Design.- Planning.- Data Acquisition.- Data Manipulation Analysis.- Inferencesty.- Dissemination.- A Case Study.- Conclusions.

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