Probability and statistics Books

Book SynopsisThis volume contains current work at the frontiers of research in quantum probability, infinite dimensional stochastic analysis, quantum information and statistics. It presents a carefully chosen collection of articles by experts to highlight the latest developments in those fields. Included in this volume are expository papers which will help increase communication between researchers working in these areas. The tools and techniques presented here will be of great value to research mathematicians, graduate students and applied mathematicians.Table of ContentsExistence of the Fock Representation for Current Algebras of the Galilei Algebra (L Accardi et al.); Modular Structures and Landau Levels (F Bagarello); On Spectral Approach to Pascal White Noise Functionals (A Barhoumi); Spectral Analysis for Twisted Waveguides (P Briet); Classification of Invarient State of Generic Quantum Markov Semigroups: The Gaussian Gauge (S Hachiha); On Difficulties Appearing in the Study of Stochastic Volterra Equations (A Karczewska); Entanglement Protection and Generation in Two Atom System (M Orszag); Hilbert Molecules - Square Roots of Positive Maps (M Skeide); Multiparameter Quantum Stochastic Processes (J Spring); and other papers.

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Book SynopsisThis festschrift includes papers authored by many collaborators, colleagues, and students of Professor Thomas P Hettmansperger, who worked in research in nonparametric statistics, rank statistics, robustness, and mixture models during a career that spanned nearly 40 years. It is a broad sample of peer-reviewed, cutting-edge research related to nonparametrics and mixture models.Table of ContentsThis festschrift includes papers authored by many collaborators, colleagues, and students of Professor Thomas P Hettmansperger, who worked in research in nonparametric statistics, rank statistics, robustness, and mixture models during a career that spanned nearly 40 years. It is a broad sample of peer-reviewed, cutting-edge research related to nonparametrics and mixture models.

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Book SynopsisThis book presents a unified approach on nonparametric estimators for models of independent observations, jump processes and continuous processes. New estimators are defined and their limiting behavior is studied. From a practical point of view, the book expounds on the construction of estimators for functionals of processes and densities, and provides asymptotic expansions and optimality properties from smooth estimators.It also presents new regular estimators for functionals of processes, compares histogram and kernel estimators, compares several new estimators for single-index models, and it examines the weak convergence of the estimators.Table of ContentsIntroduction; Kernel Estimator of a Density; Kernel Estimator of a Regression Function; Limits for the Varying Bandwidths Estimators; Nonparametric Estimation of Quantiles; Nonparametric Estimation for Stochastic Processes; Estimation in Semi-Parametric Regression Models; Diffusions Processes; Applications to Time Series.

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Book SynopsisThis volume consists of a collection of research articles on classical and emerging Statistical Paradigms — parametric, non-parametric and semi-parametric, frequentist and Bayesian — encompassing both theoretical advances and emerging applications in a variety of scientific disciplines. For advances in theory, the topics include: Bayesian Inference, Directional Data Analysis, Distribution Theory, Econometrics and Multiple Testing Procedures. The areas in emerging applications include: Bioinformatics, Factorial Experiments and Linear Models, Hotspot Geoinformatics and Reliability.Table of ContentsWeak Paradoxes And Paradigms; Nonparametrics in Modern Interdisciplinary Research: Some Perspectives and Prospectives; Stepdown GERT Analysis of Consecutive-K Systems: An Overview; Bounds on Distributions Involving Partial, Marginal and Conditional Information: The Consequences of Incomplete Prior Specification; New Wrapped Distributions; Non-Stationarity and Meta-Distribution; Moment Bounds for Strong-Mixing Processes with Applications; On Confidence Intervals for Expected Response in 2n Factorial Experiments with Exponentially Distributed Response Variables; Non-parametric Estimation in a One-Way Error Component Model: A Monte-Carlo Analysis; Predictive Influence of Variables in a Linear Regression Model When the Moment Matrix (X'X) is Singular; Bayesian Curve Registration of Functional Data; MDL Modeling Criterion for Linear Mixed Models; Procedures Controlling a Generalized False Discovery Rate; Digital Governance and Hotspot Geoinformatics with Continuous Fractional Response.

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Book SynopsisThis volume consists of 22 research papers by leading researchers in Probability and Statistics. Many of the papers are focused on themes that Professor Bhattacharya has published on research. Topics of special interest include nonparametric inference, nonparametric curve fitting, linear model theory, Bayesian nonparametrics, change point problems, time series analysis and asymptotic theory.This volume presents state-of-the-art research in statistical theory, with an emphasis on nonparametric inference, linear model theory, time series analysis and asymptotic theory. It will serve as a valuable reference to the statistics research community as well as to practitioners who utilize methodology in these areas of emphasis.Table of ContentsReview Papers: On the Scholarly Work of P.K. Bhattacharya (P Hall & F J Samaniego); The Propensity Score (C Drake & T Loux); Tests for Symmetry: A Review (S Meintanis & J Ngatchou-Wandji); Papers on General Nonparametric Inference: On Robust Versions of Classical Tests with Dependent Data (J Jiang); Density Estimation (G G Roussas & D Bhattacharya); A Short Proof of the Feigin - Tweedie Theorem (J Sethuraman); Max - Min Bernstein Polynomial Estimation (K-S Song); U-Statistics Based on Higher-Order Spacings (D Tung & S R Jammalamadaka); Nonparametric Models for Non-Gaussian Longitudinal Data (N Zhang, H-G Muller and J-L Wang); Papers on Aspects of Linear or Generalized Linear Models: Better Residuals (R Beran); The Use of Peters - Belson Regression in Legal Cases (E Bura, J L Gastwirth & H Hikawa); On a Hybrid Approach to Parametric and Nonparametric Regression (P Burman & P Chaudhuri); Nonparametric Regression Models with Integrated Covariates (Z Cai); A Dynamic Test for Misspecification of a Linear Model (M McAssey & F Hsieh); The Principal Component Decomposition of the Basic Martingale (W Stute); Papers on Time Series Analysis: Fast Scatterplot Smoothing (A Aue & T C M Lee); Semiparametric GARCH Estimation (J Di & A Gangopadhyay); Extreme Dependence in Multivariate Time Series (R Sen & Z Tan); Dynamic Mixed Models for Irregularly Observed Water Quality Data (R Shumway); Papers on Asymptotic Theory: Asymptotic Behavior of the Kernel Density Estimators (J-F Lenain, M Harel & M Puri); Convergence Rates of an Improved Isotonic Regression Estimator (H Mukerjee); Asymptotic Distribution of the Smallest Eigenvalue of Wishart(N, n) (D Paul).

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Book SynopsisThis book presents a systematic treatment of Markov chains, diffusion processes and state space models, as well as alternative approaches to Markov chains through stochastic difference equations and stochastic differential equations. It illustrates how these processes and approaches are applied to many problems in genetics, carcinogenesis, AIDS epidemiology and other biomedical systems.One feature of the book is that it describes the basic MCMC (Markov chain and Monte Carlo) procedures and illustrates how to use the Gibbs sampling method and the multilevel Gibbs sampling method to solve many problems in genetics, carcinogenesis, AIDS and other biomedical systems.As another feature, the book develops many state space models for many genetic problems, carcinogenesis, AIDS epidemiology and HIV pathogenesis. It shows in detail how to use the multilevel Gibbs sampling method to estimate (or predict) simultaneously the state variables and the unknown parameters in cancer chemotherapy, carcinogenesis, AIDS epidemiology and HIV pathogenesis. As a matter of fact, this book is the first to develop several state space models for many genetic problems, carcinogenesis and other biomedical problems.To emphasize special applications to medical problems, in this new edition the book has added a new chapter to illustrate how to develop biologically-supported stochastic models and state space models of carcinogenesis in human beings. Specific examples include hidden Markov models and state space models for human colon cancer, human liver cancer and some human pediatric cancers such as retinoblastoma and hepatoblastoma. The book also gives examples to illustrate how to develop procedures to assess cancer risk of environmental agents through initiation-promotion protocols.Table of ContentsDiscrete Time Markov Chain Models in Genetics and Biomedical Systems; Stationary Distributions and MCMC in Discrete Time Markov Chains; Continuous-Time Markov Chain Models in Genetics, Cancers and AIDS; Absorption Probabilities and Stationary Distributions in Continuous-Time Markov Chain Models; Diffusion Models in Genetics, Cancer and AIDS; Asymptotic Distributions, Stationary Distributions and Absorption Probabilities in Diffusion Models; State Space Models and Some Examples from Cancer and AIDS; Some General Theories of State Space Models and Applications.

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Book SynopsisMethods of kernel estimates represent one of the most effective nonparametric smoothing techniques. These methods are simple to understand and they possess very good statistical properties. This book provides a concise and comprehensive overview of statistical theory and in addition, emphasis is given to the implementation of presented methods in Matlab. All created programs are included in a special toolbox which is an integral part of the book. This toolbox contains many Matlab scripts useful for kernel smoothing of density, cumulative distribution function, regression function, hazard function, indices of quality and bivariate density. Specifically, methods for choosing a choice of the optimal bandwidth and a special procedure for simultaneous choice of the bandwidth, the kernel and its order are implemented. The toolbox is divided into six parts according to the chapters of the book.All scripts are included in a user interface and it is easy to manipulate with this interface. Each chapter of the book contains a detailed help for the related part of the toolbox too. This book is intended for newcomers to the field of smoothing techniques and would also be appropriate for a wide audience: advanced graduate, PhD students and researchers from both the statistical science and interface disciplines.Table of ContentsKernel and Their Properties; Univariate Kernel Density Estimate; Kernel Estimate of Distribution Function; Kernel Estimate and Reliability Assessment; Kernel Estimates of Hazard Function; Kernel Regression; Multivariate Kernel Density Estimate.

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Book SynopsisThe book is aimed at graduate students and researchers with basic knowledge of Probability and Integration Theory. It introduces classical inequalities in vector and functional spaces with applications to probability. It also develops new extensions of the analytical inequalities, with sharper bounds and generalizations to the sum or the supremum of random variables, to martingales and to transformed Brownian motions. The proofs of the new results are presented in great detail.Table of ContentsClassical Probability Inequalities; Burkholder Inequality; Cauchy Inequalities; Chernov Theorem; Donsker Classes; Martingales; Brownian Motion; Empirical Process; Solutions of Diffusion Equations; Complex Spaces; Fourier Transform; Hermite Polynomials; Laplace Transform; Tightness; Weak Convergence.

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Book SynopsisThis volume consists of a series of research papers presented at the conference Statistics 2011 Canada: 5th Canadian Conference in Applied Statistics held together with the 20th conference of the Forum for Interdisciplinary Mathematics titled, “Interdisciplinary Mathematical & Statistical Techniques”. These papers cover a wide range of topics from applications of Mathematics and Statistics such as Selection Bias in Surveys, Biomarker Discovery, Analysis of Earth Temperature, Supply Chain Management, Trimmed ANOVA, Zero-inflated Data, Non-Gaussian Time Series, and Stochastic Ordering; Classification, Nonparametric Test, and Jackknifed Ridge Estimator; Bayes Factor; Random Graphs and Error Correcting Codes; Meta Analysis; and National Health Plans and Risk Reduction through Supply Chain.The topics have been reviewed by experts in the field and the selected papers are expected to provide a topical resource on the subjects concerned.Table of ContentsPreface; Hypothesis Assessment Using the Bayes Factor and Relative Belief Ratio (Z Baskurt and M Evans); An Analysis of 1990-2011 Ontario Surface Air Temperatures (D R Brillinger); A Markov Chain Monte Carlo Sampler for Gene Genealogies Conditional on Haplotype Data (K M Burkett, B McNeney and J Graham); Jackknifing Stochastic Restricted Ridge Estimator with Heteroscedastic Errors (Y P Chaubey, M Khurana and S Chandra); Molecular Classification of Acute Leukemia (G Chen and J Wu); A Note on a Nonparametric Trend Test and Its Competitors (K Deka and B Gogoi); Local Search for Identifying Communities in Large Random Graphs (N Deo and M Vasudevan); Data Mining Approaches to Multivariate Biomarker Discovery (D M Dziuda); On Sequential Change-Point Detection Strategies (E Gombay); Multi-Item Two-Stage EOQ Model Incorporating Quantity and Freight Discounts (D Gupta, K Gandhi, S Makkar and P C Jha); An Improved Bound on Average Codeword Length of Variable Length Error Correcting Codes (R Gupta and B Sharma); Trimmed Analysis of Variance: A Robust Modification of ANOVA (G S Mudholkar, D K Srivastava, C E Marchetti and A G Mudholkar); Bayesian Predictive Inference under Sequential Sampling with Selection Bias (B Nandram and D Kim); Tests For and Against Uniform Stochastic Ordering on Multinomial Parameters Based on Φ-Divergences (J Peng); Development and Management of National Health Plans: Health Economics and Statistical Perspectives (P K Sen); A Unified Approach between Population-Averaged and Cluster-Specific Analyses for Multilevel Zero-Inflated Count Data (G Sneddon, M T Hasan and R Ma); Meta-Analysis of Binary Outcomes Data in Clinical Trials (P Subbaiah, A Mallick and T K Desai); Risk Reduction of the Supply Chain through Pooling Losses in Case of Bankruptcy of Suppliers Using the Black-Scholes-Merton Pricing Model (R Valvarde and M Talla); Random Effects Modelling of Non-Gaussian Time Series Responses with Covariates (G Yan, M T Hasan and R Ma).

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Book SynopsisThe properties of the harmonic oscillator with random frequency or/and random damping formed the content of the first edition. The second edition includes hundreds of publications on this subject since 2005. The noisy oscillator continues to be the subject of intensive studies in physics, chemistry, biology, and social sciences.The new and the latest type of a stochastic oscillator has also been considered, namely, an oscillator with random mass. Such model describes, among other phenomena, Brownian motion with adhesion, where the molecules of the surrounding medium not only randomly collide, but also stick to the Brownian particle for some (random) time, thereby changing its mass. This edition contains two new chapters, eight new sections and an expanded bibliography. A wide group of researchers, students and teachers will benefit from this book.Table of ContentsDeterministic and Random Oscillators; White and Color Noise; Brownian Motion; Overdamped Harmonic Oscillator with Additive Noise; Overdamped Harmonic Oscillator with Multiplicative Noise; Overdamped Single-Well Oscillator; Overdamped Double-Well Oscillator; Harmonic Oscillator with Additive Noise; Nonlinear Oscillator with Additive Noise; Harmonic Oscillator with Random Frequency; Harmonic Oscillator with Random Damping; Linear vs Quadratic Noise; Nonlinear Oscillator with Multiplicative Noise; Harmonic Oscillator with Random Mass; In the Future.

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Book SynopsisThe simplest mathematical model of the Brownian motion of physics is the simple, symmetric random walk. This book collects and compares current results — mostly strong theorems which describe the properties of a random walk. The modern problems of the limit theorems of probability theory are treated in the simple case of coin tossing. Taking advantage of this simplicity, the reader is familiarized with limit theorems (especially strong ones) without the burden of technical tools and difficulties. An easy way of considering the Wiener process is also given, through the study of the random walk.Since the first and second editions were published in 1990 and 2005, a number of new results have appeared in the literature. The first two editions contained many unsolved problems and conjectures which have since been settled; this third, revised and enlarged edition includes those new results. In this edition, a completely new part is included concerning Simple Random Walks on Graphs. Properties of random walks on several concrete graphs have been studied in the last decade. Some of the obtained results are also presented.Table of ContentsSimple Symmetric Random Walk in ℤ1: Introduction of Part I; Distributions; Recurrence and the Zero-One Law; From the Strong Law of Large Numbers to the Law of Iterated Logarithm; Levy Classes; Wiener Process and Invariance Principle; Increments; Strassen Type Theorems; Distribution of the Local Time; Local Time and Invariance Principle; Strong Theorems of the Local Time; Excursions; Frequently and Rarely Visited Sites; An Embedding Theorem; A Few Further Results; Summary of Part I; Simple Symmetric Random Walk in ℤd: The Recurrence Theorem; Wiener Process and Invariance Principle; The Law of Iterated Logarithm; Local Time; The Range; Heavy Points and Heavy Balls; Crossing and Self-crossing; Large Covered Balls; Long Excursions; Speed of Escape; A Few Further Problems; Random Walk in Random Environment: Introduction of Part III; In the First Six Days; After the Sixth Day; What Can a Physicist Say About the Local Time ξ(0,n)?; On the Favourite Value of the RWIRE; A Few Further Problems; Random Walks in Graphs: Introduction of Part IV; Random Walk in Comb; Random Walk in a Comb and in a Brush with Crossings; Random Walk on a Spider; Random Walk in Half-Plane-Half-Comb.

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Book SynopsisThis book provides a multi-level introduction to Bayesian reasoning (as opposed to “conventional statistics”) and its applications to data analysis. The basic ideas of this “new” approach to the quantification of uncertainty are presented using examples from research and everyday life. Applications covered include: parametric inference; combination of results; treatment of uncertainty due to systematic errors and background; comparison of hypotheses; unfolding of experimental distributions; upper/lower bounds in frontier-type measurements. Approximate methods for routine use are derived and are shown often to coincide — under well-defined assumptions! — with “standard” methods, which can therefore be seen as special cases of the more general Bayesian methods. In dealing with uncertainty in measurements, modern metrological ideas are utilized, including the ISO classification of uncertainty into type A and type B. These are shown to fit well into the Bayesian framework.Table of ContentsCritical Review and Outline of the Bayesian Alternative: Uncertainty in Physics and the Usual Methods of Handling It; A Probabilistic Theory of Measurement Uncertainty; A Bayesian Primer: Subjective Probability and Bayes' Theorem; Probability Distributions (A Concise Reminder); Bayesian Inference of Continuous Quantities; Gaussian Likelihood; Counting Experiments; Bypassing Bayes' Theorem for Routine Applications; Bayesian Unfolding; Further Comments, Examples and Applications: Miscellanea on General Issues in Probability and Inference; Combination of Experimental Results: A Closer Look; Asymmetric Uncertainties and Nonlinear Propagation; Which Priors for Frontier Physics?; Conclusion: Conclusions and Bibliography.

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Book SynopsisThe book aims to present a wide range of the newest results on multivariate statistical models, distribution theory and applications of multivariate statistical methods. A paper on Pearson-Kotz-Dirichlet distributions by Professor N Balakrishnan contains main results of the Samuel Kotz Memorial Lecture. Extensions of linear models to multivariate exponential dispersion models and Growth Curve models are presented, and several papers on classification methods are included. Applications range from insurance mathematics to medical and industrial statistics and sampling algorithms.

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Book SynopsisThis book presents the theory of probability and mathematical statistics at a level suitable for researchers at the frontiers of applied disciplines. Examples and exercises make essential concepts in measure theory and analysis accessible to those with preparation limited to vector calculus. Complete, detailed solutions to all the exercises demonstrate techniques of problem solving and provide immediate feedback.Part I, The Theory of Probability, starts with elementary set theory and proceeds through basic measure and probability, random variables, integration and mathematical expectation. It concludes with an extensive survey of models for distributions of random variables. Part II, The Theory of Statistics, begins with sampling theory and distribution theory for statistics from normal populations, proceeds to asymptotic (large-sample) theory, and on to point and interval estimation and tests of parametric hypotheses. The last three chapters cover tests of nonparametric hypotheses, Bayesian methods, and linear and nonlinear regression.Researchers and graduate students in applied fields such as actuarial science, biostatistics, economics, finance, mathematical psychology, and systems engineering will find this book to be a valuable learning tool and an essential reference.Table of ContentsThe Theory of Probability: Probability on Abstract Sets; Probability on Sets of Real Numbers; Mathematical Expectation; Models for Distributions; The Theory of Statistics: Sampling Distributions; Asymptotic Distribution Theory; Estimation; Tests of Parametric Hypotheses; Tests of Nonparametric Hypotheses; A Survey of Bayesian Methods; Modeling Relatedness: Regression Analysis.

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Book SynopsisThe purpose of this book is to present systematically all known mathematical results on Gibbs measures on Cayley trees (Bethe lattices).The Gibbs measure is a probability measure, which has been an important object in many problems of probability theory and statistical mechanics. It is the measure associated with the Hamiltonian of a physical system (a model) and generalizes the notion of a canonical ensemble. More importantly, when the Hamiltonian can be written as a sum of parts, the Gibbs measure has the Markov property (a certain kind of statistical independence), thus leading to its widespread appearance in many problems outside of physics such as biology, Hopfield networks, Markov networks, and Markov logic networks. Moreover, the Gibbs measure is the unique measure that maximizes the entropy for a given expected energy.The method used for the description of Gibbs measures on Cayley trees is the method of Markov random field theory and recurrent equations of this theory, but the modern theory of Gibbs measures on trees uses new tools such as group theory, information flows on trees, node-weighted random walks, contour methods on trees, and nonlinear analysis. This book discusses all the mentioned methods, which were developed recently.Table of ContentsProperties of a Group Representation of the Cayley Tree; Ising Model on Cayley Tree; Ising Type Models with Competing Interactions; Information Flow on Trees; The Potts Model; The Solid-on-Solid Model; Models with Hard Constraints; Potts Model with Countable Set of Spin Values; Models with Uncountable Set of Spin Values; Contour Arguments on Cayley Trees; Other Models.

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Book SynopsisThis volume first introduces the mathematical tools necessary for understanding and working with a broad class of applied stochastic models. The toolbox includes Gaussian processes, independently scattered measures such as Gaussian white noise and Poisson random measures, stochastic integrals, compound Poisson, infinitely divisible and stable distributions and processes.Next, it illustrates general concepts by handling a transparent but rich example of a “teletraffic model”. A minor tuning of a few parameters of the model leads to different workload regimes, including Wiener process, fractional Brownian motion and stable Lévy process. The simplicity of the dependence mechanism used in the model enables us to get a clear understanding of long and short range dependence phenomena. The model also shows how light or heavy distribution tails lead to continuous Gaussian processes or to processes with jumps in the limiting regime. Finally, in this volume, readers will find discussions on the multivariate extensions that admit a variety of completely different applied interpretations.The reader will quickly become familiar with key concepts that form a language for many major probabilistic models of real world phenomena but are often neglected in more traditional courses of stochastic processes.Table of ContentsBrief Reminder of Probability Theory; Compound Poisson, Infinitely Divisible and Stable Random Variables; Gaussian Processes: Wiener Process, Fractional Brownian Motion, Etc.; Levy Processes; Uncorrelated and Independently Scattered Random Measures and Respective Integrals; Limit Theorems for Processes; Teletraffic Workload Models: Weak Dependence, Long Range Dependence, Gaussian, Stable, and Intermediate Limits; Kaj - Taqqu Telecom Processes; Multivariate Workload Models.

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Book SynopsisAn overview of the asymptotic theory of optimal nonparametric tests is presented in this book. It covers a wide range of topics: Neyman-Pearson and LeCam's theories of optimal tests, the theories of empirical processes and kernel estimators with extensions of their applications to the asymptotic behavior of tests for distribution functions, densities and curves of the nonparametric models defining the distributions of point processes and diffusions. With many new test statistics developed for smooth curves, the reliance on kernel estimators with bias corrections and the weak convergence of the estimators are useful to prove the asymptotic properties of the tests, extending the coverage to semiparametric models. They include tests built from continuously observed processes and observations with cumulative intervals.Table of ContentsAsymptotic Theory of Optimal Tests; Nonparametric and Semiparametric Statistics; Kolmogorov - Smirnov Tests; Cramer - von Mises and Anderson - Darling Tests; Kernel Estimators for Densities, Regression Functions, Intensities and Diffusions; Homogeniety; Symmetry; Goodness-of-Fit; Monotony; One-Sample Tests; k-Sample Tests.

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Book SynopsisThis is a book of problems in probability and their solutions. The work has been written for undergraduate students who have a background in calculus and wish to study probability.Probability theory is a key part of contemporary mathematics. The subject plays a key role in the insurance industry, modelling financial markets, and statistics in general — including all those fields of endeavour to which statistics is applied (e.g. health, physical sciences, engineering, economics, social sciences). Every student majoring in mathematics at university ought to take a course on probability or mathematical statistics. Probability is now a standard part of high school mathematics, and teachers ought to be well versed and confident in the subject. Problem solving is important in mathematics. This book combines problem solving and probability.Table of ContentsSets, Measure and Probability; Elementary Probability; Discrete Random Variables; Continuous Random Variables; Limit Theorems; Random Walks.

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Book SynopsisThis volume consists of three parts: Part I comprises 11 chapters on the basic concepts of statistics, Part II consists of 10 chapters on multivariate statistics and Part III contains 12 chapters on design and analysis for medical research. The book is written using basic concepts and commonly used methods of design and analysis in medical statistics, incorporating the operation of statistical package SAS and 100 computer experiments for the important statistical phenomena related to each chapter. All necessary data, including reference answers for the exercises, SAS programs for all computer experiments and part of the examples, and data documents for 12 medical researches are available. The Chinese version of this book has been recommended as a textbook of statistics for postgraduate program by the Office of Education Research, Ministry of Education, People's Republic of China.Table of ContentsBasic Concepts of Statistics: Descriptive Statistics; Hypothesis Testing; Simple Linear Correlation and Regression; Non-Linear Regression; Analysis of Variance; Nonparametric Tests based on Ranks; Advanced Statistical Methods: Multiple Regression and Correlation; Multi-Variate ANOVA; Discriminant Analysis; Factor Analysis; Canonical Correlation and Correspondence Analysis; Logistic Regression; Survival Analysis; Log Linear Methods and Poisson Regression; Design and Analysis for Medical Research: Analysis of Repeated Measurements; Design and Analysis of Sequential Experiments; Design and Analysis for Epidemiological Study; Design and Analysis for Comparative Effectiveness Research; Statistical Methods for Data from Genetic Study; Statistical Methods for Data of Bioinformatics; Design and Analysis for Diagnostic and Screening Study; Systematic Review of Medical Literatures and Meta-Analysis; and others.

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Book SynopsisThis unique volume discusses some recent developments in the theory of spatial branching processes and superprocesses, with special emphasis on spines, Laws of Large Numbers, interactions and random media.Although this book is mainly written for mathematicians, the models discussed are relevant to certain models in population biology, and are thus hopefully interesting to the applied mathematician/biologist as well.The necessary background material in probability and analysis is provided in a comprehensive introductory chapter. Historical notes and several exercises are provided to complement each chapter.Table of ContentsPreliminaries; The Spine Construction and the Strong Law of Large Numbers; Examples of the Strong Law; The Strong Law for a Type of Self-Interaction; The Center of Mass; Branching Brownian Motion in a Poissonian Field of Traps; Branching Brownian Motion in a Field of Mild Obstacles; Critical Branching Random Walk in Random Environment.

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Book SynopsisThe book contains three parts: Spectral theory of large dimensional random matrices; Applications to wireless communications; and Applications to finance. In the first part, we introduce some basic theorems of spectral analysis of large dimensional random matrices that are obtained under finite moment conditions, such as the limiting spectral distributions of Wigner matrix and that of large dimensional sample covariance matrix, limits of extreme eigenvalues, and the central limit theorems for linear spectral statistics. In the second part, we introduce some basic examples of applications of random matrix theory to wireless communications and in the third part, we present some examples of Applications to statistical finance.Table of ContentsIntroduction; Limiting Spectral Distributions; Extreme Eigenvalues; CLT of LSS; Limiting Behavior of Eigenmatrix of Sample Covariance Matrix; Wireless Communications; Limiting Performances of Linear and Iterative Receivers; Applications to Finance.

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Book SynopsisContrary to common intuition that all digits should occur randomly with equal chances in real data, empirical examinations consistently show that not all digits are created equal, but rather that low digits such as {1, 2, 3} occur much more frequently than high digits such as {7, 8, 9} in almost all data types, such as those relating to geology, chemistry, astronomy, physics, and engineering, as well as in accounting, financial, econometrics, and demographics data sets. This intriguing digital phenomenon is known as Benford's Law.This book gives a comprehensive and in-depth account of all the theoretical aspects, results, causes and explanations of Benford's Law, with a strong emphasis on the connection to real-life data and the physical manifestation of the law. In addition to such a bird's eye view of the digital phenomenon, the conceptual distinctions between digits, numbers, and quantities are explored; leading to the key finding that the phenomenon is actually quantitative in nature; originating from the fact that in extreme generality, nature creates many small quantities but very few big quantities, corroborating the motto 'small is beautiful', and that therefore all this is applicable just as well to data written in the ancient Roman, Mayan, Egyptian, and other digit-less civilizations.Fraudsters are typically not aware of this digital pattern and tend to invent numbers with approximately equal digital frequencies. The digital analyst can easily check reported data for compliance with this digital law, enabling the detection of tax evasion, Ponzi schemes, and other financial scams. The forensic fraud detection section in this book is written in a very concise and reader-friendly style; gathering all known methods and standards in the accounting and auditing industry; summarizing and fusing them into a singular coherent whole; and can be understood without deep knowledge in statistical theory or advanced mathematics. In addition, a digital algorithm is presented, enabling the auditor to detect fraud even when the sophisticated cheater is aware of the law and invents numbers accordingly. The algorithm employs a subtle inner digital pattern within the Benford's pattern itself. This newly discovered pattern is deemed to be nearly universal, being even more prevalent than the Benford phenomenon, as it is found in all random data sets, Benford as well as non-Benford types.Table of ContentsBenford's Law; Forensic Digital Analysis & Fraud Detection; Data Compliance Tests; Conceptual and Mathematical Foundations; Benford's Law in the Physical Sciences; Topics in Benford's Law; The Law of Relative Quantities.

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Book SynopsisThe book contains review articles on recent advances in first-passage phenomena and applications contributed by leading international experts. It is intended for graduate students and researchers who are interested in learning about this intriguing and important topic.Table of ContentsArrival Statistics and Exploration Properties of Mortal Walkers (S B Yuste et al.); First-Passage of a Randomly Accelerated Particle (T Burkhardt); First-Passage Problems in Anomalous Diffusion (A Rosso and A Zoia); First-Passage Times of Intermittent Random Walks (O Benichou and R Voituriez); First-Passage Phenomena on Finite Inhomogeneous Networks (E Agliari and D Cassi); Effective Spectral Dimension in Scale-Free Networks (B Kahng et al.); First-Passage Statistics for Random Walks in Bounded Domains (R Voituriez and O Benichou); First-Passage Behavior of Multi-Dimensional Fractional Brownian Motion and Application to Reaction Phenomena (J-H Jeon et al.); Trajectory-to-Trajectory Fluctuations in First-Passage Phenomena in Bounded Domains (T G Mattos et al.); Exact Record and Order Statists of Random Walk via First-Passage Ideas (G Schehr and S Majumdar); First Passage in a Conical Geometry and Ordering of Brownian Particles (E Ben-Naim and P Krapivsky); First-Passage Time Problems in Biophysical Jump Processes with Fast Kinetics (Paul Bresslof and J Newby); First-Passage Problems in Biology (T Chou and M R D'Orsogna); The Effect of Detection Mechanisms on Spatial Search and Foraging (D Campos and V Mendez); Search in Random Media with Levy Flights (E Gelenbe and O H Abdelrahman); Exit Strategies: Visual Search and the Quitting Time Problem (T Horowitz); Statistical Physics of Evolutionary Trajectories on Fitness Landscapes (M Manhart and A Morozov); Some Applications of First-Passage Ideas to Finance (R Chicheportiche and J-P Bouchaud); First-Passage and Extremes in Socio-Economic Systems (J Masoliver and J Perello); Transport and the First-Passage Time Problem with Application to Cold Atoms in Optical Traps (E Barkai and D A Kessler); The Excursion Set Theory in Cosmology (M Maggiore and A Riotto); Self-Organized Escape Processes of Linear Chains in Nonlinear Potentials (L Schimanski-Geier et al.); Efficient Monte Carlo Methods for Simulating Diffusion-Reaction Processes in Complex Systems (D Grebenkov).

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Book SynopsisThis book is about a recently developed class of strategies, known as the fence methods, which fits particularly well in non-conventional and complex model selection problems with practical considerations. The idea involves a procedure to isolate a subgroup of what are known as correct models, of which the optimal model is a member. This is accomplished by constructing a statistical fence, or barrier, to carefully eliminate incorrect models. Once the fence is constructed, the optimal model is selected from amongst those within the fence according to a criterion which can be made flexible. In particular, the criterion of optimality can incorporate consideration of practical interest, thus making model selection a real life practice.Furthermore, this book introduces a data-driven approach, called adaptive fence, which can be used in a wide range of problems involving determination of tuning parameters, or constants. Instead of relying on asymptotic theory, the fence focuses on finite-sample performance, and computation. Such features are particularly suitable to statistics in the new era.

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Book SynopsisThis book contains original research papers by leading experts in the fields of probability theory, stochastic analysis, potential theory and mathematical physics. There is also a historical account on Masatoshi Fukushima's contribution to mathematics, as well as authoritative surveys on the state of the art in the field.

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Book SynopsisThis book contains a collection of research papers in mathematical finance covering recent advances in arbitrage, credit and asymmetric information risks. These subjects have attracted academic and practical attention, in particular after the international financial crisis. The volume is split into three parts which treat each of these topics.

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Book SynopsisThis is a unique book which explains the concept of probability and its applications with almost no mathematics. As the title states, the reader will discover the concept of probability, learn how to use it, and be made aware of some misuses of, and sometimes even abuse of, probability. The reader will come to know that a basic knowledge of probability is useful in life.It is a novel, self-teaching book that is easy to read, oftentimes entertaining and full of useful information on both probability and information theory. The style is reader-friendly. It will appeal to anyone who is interested in the “laws” that govern our daily lives.The detailed examples in the book are taken from daily life which anyone can identify with. The last section introduces the Shannon measure of information and its relationship to probabilities.Table of ContentsWhat is the Probability?; How Do We Calculate Probabilities?; The Axiomatic Approach to Probability; Independence and Dependence Between Events; Bayes' Theorem and Its Applications; Average, Variance and Random Variable; Probability Distributions; Shannon's Measure of Information;

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Book SynopsisThis is a unique book which explains the concept of probability and its applications with almost no mathematics. As the title states, the reader will discover the concept of probability, learn how to use it, and be made aware of some misuses of, and sometimes even abuse of, probability. The reader will come to know that a basic knowledge of probability is useful in life.It is a novel, self-teaching book that is easy to read, oftentimes entertaining and full of useful information on both probability and information theory. The style is reader-friendly. It will appeal to anyone who is interested in the “laws” that govern our daily lives.The detailed examples in the book are taken from daily life which anyone can identify with. The last section introduces the Shannon measure of information and its relationship to probabilities.Table of ContentsWhat is the Probability?; How Do We Calculate Probabilities?; The Axiomatic Approach to Probability; Independence and Dependence Between Events; Bayes' Theorem and Its Applications; Average, Variance and Random Variable; Probability Distributions; Shannon's Measure of Information;

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Book SynopsisThere are many books on lattice theory in the field, but none interfaces with the foundations of probability. This book does. It also develops new probability theories with rigorous foundations for decision theory and applies them to specific well-known problematic examples. There is only one other book that attempts this. It uses quantum probability theory from physics. The new probability theories developed in this book are different; they are not borrowed from physics but are explicitly designed for decision theory.Table of ContentsProbability Theory; Lattice Theory; Decision Theory; Intuitionistic Logic; Quantum Probability Theory; Cognitive Heurisitics;

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Book SynopsisThis book is an introduction to the mathematical analysis of probability theory and provides some understanding of how probability is used to model random phenomena of uncertainty, specifically in the context of finance theory and applications. The integrated coverage of both basic probability theory and finance theory makes this book useful reading for advanced undergraduate students or for first-year postgraduate students in a quantitative finance course.The book provides easy and quick access to the field of theoretical finance by linking the study of applied probability and its applications to finance theory all in one place. The coverage is carefully selected to include most of the key ideas in finance in the last 50 years.The book will also serve as a handy guide for applied mathematicians and probabilists to easily access the important topics in finance theory and economics. In addition, it will also be a handy book for financial economists to learn some of the more mathematical and rigorous techniques so their understanding of theory is more rigorous. It is a must read for advanced undergraduate and graduate students who wish to work in the quantitative finance area.Table of ContentsProbability Distributions; Conditional Probability; Laws of Probability; Theory of Risk and Utility; State Price and Risk-Neutral Probability; Single Period Asset Pricing Models; Stochastic Processes and Martingales; Brownian Motion and Technical Trading; Dynamic Programming and Multi-period Asset Pricing; Continuous-Time Optimization and Asset Pricing; Continuous-Time Option Pricing; Hedging and More Option Pricing; Implied Risk-Neutral Moments and Distributions; Theory of Markov Chains and Credit Markets; Interest Rate Modelling and Derivatives;

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Book SynopsisThe number of books on Nonparametric Methodology is quite small as compared to, say, on Design of Experiments, Regression Analysis, Multivariate Analysis, etc. Because of being perceived as less effective, nonparametric methods are still the second choice. Actually, it has been demonstrated time and again that they are useful. We feel that there is still need for proper texts/applications/reference books on Nonparametric Methodology.This book will introduce various types of data encountered in practice and suggest the appropriate nonparametric methods, discuss their properties through null and non-null distributions whenever possible and demonstrate the very minor loss in power and efficiency in the nonparametric method, if any.The book will cover almost all topics of current interest such as bootstrapping, ranked set sampling, techniques for censored data and Bayesian analysis under nonparametric set ups.Table of ContentsPrinciples of Statistical Inference; Order Statistics; Empirical Distribution Function; The Goodness of Fit Problem; Other One Sample Problems; Rank Tests and their Optimality; Two Sample Problems; Multisample Problems and Simultaneous Inference; Density Estimation; Nonparametric Regression and Classification; Proportional Hazards Regression; Appendix (Dealing with Pitman Efficiency, Asymptotic Distributions, etc);

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Book SynopsisThis book provides the limit theorems that can be used in the development of nonlinear cointegrating regression. The topics include weak convergence to a local time process, weak convergence to a mixture of normal distributions and weak convergence to stochastic integrals. This book also investigates estimation and inference theory in nonlinear cointegrating regression.The core context of this book comes from the author and his collaborator's current researches in past years, which is wide enough to cover the knowledge bases in nonlinear cointegrating regression. It may be used as a main reference book for future researchers.Table of ContentsConvergence to a Local Time Process; Convergence to a Mixture of Normal Distributions; Convergence to Stochastic Integrals; Nonlinear Cointegrating Regression;

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Book SynopsisThis book provides a systematic, self-sufficient and yet short presentation of the mainstream topics on introductory Probability Theory with some selected topics from Mathematical Statistics. It is suitable for a 10- to 14-week course for second- or third-year undergraduate students in Science, Mathematics, Statistics, Finance, or Economics, who have completed some introductory course in Calculus. There is a sufficient number of problems and solutions to cover weekly tutorials.Table of ContentsProbability; Random Variables; Joint Distributions; Variance and Covariance; Moment Generating Function; Analysis of Some Important Distributions; Limit Theorems; Statistical Inference: Point Estimation; Statistical Inference: Interval Estimation; Appendices: Solutions for the Problems for Weeks 1-12; Sample Problems for Final Exams; Some Bonus Challenging Problems; Statistical Tables;

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Book SynopsisChange of Time and Change of Measure provides a comprehensive account of two topics that are of particular significance in both theoretical and applied stochastics: random change of time and change of probability law.Random change of time is key to understanding the nature of various stochastic processes, and gives rise to interesting mathematical results and insights of importance for the modeling and interpretation of empirically observed dynamic processes. Change of probability law is a technique for solving central questions in mathematical finance, and also has a considerable role in insurance mathematics, large deviation theory, and other fields.The book comprehensively collects and integrates results from a number of scattered sources in the literature and discusses the importance of the results relative to the existing literature, particularly with regard to mathematical finance.In this Second Edition a Chapter 13 entitled 'A Wider View' has been added. This outlines some of the developments that have taken place in the area of Change of Time and Change of Measure since the publication of the First Edition. Most of these developments have their root in the study of the Statistical Theory of Turbulence rather than in Financial Mathematics and Econometrics, and they form part of the new research area termed 'Ambit Stochastics'.Table of ContentsRandom Change of Time; Integral Representations and Change of Time in Stochastic Integrals; Semimartingales: Basic Notions, Structures, Elements of Stochastic Analysis; Stochastic Exponential and Stochastic Logarithm. Cumulant Processes; Processes with Independent Increments. Levy Processes; Change of Measure. General Facts; Change of Measure in Models Based on Levy Processes; Change of Time in Semimartingale Models and Models Based on Brownian Motion and Levy Processes; Conditionally Gaussian Distributions and Stochastic Volatility Models for the Discrete-time Case; Martingale Measures in the Stochastic Theory of Arbitrage; Change of Measure in Option Pricing; Conditionally Brownian and Levy Processes. Stochastic Volatility Models; A Wider View. Ambit Processes and Fields, and Volatility/Intermittency;

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Book SynopsisThis volume contains original and refereed contributions from the tenth AMCTM Conference (www.nviim.ru/AMCTM2014) held in St. Petersburg (Russia) in September 2014 on the theme of advanced mathematical and computational tools in metrology and testing.The themes in this volume reflect the importance of the mathematical, statistical and numerical tools and techniques in metrology and testing and, also keeping the challenge promoted by the Metre Convention, to access a mutual recognition for the measurement standards.Table of ContentsFostering Diversity of Thought in Measurement Science (F Pavese and P De Bievre); Polynomial Calibration Functions Revisited: Numerical and Statistical Issues (M G Cox and P Harris); Empirical Functions with Pre-Assigned Correlation Behaviour (A B Forbes); Models and Methods of Dynamic Measurements: Results Presented by St. Petersburg Metrologists (V A Granovskii); Interval Computations and Interval-Related Statistical Techniques: Estimating Uncertainty of the Results of Data Processing and Indirect Measurements (V Ya Kreinovich); Classification, Modeling and Quantification of Human Errors in Chemical Analysis (I Kuselman); Application of Nonparametric Goodness-of-Fit Tests: Problems and Solution (B Yu Lemeshko); Dynamic Measurements Based on Automatic Control Theory Approach (A L Shestakov); Models for the Treatment of Apparently Inconsistent Data (R Willink); Model for Emotion Measurements in Acoustic Signals and Its Analysis (Y Baksheeva, K Sapozhnikova and R Taymanov); Uncertainty Calculation in Gravimetric Microflow Measurements (E Batista, N Almeida, I Godinho and E Filipe); Uncertainties Propagation from Published Experimental Data to Uncertainties of Model Parameters Adjusted by the Least Squares (V I Belousov, V V Ezhela, Y V Kuyanov, S B Lugovsky, K S Lugovsky and N P Tkachenko); A New Approach for the Mathematical Alignment Machine Tool-Paths on a Five-Axis Machine and Its Effect on Surface Roughness (S Boukebbab, J Chaves-Jacob, J-M Linares and N Azzam); Goodness-of-Fit Tests for One-Shot Device Testing Data (E V Chimitova and N Balakrishan); Calculation of Coverage Intervals: Some Study Cases (A Stepanov, A Chunovkina and N Burmistrova); Application of Numerical Methods in Metrology of Electromagnetic Quantities (M Cundeva-Blajer); Calibration Method of Measuring Instruments in Operating Conditions (A A Danilov, Yu V Kucherenko, M V Berzhinskaya, N P Ordinartseva); Statistical Methods for Conformity Assessment When Dealing with Computationally Expensive Systems: Application to a Fire Engineering Case Study (S Demeyer, N Fischer, F Didieux and M Binacchi); Overview of EMRP Joint Reserch Project NEW06 "Traceability for Computationally-Intensive Metrology" (A B Forbes, I M Smith, F Hartig and K Wendt); Stable Units of Account for Economic Value Correct Measuring (N Hovanov); A Novel Approach for Uncertainty Evaluation Using Characteristic Function Theory (A B Ionov, N S Chernysheva and B P Ionov); Estimation of Test Uncertainty for TraCIM Reference Pairs (F Keller, K Wendt and F Hartig); Approaches for Assigning Numerical Uncertainty to Reference Data Pairs for Software Validation (G J P Kok and I M Smith); Uncertainty Evaluation for a Computationally Expensive Model of a Sonic Nozzle (G J P Kok and N Pelevic); EllipseFit4HC: A MATLAB Algorithm for Demodulation and Uncertainty Evaluation of the Quadrature Interferometer Signals (R Koning, G Wimmer and V Witkovsky); Considerations on the Influence of Test Equipment Instability and Calibration Methods on Measurement Uncertainty of the Test Laboratory (A S Krivov, S V Marinko and I G Boyko); A Cartesian Method to Improve the Results and Save Computation Time in Bayesian Signal Analysis (G A Kyriazis); The Definition of the Reliability of Identification of Complex Organic Compounds Using HPLC and Base Chromatographic and Spectral Data (E V Kulyabina and Yu A Kudeyarov); Uncertainty Evaluation of Fluid Dynamic Simulation with One-Dimensional Riser Model by Means of Stochastic Differential Equations (E A O Lima, S B Melo, C C Dantas, F A S Teles and S Soares Bandiera); Simulation Method to Estimate the Uncertainties of ISO Specifications (J-M Linares and J M Sprauel); Adding a Virtual Layer in a Sensor Network to Improve Measurement Reliability (U Maniscalco and R Rizzo); Calibration Analysis of a Computational Optical System Applied in the Dimensional Monitoring of a Suspension Bridge (L L Martins, J M Rebordao and A S Ribeiro); Determination of Numerical Uncertainty Associated with Numerical Artefacts for Validating Coordinate Metrology Software (H D Minh, I M Smith and A B Forbes); Least-Squares Method and Type B Evaluation of Standard Uncertainty (R Palencar, S Duris, P Pavlasek, M Dovica, S Slosarcik and G Wimmer); Optimising Measurement Processes Using Automated Planning (S Parkinson, A Crampton and A P Longstaff); Software Tool for Conversion of Historical Temperature Scales (P Pavlasek, S Duris, R Palencar and A Merlone); Few Measurements, Non-Normality: A Statement on the Expanded Uncertainty (J Petry, B De Boeck, M Dobre and A Peruzzi); Quantifying Uncertainty in Accelerometer Sensitivity Studies (A L Rukhin and D J Evans); Metrological Aspects of Stopping Iterative Procedures in Inverse Problems for Static-Mode Measurements (K K Semenov); Inverse Problems in Theory and Practice of Measurements and Metrology (K K Semenov, G N Solopchenko and V Ya Kreinovich); Fuzzy Intervals as Foundation of Metrological Support for Computations with Inaccurate Data (K K Semenov, G N Solopchenko and V Ya Kreinovich); Testing Statistical Hypotheses for Generalized Semiparametric Proportional Hazards Models with Cross-Effect of Survival Functions (M A Semenova and E V Chimitova); Novel Reference Value and DOE Determination by Model Selection and Posterior Predictive Checking (K Shirono, H Tanaka, M Shiro and K Ehara); Certification of Algorithms for Constructing Calibration Curves of Measuring Instruments (T Siraya); Discrete and Fuzzy Encoding of the ECG-Signal for Multidisease Diagnostic System (V Uspenskiy, K Vorontsov, V Tselykh and V Bunakov); Application of Two Robust Methods in Inter-Laboratory Comparisons with Small Samples (E T Volodarsky and Z L Warsza); Validation of CMM Evaluation Software Using TraCIM (K Wendt, M Franke and F Hartig); Semi-Parametric Polynomial Method for Retrospective Estimation of the Change-Point of Parameters of Non-Gaussian Sequences (S V Zabolotnii and Z L Warsza); Use of a Bayesian Approach to Improve Uncertainty of Model-Based Measurements by Hybrid Multi-Tool Metrology (N-F Zhang, B M Barnes, R M Silver and H Zhou); Application of Effective Number of Observations and Effective Degrees of Freedom for Analysis of Autocorrelated Observations (A Zieba);

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Book Synopsis'Overall, the book is highly technical, including full mathematical proofs of the results stated. Potential readers are post-graduate students or researchers in Quantitative Risk Management willing to have a manual with the state-of-the-art on portfolio diversification and risk aggregation with heavy tails, including the fundamental theorems as well as collateral (but most useful) results on majorization and copula theory.'Quantitative Finance This book offers a unified approach to the study of crises, large fluctuations, dependence and contagion effects in economics and finance. It covers important topics in statistical modeling and estimation, which combine the notions of copulas and heavy tails — two particularly valuable tools of today's research in economics, finance, econometrics and other fields — in order to provide a new way of thinking about such vital problems as diversification of risk and propagation of crises through financial markets due to contagion phenomena, among others. The aim is to arm today's economists with a toolbox suited for analyzing multivariate data with many outliers and with arbitrary dependence patterns. The methods and topics discussed and used in the book include, in particular, majorization theory, heavy-tailed distributions and copula functions — all applied to study robustness of economic, financial and statistical models, and estimation methods to heavy tails and dependence.

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Book SynopsisManagers need access to some statistical advice from time to time to help in solving business problems. Students need access to statistical methods to support work in non-statistics courses, case studies and projects. What is needed will depend on the demands of the problem and how much statistics the manager or student already knows. The requirement is for flexible decision support.This unique book presents statistical ideas and models in easily accessible form describing both methods and issues of application.statsNotes are organized as a set of over one hundred notes rather than as a number of chapters. This enables managers and students to locate just what they need for the problem they have. Each note consists of a description of what to do, an example, the rationale, links to other notes.Managers and students can choose to use as many notes as necessary, which might be just one note or a set of linked notes.Deciding which method will be helpful depends not just on finding an appropriate statistical method but on the business context too. statsNotes provide advice at three levels: While the range of topics covered is similar to those in introductory textbooks and courses, the focus is on management decision and the methods for dealing with risky decisions and management judgment in this book are usually found in more specialist texts.Table of ContentsData Description; Probability and Probability Models for Data and Judgement; Evidence and Bayes' Rule; Risk and Uncertainty; Using Sample Data for Estimating Means, Proportions, Variances and Differences; Monitoring; Significance Testing; Correlation and Simple Regression; Illustrative Applications in Production and Operations and in Finance;

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Book SynopsisThis book is meant for postgraduate modules that cover lifetime data in reliability and survival analysis as taught in statistics, engineering statistics and medical statistics courses. It is helpful for researchers who wish to choose appropriate models and methods for analyzing lifetime data. There is an extensive discussion on the concept and role of ageing in choosing appropriate models for lifetime data, with a special emphasis on tests of exponentiality. There are interesting contributions related to the topics of ageing, tests for exponentiality, competing risks and repairable systems. A special feature of this book is that it introduces the public domain R-software and explains how it can be used in computations of methods discussed in the book.This new edition includes new sections on Frailty Models and Accelerated Life Time Models. Many more illustrations and exercises are also included.

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Book SynopsisMixed-effects models have found broad applications in various fields. As a result, the interest in learning and using these models is rapidly growing. On the other hand, some of these models, such as the linear mixed models and generalized linear mixed models, are highly parametric, involving distributional assumptions that may not be satisfied in real-life problems. Therefore, it is important, from a practical standpoint, that the methods of inference about these models are robust to violation of model assumptions. Fortunately, there is a full scale of methods currently available that are robust in certain aspects. Learning about these methods is essential for the practice of mixed-effects models.This research monograph provides a comprehensive account of methods of mixed model analysis that are robust in various aspects, such as to violation of model assumptions, or to outliers. It is suitable as a reference book for a practitioner who uses the mixed-effects models, and a researcher who studies these models. It can also be treated as a graduate text for a course on mixed-effects models and their applications.Table of ContentsIntroduction; Generalized Estimating Equations; Non-Gaussian Linear Mixed Models; Robust Tests; Observed Best Prediction; Model Selection; Resampling Methods; Semi-Parametric and Non-Parametric Mixed Models; Quantile and Rank-Based Inference;

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Book SynopsisCrafts of Simulation Programs is a collection of tools, techniques and theories required to develop and implement simulation models on a computer. This timely book provides the various skills and techniques needed in simulation programming with general-purpose languages. The topics range in difficulty, and several latest fields in simulation output analysis are covered such as samples sizes, order statistics, ranking and selection, comparison with a control, selection with constraints, etc.Presented in the format of research project reports, detailed descriptions, important concepts and techniques are introduced and developed. Each chapter is relatively self-contained and can be used as a study unit. Algorithms have detailed implementations in C and are readable by anyone who has done a little programming. Many chapters include simulation results. It is designed to impart to the readers the statistical techniques used in simulation. This book will prove to be invaluable not only to students and researchers in the fields of simulation programming, but also to teachers of this subject who will find this text useful as a supplement.Table of ContentsUniform Random Numbers, Random Variates, and Some Utilities; Sample Sizes and Stopping Rules; Manufacturing Independent and Identically Distributed Batch Means; Order Statistics and How They are be Applied in Simulation; Order Statistics from Correlated Normal Random Variables; Estimating Multiple Quantiles via Empirical Histograms; Construction of Metamodels; Estimating Density; Comparing Two Normal Populations; Ranking and Selection Procedures and Multiple Comparisons; Indifference-Zone Selection Procedures and Optimal Computation Allocation Strategy; Insights of Using Common Random Numbers with Selection Procedures; Parallel and Distributed Simulation; Multiple-Objective Selection; Generic Selection-with-Constraints;

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Book SynopsisThe inclusion of qualitative social data into global environmental and economic input-output (IO) models remained illusive for many years. It was not until around 2013 that researchers found ways to include data, for example, on poverty, inequality, and worker safety, into IO models capable of tracing global supply chains. The sustainable development goals have now propelled this work onto the world stage with some urgency. They have shone a spotlight onto social conditions around the world and brought global trade into the frame for its ability to influence social conditions for good or ill.This book provides a compilation of groundbreaking work on social indicators from the most prominent IO research groups from a wide range of academic backgrounds and from around the world. In addition, it frames this work in the real world of politics, human rights, and business, bringing together a multidisciplinary team to demonstrate the power of IO to illuminate some of the world’s most pressing problems. Edited by well-known researchers in the area, Joy Murray, Arunima Malik, and Arne Geschke, the book is designed to appeal to a broad academic and business audience. While many chapters include technical details and references for follow-up reading, it is possible to omit those sections and yet gain a deep appreciation of the power of IO to address seemingly intractable problems. Trade ReviewGlobal trade is a double-edged sword. It not only helps alleviate poverty and opens new market opportunities but also accelerates the exploitation and unequal use of natural resources and social capital. An ever-growing net of complex, global supply chains increases the distance between producers and consumers, diluting any sense of connectedness or responsibility. This book expertly pieces together a puzzle of global economic activity and explains how trade creates and reinforces detrimental social impacts and affects our social capital. It provides unprecedented insights into how and where our social capital is affected by trade. Written by academics and practitioners and covering a wide range of often underrepresented topics, this book is a milestone in uncovering the true social effects of global trade.Dr. Thomas WiedmannSchool of Civil and Environmental Engineering, University of New South Wales, SydneyThis important book informs readers how to quantify attributes of specific supply chains and the corresponding ‘footprints’. A crucial innovation is that it supplements the familiar economic and environmental footprints by creating social footprints, exemplified in a set of case studies that reveal instances of human rights offenses, corruption and abuse of workers. Consumers’ growing acceptance of responsibility for social consequences of their purchases makes this volume vital reading for policy makers and business leaders wanting to make public the problems they have identified, and remedied, in their supply chains. The book opens by situating trade within the wider context of neo-liberal capitalism, and it ends with examples of successful business initiatives, some voluntary and others for compliance with regulations, to eliminate problematic links in their global supply chains.Faye DuchinRensselaer Polytechnic Institute, Troy, USATable of ContentsGlobal trade in an era of neoliberal capitalism: Origins, context and implications. Regulating human rights and responsibilities in global supply chains. Calculating the cost of trade. Human rights due diligence and the Social Hotspots Database. Corruption embodied in international trade. Social footprints of nations: a look at welfare. Employment flows from and into the Arab region: A case study to measure the embodied employment in 2010. The distribution of labor and wages embodied in European consumption. Assessing the structure and social effects of China’s provincial labour landscape. Fairness and globalization in the Western European clothing supply chain. Income effects in global value chains driven by EU exports. Global trade, pollution and mortality. Sustainable supply chain solutions.

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Book SynopsisThis is an essential textbook for senior undergraduate and graduate students of statistics, stochastic processes, stochastic finance, and probability theory. It thoroughly discusses the concepts of stochastic processes, both Markov and non-Markov processes, as well as stochastic calculus.

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Book Synopsis1 Why R is essential? What are the prospects by learning R?.- 2 An overview of statistical analysis plan for clinical studies.- 3 Introduction to R environment and basic commands.- 4 Data handling and manipulation in R with Descriptive Statistics.- 5 Introduction to packages in R installation, loading, unloading and deletion.- 6 Visualisation of data basic and advanced.- 7 Inferential statistics for the hypothesis testing of parametrically distributed data.- 8 Inferential statistics for the hypothesis testing of  non-parametric data.- 9 Computation of sample size for clinical studies.- 10 Correlation and linear regression analysis for continuous outcome.- 11 Logistic regression analysis for categorical outcome.- 12 Receiver Operating Characteristic (ROC) curve analysis for diagnostic studies.- 13 Survival analysis for time to event-based outcome.- 14 Conducting randomization in clinical trials.- 15 Development of web-based interactive servers using R shiny package.

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