# Weighing the Odds: A Course in Probability and Statistics

Cambridge University Press, 2 aoűt 2001 - 547 pages
Statistics do not lie, nor is probability paradoxical. You just have to have the right intuition. In this lively look at both subjects, David Williams convinces mathematics students of the intrinsic interest of statistics and probability, and statistics students that the language of mathematics can bring real insight and clarity to their subject. He helps students build the intuition needed, in a presentation enriched with examples drawn from all manner of applications, e.g., genetics, filtering, the Black–Scholes option-pricing formula, quantum probability and computing, and classical and modern statistical models. Statistics chapters present both the Frequentist and Bayesian approaches, emphasising Confidence Intervals rather than Hypothesis Test, and include Gibbs-sampling techniques for the practical implementation of Bayesian methods. A central chapter gives the theory of Linear Regression and ANOVA, and explains how MCMC methods allow greater flexibility in modelling. C or WinBUGS code is provided for computational examples and simulations. Many exercises are included; hints or solutions are often provided.

### Avis des internautes -Rédiger un commentaire

Aucun commentaire n'a été trouvé aux emplacements habituels.

### Table des matičres

 Introduction 1 12 Sharpening our intuition 18 13 Probability as Pure Maths 23 14 Probability as Applied Maths 25 15 First remarks on Statistics 26 16 Use of Computers 31 Events and Probabilities 35 21 Possible outcome actual outcome and Events 36
 73 Joint pdfs transformations 246 74 Conditional pdfs 258 75 Multiparameter Bayesian Statistics 265 Linear Models ANOVA etc 283 82 The Orthonormality Principle and the Ftest 295 the Mathematics 304 84 Goodness of fit robustness hierarchical models 339 85 Multivariate Normal MVN Distributions 365

 22 Probabilities 39 23 Probability and Measure 42 3 Random Variables Means and Variances 47 32 DFs pmfs and pdfs 50 33 Means in the case when 12 is finite 56 34 Means in general 59 35 Variances and Covariances 65 Conditioning and Independence 73 42 Independence 96 43 Laws of large numbers 103 a first look 116 45 A simple strong Markov principle 127 46 Simulation of IID sequences 130 Generating Functions and the Central Limit Theorem 141 51 General comments on the use of Generating Functions GFs 142 52 Probability generating functions pgfs 143 53 Moment Generating Functions MGFs 146 54 The Central Limit Theorem CLT 156 55 Characteristic Functions CFs 166 Confidence Intervals for oneparameter models 169 62 Some commonsense Frequentist CIs 173 63 Likelihood sufficiency exponential family 181 64 Brief notes on Point Estimation 187 associated CIs 192 66 Bayesian Confidence Intervals 199 67 Hypothesis Testing if you must 222 Conditional pdfs and multiparameter Bayesian Statistics 240 72 Jacobians 243
 Some further Probability 383 91 Conditional Expectation 385 92 Martingales 406 93 Poisson Processes PPs 426 Quantum Probability and Quantum Computing 440 a first look 441 102 Foundations of Quantum Probability 448 a closer look 463 104 Spin and Entanglement 472 105 Spin and the Dirac equation 485 106 Epilogue 491 Some Prerequisites and Addenda 495 Appendix A3 o notation 496 Appendix A5 The Axiom of Choice 498 Appendix A6 A nonBorel subset of 01 499 Appendix A8 A nonuniqueness example for moments 500 Appendix A9 Proof of a TwoEnvelopes result 501 Discussion of some Selected Exercises 502 Tables 514 Table of the normal distribution function 515 Upper percentage points for t 516 Upper percentage points for x˛ 517 Upper 5 percentage points for F 518 A small Sample of the Literature 519 Bibliography 525 Index 539 Droits d'auteur

### Fréquemment cités

Page 530 - D 1997 Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference. Chapman and Hall, London Gílfand A E.