Probability and statistics Books
McGraw-Hill Education Loose Leaf for Elementary Statistics A Step by
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£139.39
McGraw-Hill Education Aleks 360 11 Weeks Access Card for Elementary
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£94.83
McGraw-Hill Education Aleks 360 18 Weeks Access Card for Elementary
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£126.97
McGraw-Hill Education Aleks 360 52 Weeks Access Card for Elementary
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£175.64
McGraw-Hill Education Aleks 360 Access Card 18 Weeks for Elementary
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£117.56
McGraw-Hill Education Aleks 360 Access Card 52 Weeks for Elementary
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£163.80
McGraw-Hill Education Aleks 360 Access Card 18 Weeks for Math in Our
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£126.97
McGraw-Hill Education Aleks 360 Access Card 52 Weeks for Math in Our
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£175.63
McGraw-Hill Education Principles of Statistics for Engineers
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£164.00
McGraw-Hill Education Loose Leaf for Essential Statistics
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£116.78
McGraw-Hill Companies Loose Leaf Version for Elementary Statistics
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£106.20
W. H. Freeman The Analysis of Biological Data
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£283.58
Cengage Learning, Inc Introduction to Probability and Statistics
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£238.40
Cengage Learning, Inc PreStatistics
Book SynopsisPRESTATISTICS gives you the skills you need to be successful in statistics, whether you are just out of high school or haven't taken a mathematics course in years. Each section in PRESTATISTICS concludes with a paragraph titled "Why We Learned It" that shows you the connection between the topics learned in that section and statistics--and how it will be helpful to you in an introductory statistics course. Nine hundred videos including lectures, example solutions and quick-check exercise walkthroughs enable you to learn the way you want to learn, and WebAssign--a flexible and fully customizable online solution available with this text--empowers you to prepare for class with confidenceTable of Contents1. Arithmetic Operations used in Statistics. Rounding Numbers. Types of Numbers and the Number Line. Fractions, Decimals and Percentages. Operations with Fractions. Absolute, Relative and Percent Error. Scientific Notation and E-Notation. Read and Use Mathematical Tables. 2. Algebraic Expressions used in Statistics and Basics of Solving Equations. Translating English into Algebra: Expressions, Equations and Inequalities. Order of Operations and Evaluating Numerical Expressions. Basics of Solving Linear Equations. 3. Equations, Inequalities and Problem-Solving Techniques. Solving Equations used in Statistics. Inequalities, Interval Notation and Plus/Minus Notation. Solving Absolute Value Inequalities. Introduction to Problem Solving. Literal Equations. 4. Graphing Linear Equations in Two Variables. Properties of Rectangular Coordinate System. Interpretation of Graphs. Graphing Linear Equations. Slope and Marginal Change. Equations of Lines in Statistics. 5. Sets, Counting and Sums. Fundamentals of Sets. Cardinality of Sets. Principles of Counting. Writing and Computing Sums. 6. Functions and Area Under Functions. Introduction to Functions. Linear and Piecewise Defined Functions. Area Under a Constant Function. Area Under a Linear Function. 7. Survey of Functions used in Statistics. Exponential and Logarithmic Functions. Rational Exponent and Power Functions. Multivariable Linear Functions.
£165.96
Wiley Statistics
£119.08
Johns Hopkins University Press Sandlot Stats
Book SynopsisExplains the mathematical underpinnings of baseball so that students can understand the world of statistics and probability. This book teaches fundamentals of probability and statistics through the feats of baseball legends such as Hank Aaron, Joe DiMaggio, and Ted Williams and more recent players Barry Bonds, Albert Pujols, and Alex Rodriguez.Trade ReviewSandlot Stats served as an instrumental and informative piece to the Baseball Statistics course. The amount of time and tedious effort put into the project is evident, as this book is absolutely packed with information. The book puts a new spin on mathematics, and makes it more understandable for even the most casual of baseball fans. Baseball purists and sabermetric geeks alike will love this book. -- Jon Alba Sports Paws Dr. Rothman has hit a 'home run.' Sandlot Stats: Learning Statistics with Baseball is not only a fine book to read, but a text which can also serve as an excellent resource book. -- Father Gabe Costa CBS New York For those interested in this subject-this is your book. -- Harvey Frommer Epoch Times If this had been the textbook for a basic statistics course that I took as a student, I might have remembered that course forever as the best class I ever had. -- Charles Ashbacher MAA Reviews Sandlot Stats is a readable and resourceful introductory textbook for statistics. -- Graham Wheeler Significance The book is very readable and well organized... High school statistics teachers could use this book as a course supplement or an enrichment source for sports-crazy students. Any college professor teaching a sports statistics course or looking for ways to enliven a traditional course would also find it interesting. Even baseball fans wanting to learn more about descriptive measures used in the game could benefit from Rothman's interesting exposition. -- Marc Michael Mathematics TeacherTable of ContentsAcknowledgmentsList of AbbreviationsIntroduction1. Basic Statistical Definitions2. Descriptive Statistics for One Quantitative Variable3. Descriptive Measures Used in Baseball4. Comparing Two Quantitative Data Sets5. Linear Regression and Correlation Analysis for Two Quantitative Variables6. Descriptive Statistics Applied to Qualitative Variables7. Probability8. Sports Betting9. Baseball and Traditional Descriptive Measures10. Final Comparison of Batting Performance between Aaron and Bonds11. Probability Distribution Functions for a Discrete Random Variable12. Probability Density Functions for a Continuous Variable13. Sampling Distributions14. Confidence Intervals15. Hypothesis Testing for One Population16. Streaking17. Mission Impossible: Batting .400 for a Season18. PostseasonAppendix A: Hypothesis Testing for Two Population ProportionsAppendix B: The Chi-Square DistributionAppendix C: Statistical TablesIndex
£76.50
Kendall/Hunt Publishing Co ,U.S. Understanding Statistics: Activities and Exercises for a First Statistics Course
£43.16
Basic Books How to Expect the Unexpected: The Science of
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£26.00
Rowman & Littlefield Applied Statistics in Occupational Safety and
Book SynopsisThis completely updated fourth edition is designed to provide safety professionals or those studying to become safety professionals with the basic methods and principles necessary to apply statistics properly. Safety professionals often encounter statistics in the literature they read and are required to present findings or make decisions based on data analyses. Statistics can be used to justify the implementation of a program, identify areas that need to be addressed, or justify the impact that various safety programs have on losses and accidents. Safety professionals also use a variety of data in their day-to-day work.Applied Statistics in Occupational Safety and Health presents the reader with practical information to make their job easier. In addition to sample problems and solutions, the authors include easy-to-read charts and tables, appendices containing statistical tables, and a glossary of terms.
£81.00
ISTE Ltd and John Wiley & Sons Inc Stochastic Risk Analysis and Management
Book SynopsisThe author investigates the Cramer –Lundberg model, collecting the most interesting theorems and methods, which estimate probability of default for a company of insurance business. These offer different kinds of approximate values for probability of default on the base of normal and diffusion approach and some special asymptotic.Table of ContentsChapter 1. Mathematical Bases 1 1.1. Introduction to stochastic risk analysis 1 1.1.1. About the subject 1 1.1.2. About the ruin model 2 1.2. Basic methods 4 1.2.1. Some concepts of probability theory 4 1.2.2. Markov processes 14 1.2.3. Poisson process 18 1.2.4. Gamma process 21 1.2.5. Inverse gamma process 23 1.2.6. Renewal process 24 Chapter 2. Cramér-Lundberg Model 29 2.1. Infinite horizon 29 2.1.1. Initial probability space 29 2.1.2. Dynamics of a homogeneous insurance company portfolio 30 2.1.3. Ruin time 33 2.1.4. Parameters of the gain process 33 2.1.5. Safety loading 35 2.1.6. Pollaczek-Khinchin formula 36 2.1.7. Sub-probability distribution G+ 38 2.1.8. Consequences from the Pollaczek-Khinchin formula 41 2.1.9. Adjustment coefficient of Lundberg 44 2.1.10. Lundberg inequality 45 2.1.11. Cramér asymptotics 46 2.2. Finite horizon 49 2.2.1. Change of measure 49 2.2.2. Theorem of Gerber 54 2.2.3. Change of measure with parameter gamma 56 2.2.4. Exponential distribution of claim size 57 2.2.5. Normal approximation 64 2.2.6. Diffusion approximation 68 2.2.7. The first exit time for the Wiener process 70 Chapter 3. Models With the Premium Dependent on the Capital 77 3.1. Definitions and examples 77 3.1.1. General properties 78 3.1.2. Accumulation process 81 3.1.3. Two levels 86 3.1.4. Interest rate 90 3.1.5. Shift on space 91 3.1.6. Discounted process 92 3.1.7. Local factor of Lundberg 98 Chapter 4. Heavy Tails 107 4.1. Problem of heavy tails 107 4.1.1. Tail of distribution 107 4.1.2. Subexponential distribution 109 4.1.3. Cramér-Lundberg process 117 4.1.4. Examples 120 4.2. Integro-differential equation 124 Chapter 5. Some Problems of Control 129 5.1. Estimation of probability of ruin on a finite interval 129 5.2. Probability of the credit contract realization 130 5.2.1. Dynamics of the diffusion-type capital 132 5.3. Choosing the moment at which insurance begins 135 5.3.1. Model of voluntary individual insurance 135 5.3.2. Non-decreasing continuous semi-Markov process 139 Bibliography 147 Index 149
£125.06
Atlantic Books Numb and Number: How to Avoid Being Mystified by
Book Synopsis'A wise, witty and insightful guide to clear thinking amid a deluge of percentages and probabilities.' Ian StewartLike it or not, our lives are dominated by mathematics. Our daily diet of news regales us with statistical forecasts, opinion polls, risk assessments, inflation figures, weather and climate predictions and all sorts of political decisions and advice backed up by supposedly accurate numbers. Most of us do not even pause and question such figures even to ask what they really mean and whether they raise more questions than they answer. In this simple guide for anyone numbed by numbers, William Hartston reveals with clarity and humour why the figures being flung at us may not tell the whole story. Along the way he explains commonly misused mathematical terms, solves everyday mathematical problems and shows how to steer a safe path through the minefield of mathematics that surrounds us.Trade ReviewIf you're not one of the lucky few who can say, "Oh, mathematics was my best subject at school," then you might find yourself stumped by the news, or personal finance, or chaos and catastrophe (yes, William Hartston shows us there's maths involved there, too). Luckily, Numb and Number is able to explain these things and more, in a way that's easy to understand and even enjoyable to read. * BBC Science Focus *A wise, witty, and insightful guide to clear thinking amid a deluge of percentages and probabilities. Learn to spot the fake formulas and the spurious statistics. Up to 100% of readers will find this book utterly fascinating. Recommended by 92.53% of mathematicians. -- Ian Stewart, author of Do Dice Play God?Table of Contents1: The Number of Our Days 2: Surveying the Scene 3: Risk and Behaviour 4: The Mathematics of Sport 5: Saved You! 6: Numbers Large and Small 7: The Insignificance of Significance 8: Cause and Effect 9: Percentages and More Misleading Mathematics 10: Chaotic Butterflies 11: Torpedoes, Toilets and True Love 12: Formula Milking 13: Monkey Maths 14: Pandemic Pandemonium
£15.80
ISTE Ltd and John Wiley & Sons Inc Mathematical Methods in Survival Analysis,
Book SynopsisReliability and survival analysis are important applications of stochastic mathematics (probability, statistics and stochastic processes) that are usually covered separately in spite of the similarity of the involved mathematical theory. This title aims to redress this situation: it includes 21 chapters divided into four parts: Survival analysis, Reliability, Quality of life, and Related topics. Many of these chapters were presented at the European Seminar on Mathematical Methods for Survival Analysis, Reliability and Quality of Life in 2006.Table of ContentsPreface 13 PART I 15 Chapter 1. Model Selection for Additive Regression in the Presence of Right-Censoring 17 Elodie BRUNEL and Fabienne COMTE 1.1. Introduction 17 1.2. Assumptions on the model and the collection of approximation spaces 18 1.2.1. Non-parametric regression model with censored data 18 1.2.2. Description of the approximation spaces in the univariate case 19 1.2.3. The particular multivariate setting of additive models 20 1.3. The estimation method 20 1.3.1. Transformation of the data 20 1.3.2. The mean-square contrast 21 1.4. Main result for the adaptive mean-square estimator 22 1.5. Practical implementation 23 1.5.1. The algorithm 23 1.5.2. Univariate examples 24 1.5.3. Bivariate examples 27 1.5.4. A trivariate example 28 1.6. Bibliography 30 Chapter 2. Non-parametric Estimation of Conditional Probabilities, Means and Quantiles under Bias Sampling 33 Odile PONS 2.1. Introduction 33 2.2. Non-parametric estimation of p 34 2.3. Bias depending on the value of Y 35 2.4. Bias due to truncation on X 37 2.5. Truncation of a response variable in a non-parametric regression model 37 2.6. Double censoring of a response variable in a non-parametric model 42 2.7. Other truncation and censoring of Y in a non-parametric model 44 2.8. Observation by interval 47 2.9. Bibliography 48 Chapter 3. Inference in Transformation Models for Arbitrarily Censored and Truncated Data 49 Filia VONTA and Catherine HUBER 3.1. Introduction 49 3.2. Non-parametric estimation of the survival function S 50 3.3. Semi-parametric estimation of the survival function S 51 3.4. Simulations 54 3.5. Bibliography 59 Chapter 4. Introduction of Within-area Risk Factor Distribution in Ecological Poisson Models 61 Lea FORTUNATO, Chantal GUIHENNEUC-JOUYAUX, Dominique LAURIER,Margot TIRMARCHE, Jacqueline CLAVEL and Denis HEMON 4.1. Introduction 61 4.2. Modeling framework 62 4.2.1. Aggregated model 62 4.2.2. Prior distributions 65 4.3. Simulation framework 65 4.4. Results 66 4.4.1. Strong association between relative risk and risk factor, correlated within-area means and variances (mean-dependent case) 67 4.4.2. Sensitivity to within-area distribution of the risk factor 68 4.4.3. Application: leukemia and indoor radon exposure 69 4.5. Discussion 71 4.6. Bibliography 72 Chapter 5. Semi-Markov Processes and Usefulness in Medicine 75 Eve MATHIEU-DUPAS, Claudine GRAS-AYGON and Jean-Pierre DAURES 5.1. Introduction 75 5.2. Methods 76 5.2.1. Model description and notation 76 5.2.2. Construction of health indicators 79 5.3. An application to HIV control 82 5.3.1. Context 82 5.3.2. Estimation method 82 5.3.3. Results: new indicators of health state 84 5.4. An application to breast cancer 86 5.4.1. Context 86 5.4.2. Age and stage-specific prevalence 87 5.4.3. Estimation method 88 5.4.4. Results: indicators of public health 88 5.5. Discussion 89 5.6. Bibliography 89 Chapter 6. Bivariate Cox Models 93 Michel BRONIATOWSKI, Alexandre DEPIRE and Ya’acov RITOV 6.1. Introduction 93 6.2. A dependence model for duration data 93 6.3. Some useful facts in bivariate dependence 95 6.4. Coherence 98 6.5. Covariates and estimation 102 6.6. Application: regression of Spearman’s rho on covariates 104 6.7. Bibliography 106 Chapter 7. Non-parametric Estimation of a Class of Survival Functionals 109 Belkacem ABDOUS 7.1. Introduction 109 7.2. Weighted local polynomial estimates 111 7.3. Consistency of local polynomial fitting estimators 114 7.4. Automatic selection of the smoothing parameter 116 7.5. Bibliography 119 Chapter 8. Approximate Likelihood in Survival Models 121 Henning LAUTER 8.1. Introduction 121 8.2. Likelihood in proportional hazard models 122 8.3. Likelihood in parametric models 122 8.4. Profile likelihood 123 8.4.1. Smoothness classes 124 8.4.2. Approximate likelihood function 125 8.5. Statistical arguments 127 8.6. Bibliography 129 PART II 131 Chapter 9.Cox Regression with Missing Values of a Covariate having a Non-proportional Effect on Risk of Failure 133 Jean-Francois DUPUY and Eve LECONTE 9.1. Introduction 133 9.2. Estimation in the Cox model with missing covariate values: a short review 136 9.3. Estimation procedure in the stratified Cox model with missing stratum indicator values 139 9.4. Asymptotic theory 141 9.5. A simulation study 145 9.6. Discussion 147 9.7. Bibliography 149 Chapter 10.Exact Bayesian Variable Sampling Plans for Exponential Distribution under Type-I Censoring 151 Chien-Tai LIN, Yen-Lung HUANG and N. BALAKRISHNAN 10.1. Introduction 151 10.2. Proposed sampling plan and Bayes risk 152 10.3. Numerical examples and comparison 156 10.4. Bibliography 161 Chapter 11. Reliability of Stochastic Dynamical Systems Applied to Fatigue Crack Growth Modeling 163 Julien CHIQUET and Nikolaos LIMNIOS 11.1. Introduction 163 11.2. Stochastic dynamical systems with jump Markov process 165 11.3. Estimation 168 11.4. Numerical application 170 11.5. Conclusion 175 11.6. Bibliography 175 Chapter 12. Statistical Analysis of a Redundant System with One Standby Unit 179 Vilijandas BAGDONAVIC¡ IUS, Inga MASIULAITYTE and Mikhail NIKULIN 12.1. Introduction 179 12.2. The models 180 12.3. The tests 181 12.4. Limit distribution of the test statistics 182 12.5. Bibliography 187 Chapter 13.A Modified Chi-squared Goodness-of-fit Test for the ThreeparameterWeibull Distribution and its Applications in Reliability 189 Vassilly VOINOV, Roza ALLOYAROVA and Natalie PYA 13.1. Introduction 189 13.2. Parameter estimation and modified chi-squared tests 191 13.3. Power estimation 194 13.4. Neyman-Pearson classes 194 13.5. Discussion 197 13.6. Conclusion 198 13.7. Appendix 198 13.8. Bibliography 201 Chapter 14.Accelerated Life Testing when the Hazard Rate Function has Cup Shape 203 Vilijandas BAGDONAVIC¡ IUS, Luc CLERJAUD and Mikhail NIKULIN 14.1. Introduction 203 14.2. Estimation in the AFT-GW model 204 14.2.1. AFT model 204 14.2.2. AFT-Weibull, AFT-lognormal and AFT-GW models 205 14.2.3. Plans of ALT experiments 205 14.2.4. Parameter estimation: AFT-GW model 206 14.3. Properties of estimators: simulation results for the AFT-GW model 207 14.4. Some remarks on the second plan of experiments 211 14.5. Conclusion 213 14.6. Appendix 213 14.7. Bibliography 215 Chapter 15. Point Processes in Software Reliability 217 James LEDOUX 15.1. Introduction 217 15.2. Basic concepts for repairable systems 219 15.3. Self-exciting point processes and black-box models 221 15.4. White-box models and Markovian arrival processes 225 15.4.1. A Markovian arrival model 226 15.4.2. Parameter estimation 228 15.4.3. Reliability growth 232 15.5. Bibliography 234 PART III 237 Chapter 16. Likelihood Inference for the Latent Markov Rasch Model 239 Francesco BARTOLUCCI, Fulvia PENNONI and Monia LUPPARELLI 16.1. Introduction 239 16.2. Latent class Rasch model 240 16.3. Latent Markov Rasch model 241 16.4. Likelihood inference for the latent Markov Rasch model 243 16.4.1. Log-likelihood maximization 244 16.4.2. Likelihood ratio testing of hypotheses on the parameters 245 16.5. An application 246 16.6. Possible extensions 247 16.6.1. Discrete response variables 248 16.6.2. Multivariate longitudinal data 248 16.7. Conclusions 251 16.8. Bibliography 252 Chapter 17. Selection of Items Fitting a Rasch Model 255 Jean-Benoit HARDOUIN and Mounir MESBAH 17.1. Introduction 255 17.2. Notations and assumptions 256 17.2.1. Notations 256 17.2.2. Fundamental assumptions of the Item Response Theory (IRT) 256 17.3. The Rasch model and the multidimensional marginally sufficient Rasch model 256 17.3.1. The Rasch model 256 17.3.2. The multidimensional marginally sufficient Rasch model 257 17.4. The Raschfit procedure 258 17.5. A fast version of Raschfit 259 17.5.1. Estimation of the parameters under the fixed effects Rasch model 259 17.5.2. Principle of Raschfit-fast 260 17.5.3. A model where the new item is explained by the same latent trait as the kernel 260 17.5.4. A model where the new item is not explained by the same latent trait as the kernel 260 17.5.5. Selection of the new item in the scale 261 17.6. A small set of simulations to compare Raschfit and Raschfit-fast 261 17.6.1. Parameters of the simulation study 261 17.6.2. Results and computing time 264 17.7. A large set of simulations to compare Raschfit-fast, MSP and HCA/CCPROX 269 17.7.1. Parameters of the simulations 269 17.7.2. Discussion 270 17.8. The Stata module “Raschfit” 270 17.9. Conclusion 271 17.10.Bibliography 273 Chapter 18. Analysis of Longitudinal HrQoL using Latent Regression in the Context of Rasch Modeling 275 Silvia BACCI 18.1. Introduction 275 18.2. Global models for longitudinal data analysis 276 18.3. A latent regression Rasch model for longitudinal data analysis 278 18.3.1. Model structure 278 18.3.2. Correlation structure 280 18.3.3. Estimation 281 18.3.4. Implementation with SAS 281 18.4. Case study: longitudinal HrQoL of terminal cancer patients 283 18.5. Concluding remarks 287 18.6. Bibliography 289 Chapter 19. Empirical Internal Validation and Analysis of a Quality of Life Instrument in French Diabetic Patients during an Educational Intervention 291 Judith CHWALOW, Keith MEADOWS, Mounir MESBAH, Vincent COLICHE and Etienne MOLLET 19.1. Introduction 291 19.2. Material and methods 292 19.2.1. Health care providers and patients 292 19.2.2. Psychometric validation of the DHP 293 19.2.3. Psychometric methods 293 19.2.4. Comparative analysis of quality of life by treatment group 294 19.3. Results 295 19.3.1. Internal validation of the DHP 295 19.3.2. Comparative analysis of quality of life by treatment group 303 19.4. Discussion 304 19.5. Conclusion 305 19.6. Bibliography 306 19.7. Appendices 309 PART IV 315 Chapter 20. Deterministic Modeling of the Size of the HIV/AIDS Epidemic in Cuba 317 Rachid LOUNES, Hector DE ARAZOZA, Y.H. HSIEH and Jose JOANES 20.1. Introduction 317 20.2. The models 319 20.2.1. The k2X model 322 20.2.2. The k2Y model 322 20.2.3. The k2XY model 323 20.2.4. The k2 XYX+Y model 324 20.3. The underreporting rate 324 20.4. Fitting the models to Cuban data 325 20.5. Discussion and concluding remarks 326 20.6. Bibliography 330 Chapter 21.Some Probabilistic Models Useful in Sport Sciences 333 Leo GERVILLE-REACHE, Mikhail NIKULIN, Sebastien ORAZIO, Nicolas PARIS and Virginie ROSA 21.1. Introduction 333 21.2. Sport jury analysis: the Gauss-Markov approach 334 21.2.1. Gauss-Markov model 334 21.2.2. Test for non-objectivity of a variable 334 21.2.3. Test of difference between skaters 335 21.2.4. Test for the less precise judge 336 21.3. Sport performance analysis: the fatigue and fitness approach 337 21.3.1. Model characteristics 337 21.3.2. Monte Carlo simulation 338 21.3.3. Results 339 21.4. Sport equipment analysis: the fuzzy subset approach 339 21.4.1. Statistical model used 340 21.4.2. Sensorial analysis step 341 21.4.3. Results 342 21.5. Sport duel issue analysis: the logistic simulation approach 343 21.5.1. Modeling by logistic regression 344 21.5.2. Numerical simulations 345 21.5.3. Results 345 21.6. Sport epidemiology analysis: the accelerated degradation approach 347 21.6.1. Principle of degradation in reliability analysis 347 21.6.2. Accelerated degradation model 348 21.7. Conclusion 350 21.8. Bibliography 350 Appendices 353 A. European Seminar: Some Figures 353 A.1. Former international speakers invited to the European Seminar 353 A.2. Former meetings supported by the European Seminar 353 A.3. Books edited by the organizers of the European Seminar 354 A.4. Institutions supporting the European Seminar (names of colleagues) 355 B. Contributors 357 Index 367
£194.70
ISTE Ltd and John Wiley & Sons Inc Bayesian Approach to Inverse Problems
Book SynopsisMany scientific, medical or engineering problems raise the issue of recovering some physical quantities from indirect measurements; for instance, detecting or quantifying flaws or cracks within a material from acoustic or electromagnetic measurements at its surface is an essential problem of non-destructive evaluation. The concept of inverse problems precisely originates from the idea of inverting the laws of physics to recover a quantity of interest from measurable data. Unfortunately, most inverse problems are ill-posed, which means that precise and stable solutions are not easy to devise. Regularization is the key concept to solve inverse problems. The goal of this book is to deal with inverse problems and regularized solutions using the Bayesian statistical tools, with a particular view to signal and image estimation. The first three chapters bring the theoretical notions that make it possible to cast inverse problems within a mathematical framework. The next three chapters address the fundamental inverse problem of deconvolution in a comprehensive manner. Chapters 7 and 8 deal with advanced statistical questions linked to image estimation. In the last five chapters, the main tools introduced in the previous chapters are put into a practical context in important applicative areas, such as astronomy or medical imaging.Table of ContentsIntroduction 15 Jérôme IDIER PART I. FUNDAMENTAL PROBLEMS AND TOOLS 23 Chapter 1. Inverse Problems, Ill-posed Problems 25 Guy DEMOMENT, Jérôme IDIER 1.1. Introduction 25 1.2. Basic example 26 1.3. Ill-posed problem 30 1.3.1. Case of discrete data 31 1.3.2. Continuous case 32 1.4. Generalized inversion 34 1.4.1. Pseudo-solutions 35 1.4.2. Generalized solutions 35 1.4.3. Example 35 1.5. Discretization and conditioning 36 1.6. Conclusion 38 1.7. Bibliography 39 Chapter 2. Main Approaches to the Regularization of Ill-posed Problems 41 Guy DEMOMENT, Jérôme IDIER 2.1. Regularization 41 2.1.1. Dimensionality control 42 2.1.2. Minimization of a composite criterion 44 2.2. Criterion descent methods 48 2.2.1.Criterion minimization for inversion 48 2.2.2. The quadratic case 49 2.2.3. The convex case 51 2.2.4. General case 52 2.3. Choice of regularization coefficient 53 2.3.1. Residual error energy control 53 2.3.2. “L-curve” method 53 2.3.3. Cross-validation 54 2.4. Bibliography 56 Chapter 3. Inversion within the Probabilistic Framework 59 Guy DEMOMENT, Yves GOUSSARD 3.1. Inversion and inference 59 3.2. Statistical inference 60 3.2.1. Noise law and direct distribution for data 61 3.2.2. Maximum likelihood estimation 63 3.3. Bayesian approach to inversion 64 3.4. Links with deterministic methods 66 3.5. Choice of hyperparameters 67 3.6. A priori model68 3.7. Choice of criteria 70 3.8. The linear, Gaussian case 71 3.8.1. Statistical properties of the solution 71 3.8.2. Calculation of marginal likelihood 73 3.8.3. Wiener filtering 74 3.9. Bibliography 76 PART II. DECONVOLUTION 79 Chapter 4. Inverse Filtering and Other Linear Methods 81 Guy LE BESNERAIS, Jean-François GIOVANNELLI, Guy DEMOMENT 4.1. Introduction 81 4.2. Continuous-time deconvolution 82 4.2.1. Inverse filtering 82 4.2.2. Wiener filtering 84 4.3. Discretization of the problem 85 4.3.1. Choice of a quadrature method 85 4.3.2. Structure of observation matrix H 87 4.3.3. Usual boundary conditions 89 4.3.4. Problem conditioning 89 4.3.5.Generalized inversion 91 4.4. Batch deconvolution 92 4.4.1. Preliminary choices 92 4.4.2. Matrix form of the estimate 93 4.4.3. Hunt’s method (periodic boundary hypothesis) 94 4.4.4. Exact inversion methods in the stationary case 96 4.4.5. Case of non-stationary signals 98 4.4.6. Results and discussion on examples 98 4.5. Recursive deconvolution 102 4.5.1. Kalman filtering 102 4.5.2. Degenerate state model and recursive least squares 104 4.5.3. Autoregressive state model 105 4.5.4. Fast Kalman filtering 108 4.5.5. Asymptotic techniques in the stationary case 110 4.5.6. ARMA model and non-standard Kalman filtering 111 4.5.7. Case of non-stationary signals 111 4.5.8. On-lineprocessing: 2Dcase 112 4.6. Conclusion 112 4.7. Bibliography 113 Chapter 5. Deconvolution of Spike Trains 117 Frédéric CHAMPAGNAT, Yves GOUSSARD, Stéphane GAUTIER, Jérôme IDIER 5.1. Introduction 117 5.2. Penalization of reflectivities, L2LP/L2Hy deconvolutions 119 5.2.1. Quadratic regularization 121 5.2.2. Non-quadratic regularization 122 5.2.3. L2LPorL2Hy deconvolution 123 5.3. Bernoulli-Gaussian deconvolution 124 5.3.1. Compound BG model 124 5.3.2. Various strategies for estimation 124 5.3.3. General expression for marginal likelihood 125 5.3.4. An iterative method for BG deconvolution 126 5.3.5. Other methods 128 5.4. Examples of processing and discussion 130 5.4.1. Nature of the solutions 130 5.4.2. Setting the parameters 132 5.4.3. Numerical complexity 133 5.5. Extensions 133 5.5.1. Generalization of structures of R and H 134 5.5.2. Estimation of the impulse response . . . 134 5.6. Conclusion 136 5.7. Bibliography 137 Chapter 6. Deconvolution of Images 141 Jérôme IDIER, Laure BLANC-FÉRAUD 6.1. Introduction 141 6.2. Regularization in the Tikhonov sense 142 6.2.1. Principle 142 6.2.2. Connection with image processing by linear PDE 144 6.2.3. Limits of Tikhonov’s approach 145 6.3. Detection-estimation 148 6.3.1. Principle 148 6.3.2. Disadvantages 149 6.4. Non-quadratic approach 150 6.4.1. Detection-estimation and non-convex penalization 154 6.4.2. Anisotropic diffusion by PDE 155 6.5. Half-quadratic augmented criteria 156 6.5.1. Duality between non-quadratic criteria and HQ criteria 157 6.5.2. Minimization of HQ criteria 158 6.6. Application in image deconvolution 159 6.6.1. Calculation of the solution 159 6.6.2. Example 161 6.7. Conclusion 164 6.8. Bibliography 165 PART III. ADVANCED PROBLEMS AND TOOLS 169 Chapter 7. Gibbs-Markov Image Models 171 Jérôme IDIER 7.1. Introduction 171 7.2. Bayesian statistical framework 172 7.3. Gibbs-Markov fields 173 7.3.1. Gibbs fields 174 7.3.2. Gibbs-Markov equivalence 177 7.3.3. Posterior law of a GMRF 180 7.3.4. Gibbs-Markov models for images 181 7.4. Statistical tools, stochastic sampling 185 7.4.1. Statistical tools 185 7.4.2. Stochastic sampling 188 7.5. Conclusion 194 7.6. Bibliography 195 Chapter 8. Unsupervised Problems 197 Xavier DESCOMBES, Yves GOUSSARD 8.1. Introduction and statement of problem 197 8.2. Directly observed field 199 8.2.1. Likelihood properties 199 8.2.2. Optimization 200 8.2.3. Approximations 202 8.3. Indirectly observed field 205 8.3.1. Statement of problem 205 8.3.2. EM algorithm 206 8.3.3. Application to estimation of the parameters of a GMRF 207 8.3.4. EM algorithm and gradient 208 8.3.5. Linear GMRF relative to hyperparameters 210 8.3.6. Extensions and approximations 212 8.4. Conclusion 215 8.5. Bibliography 216 PART IV. SOME APPLICATIONS 219 Chapter 9. Deconvolution Applied to Ultrasonic Non-destructive Evaluation 221 Stéphane GAUTIER, Frédéric CHAMPAGNAT, Jérôme IDIER 9.1. Introduction 221 9.2. Example of evaluation and difficulties of interpretation 222 9.2.1. Description of the part to be inspected 222 9.2.2. Evaluation principle 222 9.2.3. Evaluation results and interpretation 223 9.2.4. Help with interpretation by restoration of discontinuities 224 9.3. Definition of direct convolution model 225 9.4. Blind deconvolution 226 9.4.1. Overview of approaches for blind deconvolution 226 9.4.2. DL2Hy/DBGd econvolution 230 9.4.3. Blind DL2Hy/DBG deconvolution 232 9.5. Processing real data 232 9.5.1. Processing by blind deconvolution 233 9.5.2. Deconvolution with a measured wave 234 9.5.3. Comparison between DL2Hy and DBG 237 9.5.4. Summary 240 9.6. Conclusion 240 9.7. Bibliography 241 Chapter 10. Inversion in Optical Imaging through Atmospheric Turbulence 243 Laurent MUGNIER, Guy LE BESNERAIS, Serge MEIMON 10.1. Optical imaging through turbulence 243 10.1.1. Introduction 243 10.1.2. Image formation 244 10.1.4. Imaging techniques 249 10.2. Inversion approach and regularization criteria used 253 10.3. Measurement of aberrations 254 10.3.1. Introduction 254 10.3.2. Hartmann-Shack sensor 255 10.3.3. Phase retrieval and phase diversity 257 10.4. Myopic restoration in imaging 258 10.4.1. Motivation and noise statistic 258 10.4.2. Data processing in deconvolution from wavefront sensing 259 10.4.3. Restoration of images corrected by adaptive optics 263 10.4.4. Conclusion 267 10.5. Image reconstruction in optical interferometry (OI) 268 10.5.1. Observation model 268 10.5.2. Traditional Bayesian approach 271 10.5.3. Myopic modeling 272 10.5.4. Results 274 10.6. Bibliography 277 Chapter 11. Spectral Characterization in Ultrasonic Doppler Velocimetry 285 Jean-François GIOVANNELLI, Alain HERMENT 11.1. Velocity measurement in medical imaging 285 11.1.1. Principle of velocity measurement in ultrasound imaging 286 11.1.2. Information carried by Doppler signals 286 11.1.3.Some characteristics and limitations 288 11.1.4. Data and problems treated 288 11.2. Adaptive spectral analysis 290 11.2.1. Least squares and traditional extensions 290 11.2.2. Long AR models – spectral smoothness – spatial continuity 291 11.2.3. Kalman smoothing 293 11.2.4. Estimation of hyperparameters 294 11.2.5. Processing results and comparisons 296 11.3. Tracking spectral moments 297 11.3.1. Proposed method 298 11.3.2. Likelihood of the hyperparameters 302 11.3.3. Processing results and comparisons 304 11.4. Conclusion 306 11.5. Bibliography 307 Chapter 12. Tomographic Reconstruction from Few Projections 311 Ali MOHAMMAD-DJAFARI, Jean-Marc DINTEN 12.1. Introduction 311 12.2. Projection generation model 312 12.3. 2D analytical methods 313 12.4. 3D analytical methods 317 12.5. Limitations of analytical methods 317 12.6. Discrete approach to reconstruction 319 12.7. Choice of criterion and reconstruction methods 321 12.8. Reconstruction algorithms 323 12.8.1. Optimization algorithms for convex criteria 323 12.8.2. Optimization or integration algorithms 327 12.9. Specific models for binary objects 328 12.10. Illustrations 328 12.10.1.2D reconstruction 328 12.10.2.3Dreconstruction 329 12.11. Conclusions 331 12.12. Bibliography 332 Chapter 13. Diffraction Tomography 335 Hervé CARFANTAN, Ali MOHAMMAD-DJAFARI 13.1. Introduction 335 13.2. Modeling the problem 336 13.2.1. Examples of diffraction tomography applications 336 13.2.2. Modeling the direct problem 338 13.3. Discretization of the direct problem 340 13.3.1. Choice of algebraic framework 340 13.3.2. Method of moments 341 13.3.3. Discretization by the method of moments 342 13.4. Construction of criteria for solving the inverse problem 343 13.4.1. First formulation: estimation of x 344 13.4.2. Second formulation: simultaneous estimation of x and φ 345 13.4.3. Properties of the criteria 347 13.5. Solving the inverse problem 347 13.5.1. Successive linearizations 348 13.5.2. Joint minimization 350 13.5.3. Minimizing MAP criterion 351 13.6. Conclusion 353 13.7. Bibliography 354 Chapter 14. Imaging from Low-intensity Data 357 Ken SAUER, Jean-Baptiste THIBAULT 14.1. Introduction 357 14.2. Statistical properties of common low-intensity image data 359 14.2.1. Likelihood functions and limiting behavior 359 14.2.2. Purely Poisson measurements 360 14.2.3. Inclusion of background counting noise 362 14.2.4. Compound noise models with Poisson information 362 14.3. Quantum-limited measurements in inverse problems 363 14.3.1. Maximum likelihood properties 363 14.3.2. Bayesian estimation 366 14.4. Implementation and calculation of Bayesian estimates 368 14.4.1. Implementation for pure Poisson model 368 14.4.2. Bayesian implementation for a compound data model 370 14.5. Conclusion 372 14.6. Bibliography 372 List of Authors 375 Index 377
£170.95
ISTE Ltd and John Wiley & Sons Inc Advanced Mapping of Environmental Data
Book SynopsisThis book combines geostatistics and global mapping systems to present an up-to-the-minute study of environmental data. Featuring numerous case studies, the reference covers model dependent (geostatistics) and data driven (machine learning algorithms) analysis techniques such as risk mapping, conditional stochastic simulations, descriptions of spatial uncertainty and variability, artificial neural networks (ANN) for spatial data, Bayesian maximum entropy (BME), and more.Trade Review"It gives a good overview, is clearly written, is concise, and includes many references to papers published in the different areas." (Zentralblatt MATH, 2011)Table of ContentsPreface xi Chapter 1. Advanced Mapping of Environmental Data: Introduction 1 M. KANEVSKI 1.1. Introduction 1 1.2. Environmental data analysis: problems and methodology 3 1.2.1. Spatial data analysis: typical problems 3 1.2.2. Spatial data analysis: methodology 5 1.2.3. Model assessment and model selection 8 1.3. Resources 12 1.3.1. Books, tutorials 12 1.3.2. Software 12 1.4. Conclusion 14 1.5. References 15 Chapter 2. Environmental Monitoring Network Characterization and Clustering 19 D. TUIA and M. KANEVSKI 2.1. Introduction 19 2.2. Spatial clustering and its consequences 20 2.2.1. Global parameters 21 2.2.2. Spatial predictions 22 2.3. Monitoring network quantification 23 2.3.1. Topological quantification 23 2.3.2. Global measures of clustering 23 2.3.2.1. Topological indices 23 2.3.2.2. Statistical indices 24 2.3.3. Dimensional resolution: fractal measures of clustering 26 2.3.3.1. Sandbox method 27 2.3.3.2. Box-counting method 30 2.3.3.3. Lacunarity 33 2.4. Validity domains 34 2.5. Indoor radon in Switzerland: an example of a real monitoring network 36 2.5.1. Validity domains 37 2.5.2. Topological index 37 2.5.3. Statistical indices 38 2.5.3.1. Morisita index 38 2.5.3.2. K-function 39 2.5.4. Fractal dimension 40 2.5.4.1. Sandbox and box-counting fractal dimension 40 2.5.4.2. Lacunarity 42 2.6. Conclusion 43 2.7. References 44 Chapter 3. Geostatistics: Spatial Predictions and Simulations 47 E. SAVELIEVA, V. DEMYANOV and M. MAIGNAN 3.1. Assumptions of geostatistics 47 3.2. Family of kriging models 49 3.2.1. Simple kriging 50 3.2.2. Ordinary kriging 50 3.2.3. Basic features of kriging estimation 51 3.2.4. Universal kriging (kriging with trend) 56 3.2.5. Lognormal kriging 56 3.3. Family of co-kriging models 58 3.3.1. Kriging with linear regression 58 3.3.2. Kriging with external drift 58 3.3.3. Co-kriging 59 3.3.4. Collocated co-kriging 60 3.3.5. Co-kriging application example 61 3.4. Probability mapping with indicator kriging 64 3.4.1. Indicator coding 64 3.4.2. Indicator kriging 66 3.4.3. Indicator kriging applications 69 3.4.3.1. Indicator kriging for 241Am analysis 69 3.4.3.2. Indicator kriging for aquifer layer zonation 71 3.4.3.3. Indicator kriging for localization of crab crowds 74 3.5. Description of spatial uncertainty with conditional stochastic simulations 76 3.5.1. Simulation vs. estimation 76 3.5.2. Stochastic simulation algorithms 77 3.5.3. Sequential Gaussian simulation 81 3.5.4. Sequential indicator simulations 84 3.5.5. Co-simulations of correlated variables 88 3.6. References 92 Chapter 4. Spatial Data Analysis and Mapping Using Machine Learning Algorithms 95 F. RATLE, A. POZDNOUKHOV, V. DEMYANOV, V. TIMONIN and E. SAVELIEVA 4.1. Introduction 95 4.2. Machine learning: an overview 96 4.2.1. The three learning problems 96 4.2.2. Approaches to learning from data 100 4.2.3. Feature selection 101 4.2.4. Model selection 103 4.2.5. Dealing with uncertainties 107 4.3. Nearest neighbor methods 108 4.4. Artificial neural network algorithms 109 4.4.1. Multi-layer perceptron neural network 109 4.4.2. General Regression Neural Networks 119 4.4.3. Probabilistic Neural Networks 122 4.4.4. Self-organizing (Kohonen) maps 124 4.5. Statistical learning theory for spatial data: concepts and examples 131 4.5.1. VC dimension and structural risk minimization 131 4.5.2. Kernels 132 4.5.3. Support vector machines 133 4.5.4. Support vector regression 137 4.5.5. Unsupervised techniques 141 4.5.5.1. Clustering 142 4.5.5.2. Nonlinear dimensionality reduction 144 4.6. Conclusion 146 4.7. References 146 Chapter 5. Advanced Mapping of Environmental Spatial Data: Case Studies 149 L. FORESTI, A. POZDNOUKHOV, M. KANEVSKI, V. TIMONIN, E. SAVELIEVA, C. KAISER, R. TAPIA and R. PURVES 5.1. Introduction 149 5.2. Air temperature modeling with machine learning algorithms and geostatistics 150 5.2.1. Mean monthly temperature 151 5.2.1.1. Data description 151 5.2.1.2. Variography 152 5.2.1.3. Step-by-step modeling using a neural network 153 5.2.1.4. Overfitting and undertraining 154 5.2.1.5. Mean monthly air temperature prediction mapping 156 5.2.2. Instant temperatures with regionalized linear dependencies 159 5.2.2.1. The Föhn phenomenon 159 5.2.2.2. Modeling of instant air temperature influenced by Föhn 160 5.2.3. Instant temperatures with nonlinear dependencies 163 5.2.3.1. Temperature inversion phenomenon 163 5.2.3.2. Terrain feature extraction using Support Vector Machines 164 5.2.3.3. Temperature inversion modeling with MLP 165 5.3. Modeling of precipitation with machine learning and geostatistics 168 5.3.1. Mean monthly precipitation 169 5.3.1.1. Data description 169 5.3.1.2. Precipitation modeling with MLP 171 5.3.2. Modeling daily precipitation with MLP 173 5.3.2.1. Data description 173 5.3.2.2. Practical issues of MLP modeling 174 5.3.2.3. The use of elevation and analysis of the results 177 5.3.3. Hybrid models: NNRK and NNRS 179 5.3.3.1. Neural network residual kriging 179 5.3.3.2. Neural network residual simulations 182 5.3.4. Conclusions 184 5.4. Automatic mapping and classification of spatial data using machine learning 185 5.4.1. k-nearest neighbor algorithm 185 5.4.1.1. Number of neighbors with cross-validation 187 5.4.2. Automatic mapping of spatial data 187 5.4.2.1. KNN modeling 188 5.4.2.2. GRNN modeling 190 5.4.3. Automatic classification of spatial data 192 5.4.3.1. KNN classification 193 5.4.3.2. PNN classification 194 5.4.3.3. Indicator kriging classification 197 5.4.4. Automatic mapping – conclusions 199 5.5. Self-organizing maps for spatial data – case studies 200 5.5.1. SOM analysis of sediment contamination 200 5.5.2. Mapping of socio-economic data with SOM 204 5.6. Indicator kriging and sequential Gaussian simulations for probability mapping. Indoor radon case study 209 5.6.1. Indoor radon measurements 209 5.6.2. Probability mapping 211 5.6.3. Exploratory data analysis 212 5.6.4. Radon data variography 216 5.6.4.1. Variogram for indicators 216 5.6.4.2. Variogram for Nscores 217 5.6.5. Neighborhood parameters 218 5.6.6. Prediction and probability maps 219 5.6.6.1. Probability maps with IK 219 5.6.6.2. Probability maps with SGS 220 5.6.7. Analysis and validation of results 221 5.6.7.1. Influence of the simulation net and the number of neighbors 221 5.6.7.2. Decision maps and validation of results 222 5.6.8. Conclusions 225 5.7. Natural hazards forecasting with support vector machines – case study: snow avalanches 225 5.7.1. Decision support systems for natural hazards 227 5.7.2. Reminder on support vector machines 228 5.7.2.1. Probabilistic interpretation of SVM 229 5.7.3. Implementing an SVM for avalanche forecasting 230 5.7.4. Temporal forecasts 230 5.7.4.1. Feature selection 231 5.7.4.2. Training the SVM classifier 232 5.7.4.3. Adapting SVM forecasts for decision support 233 5.7.5. Extending the SVM to spatial avalanche predictions 237 5.7.5.1. Data preparation 237 5.7.5.2. Spatial avalanche forecasting 239 5.7.6. Conclusions 241 5.8. Conclusion 241 5.9. References 242 Chapter 6. Bayesian Maximum Entropy – BME 247 G. CHRISTAKOS 6.1. Conceptual framework 247 6.2. Technical review of BME 251 6.2.1. The spatiotemporal continuum 251 6.2.2. Separable metric structures 253 6.2.3. Composite metric structures 255 6.2.4. Fractal metric structures 256 6.3. Spatiotemporal random field theory 257 6.3.1. Pragmatic S/TRF tools 258 6.3.2. Space-time lag dependence: ordinary S/TRF 260 6.3.3. Fractal S/TRF 262 6.3.4. Space-time heterogenous dependence: generalized S/TRF 264 6.4. About BME 267 6.4.1. The fundamental equations 267 6.4.2. A methodological outline 273 6.4.3. Implementation of BME: the SEKS-GUI 275 6.5. A brief review of applications 281 6.5.1. Earth and atmospheric sciences 282 6.5.2. Health, human exposure and epidemiology 291 6.6. References 299 List of Authors 307 Index 309
£150.05
ISTE Ltd and John Wiley & Sons Inc The Wigner Monte Carlo Method for Nanoelectronic
Book SynopsisThe emergence of nanoelectronics has led us to renew the concepts of transport theory used in semiconductor device physics and the engineering community. It has become crucial to question the traditional semi-classical view of charge carrier transport and to adequately take into account the wave-like nature of electrons by considering not only their coherent evolution but also the out-of-equilibrium states and the scattering effects. This book gives an overview of the quantum transport approaches for nanodevices and focuses on the Wigner formalism. It details the implementation of a particle-based Monte Carlo solution of the Wigner transport equation and how the technique is applied to typical devices exhibiting quantum phenomena, such as the resonant tunnelling diode, the ultra-short silicon MOSFET and the carbon nanotube transistor. In the final part, decoherence theory is used to explain the emergence of the semi-classical transport in nanodevices.Table of ContentsSymbols ix Abbreviations xiii Introduction xv Acknowledgements xxi Chapter 1. Theoretical Framework of Quantum Transport in Semiconductors and Devices 1 1.1. The fundamentals: a brief introduction to phonons, quasi-electrons and envelope functions 2 1.2. The semi-classical approach of transport 11 1.3. The quantum treatment of envelope functions 16 1.4. The two main problems of quantum transport 29 Chapter 2. Particle-based Monte Carlo Approach to Wigner-Boltzmann Device Simulation 57 2.1. The particle Monte Carlo technique to solve the BTE 59 2.2. Extension of the particle Monte Carlo technique to the WBTE: principles 71 2.3. Simple validations via two typical cases 83 2.4. Conclusion 86 Chapter 3. Application of the Wigner Monte Carlo Method to RTD, MOSFET and CNTFET 89 3.1. The resonant tunneling diode (RTD) 90 3.2. The double-gate metal-oxide-semiconductor field-effect transistor (DG-MOSFET) 99 3.3. The carbon nanotube field-effect transistor (CNTFET) 134 3.4. Conclusion 148 Chapter 4. Decoherence and Transition from Quantum to Semi-classical Transport 151 4.1. Simple illustration of the decoherence mechanism 152 4.2. Coherence and decoherence of Gaussian wave packets in GaAs 157 4.3. Coherence and decoherence in RTD: transition between semi-classical and quantum regions 171 4.4. Quantum coherence and decoherence in DG-MOSFET 175 4.5. Conclusion 180 Conclusion 183 Appendix A. Average Value of Operators in the Wigner Formalism 187 Appendix B. Boundaries of the Wigner Potential 189 Appendix C. Hartree Wave Function 191 Appendix D. Asymmetry Between Phonon Absorption and Emission Rates 193 Appendix E. Quantum Brownian Motion 195 Appendix F. Purity in the Wigner formalism 201 Appendix G. Propagation of a Free Wave Packet Subject to Quantum Brownian Motion 203 Appendix H. Coherence Length at Thermal Equilibrium 205 Bibliography 207 Index 241
£132.00
ISTE Ltd and John Wiley & Sons Inc Digital Spectral Analysis: Parametric,
Book SynopsisDigital Spectral Analysis provides a single source that offers complete coverage of the spectral analysis domain. This self-contained work includes details on advanced topics that are usually presented in scattered sources throughout the literature. The theoretical principles necessary for the understanding of spectral analysis are discussed in the first four chapters: fundamentals, digital signal processing, estimation in spectral analysis, and time-series models. An entire chapter is devoted to the non-parametric methods most widely used in industry. High resolution methods are detailed in a further four chapters: spectral analysis by stationary time series modeling, minimum variance, and subspace-based estimators. Finally, advanced concepts are the core of the last four chapters: spectral analysis of non-stationary random signals, space time adaptive processing: irregularly sampled data processing, particle filtering and tracking of varying sinusoids. Suitable for students, engineers working in industry, and academics at any level, this book provides a rare complete overview of the spectral analysis domain.Table of ContentsPreface xiii PART 1. TOOLS AND SPECTRAL ANALYSIS 1 Chapter 1. Fundamentals 3 Francis CASTANIÉ 1.1. Classes of signals 3 1.2. Representations of signals 9 1.3. Spectral analysis: position of the problem 20 1.4. Bibliography 21 Chapter 2. Digital Signal Processing 23 Éric LE CARPENTIER 2.1. Introduction 23 2.2. Transform properties 24 2.3. Windows 49 2.4. Examples of application 57 2.5. Bibliography 64 Chapter 3. Introduction to Estimation Theory with Application in Spectral Analysis 67 Olivier BESSON and André FERRARI 3.1. Introduction 67 3.2. Covariance-based estimation 86 3.3. Performance assessment of some spectral estimators 95 3.4. Bibliography 102 Chapter 4. Time-Series Models 105 Francis CASTANIÉ 4.1. Introduction 105 4.2. Linear models 107 4.3. Exponential models 117 4.4. Nonlinear models 120 4.5. Bibliography 121 PART 2. NON-PARAMETRIC METHODS 123 Chapter 5. Non-Parametric Methods 125 Éric LE CARPENTIER 5.1. Introduction 125 5.2. Estimation of the power spectral density 130 5.3. Generalization to higher-order spectra 141 5.4. Bibliography 142 PART 3. PARAMETRIC METHODS 143 Chapter 6. Spectral Analysis by Parametric Modeling145 Corinne MAILHES and Francis CASTANIÉ 6.1. Which kind of parametric models? 145 6.2. AR modeling 146 6.3. ARMA modeling 154 6.4. Prony modeling 156 6.5. Order selection criteria 158 6.6. Examples of spectral analysis using parametric modeling 162 6.7. Bibliography 166 Chapter 7. Minimum Variance 169 Nadine MARTIN 7.1. Principle of the MV method . . 174 7.2. Properties of the MV estimator 177 7.3. Link with the Fourier estimators 188 7.4. Link with a maximum likelihood estimator 190 7.5. Lagunas methods: normalized MV and generalized MV 192 7.6. A new estimator: the CAPNORM estimator 200 7.7. Bibliography 204 Chapter 8. Subspace-Based Estimators and Application to Partially Known Signal Subspaces 207 Sylvie MARCOS and Rémy BOYER 8.1. Model, concept of subspace, definition of high resolution 207 8.2. MUSIC 211 8.3. Determination criteria of the number of complex sine waves 216 8.4. The MinNorm method 217 8.5. “Linear” subspace methods 219 8.6. The ESPRIT method 223 8.7. Illustration of the subspace-based methods performance 226 8.8. Adaptive research of subspaces 229 8.9. Integrating a priori known frequencies into the MUSIC criterion. 233 8.10. Bibliography 243 PART 4. ADVANCED CONCEPTS 251 Chapter 9. Multidimensional Harmonic Retrieval: Exact, Asymptotic, and Modified Cramér-Rao Bounds 253 Rémy BOYER 9.1. Introduction 253 9.2. CanDecomp/Parafac decomposition of the multidimensional harmonic model 255 9.3. CRB for the multidimensional harmonic model 257 9.4. Modified CRB for the multidimensional harmonic model 266 9.5. Conclusion 272 9.6. Appendices 273 9.7. Bibliography 284 Chapter 10. Introduction to Spectral Analysis of Non-Stationary Random Signals 287 Corinne MAILHES and Francis CASTANIÉ 10.1. Evolutive spectra 288 10.2. Non-parametric spectral estimation 290 10.3. Parametric spectral estimation 291 10.4. Bibliography 297 Chapter 11. Spectral Analysis of Non-uniformly Sampled Signals 301 Arnaud RIVOIRA and Gilles FLEURY 11.1. Applicative context 301 11.2. Theoretical framework 302 11.3. Generation of a randomly sampled stochastic process 302 11.4. Spectral analysis using undated samples 305 11.5. Spectral analysis using dated samples 309 11.6. Perspectives 314 11.7. Bibliography 315 Chapter 12. Space–Time Adaptive Processing 317 Laurent SAVY and François LE CHEVALIER 12.1. STAP, spectral analysis, and radar signal processing 319 12.2. Space–time processing as a spectral estimation problem 327 12.3. STAP architectures 334 12.4. Relative advantages of pre-Doppler and post-Doppler STAP 354 12.5. Conclusion 358 12.6. Bibliography 359 12.7. Glossary 360 Chapter 13. Particle Filtering and Tracking of Varying Sinusoids 361 David BONACCI 13.1. Particle filtering 361 13.2. Application to spectral analysis 370 13.3. Bibliography 375 List of Authors 377 Index 379
£135.80
ISTE Ltd and John Wiley & Sons Inc Tree-based Graph Partitioning Constraint
Book SynopsisCombinatorial problems based on graph partitioning enable us to mathematically represent and model many practical applications. Mission planning and the routing problems occurring in logistics perfectly illustrate two such examples. Nevertheless, these problems are not based on the same partitioning pattern: generally, patterns like cycles, paths, or trees are distinguished. Moreover, the practical applications are often not limited to theoretical problems like the Hamiltonian path problem, or K-node disjoint path problems. Indeed, they usually combine the graph partitioning problem with several restrictions related to the topology of nodes and arcs. The diversity of implied constraints in real-life applications is a practical limit to the resolution of such problems by approaches considering the partitioning problem independently from each additional restriction. This book focuses on constraint satisfaction problems related to tree partitioning problems enriched by several additional constraints that restrict the possible partitions topology. On the one hand, this title focuses on the structural properties of tree partitioning constraints. On the other hand, it is dedicated to the interactions between the tree partitioning problem and classical restrictions (such as precedence relations or incomparability relations between nodes) involved in practical applications. Precisely, Tree-based Graph Partitioning Constraint shows how to globally take into account several restrictions within one single tree partitioning constraint. Another interesting aspect of this book is related to the implementation of such a constraint. In the context of graph-based global constraints, the book illustrates how a fully dynamic management of data structures makes the runtime of filtering algorithms independent of the graph density.Table of ContentsPART 1. CONSTRAINT PROGRAMMING AND FOUNDATIONS OF GRAPH THEORY 1 Introduction to Part 1 3 Chapter 1. Introduction to Constraint Programming 5 1.1. What is a variable? 7 1.2. What is a constraint? 8 1.3. What is a global constraint? 10 1.4. What is a propagation algorithm? 11 1.5. What is a consistency level? 14 1.6. What is a constraint solver? 15 1.7. Constraint solvers at work 17 1.8. Organization structure 21 Chapter 2. Graph Theory and Constraint Programming 23 2.1. Modeling graphs with constraint programming 24 2.2. Graph theory at work in constraint programming 34 2.3. Constraint programming at work in graph theory 37 Chapter 3. Tree Graph Partitioning 39 3.1. In undirected graphs 39 3.2. In directed graphs 42 PART 2. CHARACTERIZATION OF TREE-BASED GRAPH PARTITIONING CONSTRAINTS 47 Chapter 4. Tree Constraints in Undirected Graphs 49 4.1. Decomposition 49 4.2. Definition of constraints 51 4.3. A filtering algorithm for the proper-forest constraint 56 4.4. Filtering algorithm for the resource-forest constraint 70 4.5. Summary of undirected tree constraints 80 Chapter 5. Tree Constraints in Directed Graphs 83 5.1. Decomposition 83 5.2. Definition of constraints 86 5.3. Filtering algorithm for the tree constraint 89 5.4. Filtering algorithm for the proper-tree constraint 96 5.5. Summary of tree constraints in directed and undirected graphs 113 Chapter 6. Additional Constraints Linked to Graph Partitioning 117 6.1. Definition of restrictions 118 6.2. Complexity zoo 123 6.3. Interaction between the number of trees and the number of proper trees 129 6.4. Relation of precedence between the vertices of the graph 130 6.5. Relation of conditional precedence 137 6.6. Relation of incomparability between graph vertices 140 6.7. Interactions between precedence and incomparability constraints 143 6.8. Constraining the interior half-degree of each vertex 148 6.9. Summary 151 Chapter 7. The Case of Disjoint Paths 153 7.1. Minimum number of paths in acyclic directed graphs 156 7.2. Minimum number of paths in any directed graph 161 7.3. A path partitioning constraint 169 7.4. Summary 173 Chapter 8. Implementation of a Tree Constraint 175 8.1. Original implementation 176 8.2. Toward a “portable” implementation 181 8.3. Conclusion 191 PART 3. IMPLEMENTATION: TASK PLANNING 193 Introduction to Part 3 195 Chapter 9. First Model in Constraint Programming 199 9.1. Model for the coherence of displacements in space 199 9.2. Modeling resource consumption 200 9.3. Modeling time windows 201 9.4. Modeling coordination constraints between units 202 9.5. Limitations of the proposed model 203 Chapter 10. Advanced Model in Constraint Programming 205 10.1. Modeling the coherence of displacements in space 206 10.2. Modeling resource consumption 208 10.3. Integration of temporal aspects 208 10.4. Propagating time windows 213 PART 4. CONCLUSION AND FUTURE WORK 225 Chapter 11. Conclusion 227 Chapter 12. Perspectives and Criticisms 231 Bibliography 233 Index 239
£132.00
ISTE Ltd and John Wiley & Sons Inc Mathematical Statistics and Stochastic Processes
Book SynopsisGenerally, books on mathematical statistics are restricted to the case of independent identically distributed random variables. In this book however, both this case AND the case of dependent variables, i.e. statistics for discrete and continuous time processes, are studied. This second case is very important for today’s practitioners. Mathematical Statistics and Stochastic Processes is based on decision theory and asymptotic statistics and contains up-to-date information on the relevant topics of theory of probability, estimation, confidence intervals, non-parametric statistics and robustness, second-order processes in discrete and continuous time and diffusion processes, statistics for discrete and continuous time processes, statistical prediction, and complements in probability. This book is aimed at students studying courses on probability with an emphasis on measure theory and for all practitioners who apply and use statistics and probability on a daily basis.Table of ContentsPreface xiii PART 1. MATHEMATICAL STATISTICS 1 Chapter 1. Introduction to Mathematical Statistics 3 1.1. Generalities 3 1.2. Examples of statistics problems 4 Chapter 2. Principles of Decision Theory 9 2.1. Generalities 9 2.2. The problem of choosing a decision function 11 2.3. Principles of Bayesian statistics 13 2.4. Complete classes 17 2.5. Criticism of decision theory – the asymptotic point of view 18 2.6. Exercises 18 Chapter 3. Conditional Expectation 21 3.1. Definition 21 3.2. Properties and extension 22 3.3. Conditional probabilities and conditional distributions 24 3.4. Exercises 26 Chapter 4. Statistics and Sufficiency 29 4.1. Samples and empirical distributions 29 4.2. Sufficiency 31 4.3. Examples of sufficient statistics – an exponential model 33 4.4. Use of a sufficient statistic 35 4.5. Exercises 36 Chapter 5. Point Estimation 39 5.1. Generalities 39 5.2. Sufficiency and completeness 42 5.3. The maximum-likelihood method 45 5.4. Optimal unbiased estimators 49 5.5. Efficiency of an estimator 56 5.6. The linear regression model 65 5.7. Exercises 68 Chapter 6. Hypothesis Testing and Confidence Regions 73 6.1. Generalities 73 6.2. The Neyman–Pearson (NP) lemma 75 6.3. Multiple hypothesis tests (general methods) 80 6.4. Case where the ratio of the likelihoods is monotonic 84 6.5. Tests relating to the normal distribution 86 6.6. Application to estimation: confidence regions 86 6.7. Exercises 90 Chapter 7. Asymptotic Statistics 101 7.1. Generalities 101 7.2. Consistency of the maximum likelihood estimator 103 7.3. The limiting distribution of the maximum likelihood estimator 104 7.4. The likelihood ratio test 106 7.5. Exercises 108 Chapter 8. Non-Parametric Methods and Robustness 113 8.1. Generalities 113 8.2. Non-parametric estimation 114 8.3. Non-parametric tests 117 8.4. Robustness 121 8.5. Exercises 124 PART 2. STATISTICS FOR STOCHASTIC PROCESSES 131 Chapter 9. Introduction to Statistics for Stochastic Processes 133 9.1. Modeling a family of observations 133 9.2. Processes 134 9.3. Statistics for stochastic processes 137 9.4. Exercises 138 Chapter 10. Weakly Stationary Discrete-Time Processes 141 10.1. Autocovariance and spectral density 141 10.2. Linear prediction and Wold decomposition 144 10.3. Linear processes and the ARMA model 146 10.4. Estimating the mean of a weakly stationary process 149 10.5. Estimating the autocovariance 151 10.6. Estimating the spectral density 151 10.7. Exercises 155 Chapter 11. Poisson Processes – A Probabilistic and Statistical Study 163 11.1. Introduction 163 11.2. The axioms of Poisson processes 164 11.3. Interarrival time 166 11.4. Properties of the Poisson process 168 11.5. Notions on generalized Poisson processes 170 11.6. Statistics of Poisson processes 172 11.7. Exercises 177 Chapter 12. Square-Integrable Continuous-Time Processes 183 12.1. Definitions 183 12.2. Mean-square continuity 183 12.3. Mean-square integration 184 12.4. Mean-square differentiation 187 12.5. The Karhunen–Loeve theorem 188 12.6. Wiener processes 189 12.7. Notions on weakly stationary continuous-time processes 195 12.8. Exercises 197 Chapter 13. Stochastic Integration and Diffusion Processes 203 13.1. Itô integral 203 13.2. Diffusion processes 206 13.3. Processes defined by stochastic differential equations and stochastic integrals 212 13.4. Notions on statistics for diffusion processes 215 13.5. Exercises 216 Chapter 14. ARMA Processes 219 14.1. Autoregressive processes 219 14.2. Moving average processes 223 14.3. General ARMA processes 224 14.4. Non-stationary models 226 14.5. Statistics of ARMA processes 228 14.6. Multidimensional processes 232 14.7. Exercises 233 Chapter 15. Prediction 239 15.1. Generalities 239 15.2. Empirical methods of prediction 240 15.3. Prediction in the ARIMA model 242 15.4. Prediction in continuous time 244 15.5. Exercises 245 PART 3. SUPPLEMENT 249 Chapter 16. Elements of Probability Theory 251 16.1. Measure spaces: probability spaces 251 16.2. Measurable functions: real random variables 253 16.3. Integrating real random variables 255 16.4. Random vectors 259 16.5. Independence 261 16.6. Gaussian vectors 262 16.7. Stochastic convergence 264 16.8. Limit theorems 265 Appendix. Statistical Tables 267 A1.1. Random numbers 267 A1.2. Distribution function of the standard normal distribution 268 A1.3. Density of the standard normal distribution 269 A1.4. Percentiles (tp) of Student’s distribution 270 A1.5. Ninety-fifth percentiles of Fisher–Snedecor distributions 271 A1.6. Ninety-ninth percentiles of Fisher–Snedecor distributions 272 A1.7. Percentiles (χ2 p) of the χ2 distribution with n degrees of freedom 273 A1.8. Individual probabilities of the Poisson distribution 274 A1.9. Cumulative probabilities of the Poisson distribution 275 A1.10. Binomial coefficients Ck n for n ≤ 30 and 0 ≤ k ≤ 7 276 A1.11. Binomial coefficients Ck n for n ≤ 30 and 8 ≤ k ≤ 15 277 Bibliography 279 Index 281
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Appraisal Institute An Introduction to Statistics for Appraisers
Book Synopsis
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Roberts & Company Publishers The Analysis of Biological Data
Book SynopsisKnowledge of statistics is essential in modern biology and medicine. Biologists and health professionals learn statistics best with real and interesting examples. The Analysis of Biological Data, Second Edition, by Whitlock and Schluter, teaches modern methods of statistics through the use of fascinating biological and medical cases.
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Springer Nature Switzerland AG Random Graphs, Phase Transitions, and the Gaussian Free Field: PIMS-CRM Summer School in Probability, Vancouver, Canada, June 5–30, 2017
Book SynopsisThe 2017 PIMS-CRM Summer School in Probability was held at the Pacific Institute for the Mathematical Sciences (PIMS) at the University of British Columbia in Vancouver, Canada, during June 5-30, 2017. It had 125 participants from 20 different countries, and featured two main courses, three mini-courses, and twenty-nine lectures. The lecture notes contained in this volume provide introductory accounts of three of the most active and fascinating areas of research in modern probability theory, especially designed for graduate students entering research: Scaling limits of random trees and random graphs (Christina Goldschmidt) Lectures on the Ising and Potts models on the hypercubic lattice (Hugo Duminil-Copin) Extrema of the two-dimensional discrete Gaussian free field (Marek Biskup) Each of these contributions provides a thorough introduction that will be of value to beginners and experts alike.Table of ContentsScaling Limits of Random Trees and Random Graphs (C. Goldschmidt).- Lectures on the Ising and Potts Models on the Hypercubic Lattice (H. Duminil-Copin).- Extrema of the Two-Dimensional Discrete Gaussian Free Field (M. Biskup).
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Springer Time Series Analysis and Forecasting
Book Synopsis- Part I Advanced Econometric Methods.- Banking sector development and economic growth in developing countries. Does the change in the shadow economy matter? A Nonlinear Panel ARDL.- Improving the prediction of Norwegian household consumption by adjusting for temporary fluctuations in dividend income.- Inflation expectations change during the pre-war and war period. A comparison of Ukraine and neighboring economies.- Analysis of diversification in investment portfolios Return and Risk for different time horizons.- Economic Diversity and the Dutch Disease in Angola.- Part II Artificial Intelligence and Time Series.- Increasing the Performance and Plausibility of Machine Learning via Data Analysis Techniques.- Combining Forecasts of Time Series with Complex Seasonality using LSTM-based Meta-Learning.- Bayesian Robust Multivariate Time Series Analysis in Nonlinear Regression Models with Vector Autoregressive and t-distributed Errors.- Forecasting of the F10.7 solar radio index: A Multivariate Deep Learning Approach.- Part III Financial Forecasting and Risk Analysis.- Risk-adjusted Returns of Croatian Largest Manufacturers and Their Determinants.- Usage of portfolio replication in non-life insurance.- Encoding Stock Returns Relationships via Latent Embeddings for Enhanced Portfolio Optimization.- A Measure of Bivariate Long Memories in Financial Time Series with Applications to Granger Causality Networks.- Volatility-inspired s-LSTM cell.- Part IV Theoretical Aspects of Time Series.- Bayesian Analysis of Systemic Risks Distributions.- Empirical function-based time series analysis for high-dimensional ground motion data: A focus on nonstationary and nonlinear phenomena.- Extended Research on Categorical Data Encoding Techniques for Recursive Multi-Step Prediction of Vessel Trajectory.- Part V Time Series Analysis Applications.- Predicting Safety- Critical Events in Traffic Flow Based on Time-Series.- Two-Factor and ARIMA-LS-SVR Models for Forecasting of EUA Futures Prices.- Interest Rate Sensitivity of the largest European Pharmaceutical Companies. An Extension of The Fama and French Five-Factor Model.
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