Bayesian Analysis with Python: A practical guide to probabilistic modeling. 3 Ed

Cover....1 Copyright....3 Foreword....5 Contributors....8 Table of Contents....12 Preface....20 Who this book is for....21 What this book covers....21 What's new in this edition?....23 Installation instructions....25 Conventions used....27 Chapter 1: Thinking Probabilistically....30 Statistics, models, and this book's approach....31 Working with data....32 Bayesian modeling....33 A probability primer for Bayesian practitioners....34 Sample space and events....34 Random variables....38 Discrete random variables and their distributions....40 Continuous random variables and their distributions....45 Cumulative distribution function....47 Conditional probability....49 Expected values....51 Bayes' theorem....52 Interpreting probabilities....55 Probabilities, uncertainty, and logic....57 Single-parameter inference....58 The coin-flipping problem....58 Choosing the likelihood....59 Choosing the prior....60 Getting the posterior....62 The influence of the prior....66 How to choose priors....67 Communicating a Bayesian analysis....70 Model notation and visualization....70 Summarizing the posterior....71 Summary....73 Exercises....74 Chapter 2: Programming Probabilistically....78 Probabilistic programming....79 Flipping coins the PyMC way....80 Summarizing the posterior....83 Posterior-based decisions....86 Savage-Dickey density ratio....87 Region Of Practical Equivalence....88 Loss functions....90 Gaussians all the way down....93 Gaussian inferences....93 Posterior predictive checks....97 Robust inferences....99 Degrees of normality....100 A robust version of the Normal model....101 InferenceData....105 Groups comparison....107 The tips dataset....109 Cohen's d....112 Probability of superiority....113 Posterior analysis of mean differences....114 Summary....116 Exercises....117 Chapter 3: Hierarchical Models....120 Sharing information, sharing priors....121 Hierarchical shifts....122 Water quality....126 Shrinkage....129 Hierarchies all the way up....132 Summary....136 Exercises....137 Chapter 4: Modeling with Lines....140 Simple linear regression....141 Linear bikes....143 Interpreting the posterior mean....145 Interpreting the posterior predictions....148 Generalizing the linear model....149 Counting bikes....150 Robust regression....152 Logistic regression....155 The logistic model....155 Classification with logistic regression....158 Interpreting the coefficients of logistic regression....160 Variable variance....162 Hierarchical linear regression....165 Centered vs. noncentered hierarchical models....168 Multiple linear regression....170 Summary....173 Exercises....174 Chapter 5: Comparing Models....176 Posterior predictive checks....177 The balance between simplicity and accuracy....183 Many parameters (may) lead to overfitting....183 Too few parameters lead to underfitting....185 Measures of predictive accuracy....186 Information criteria....187 Akaike Information Criterion....188 Widely applicable information criteria....189 Other information criteria....189 Cross-validation....190 Approximating cross-validation....191 Calculating predictive accuracy with ArviZ....193 Model averaging....196 Bayes factors....197 Some observations....199 Calculation of Bayes factors....200 Analytically....200 Sequential Monte Carlo....203 Savage–Dickey ratio....204 Bayes factors and inference....207 Regularizing priors....208 Summary....210 Exercises....211 Chapter 6: Modeling with Bambi....214 One syntax to rule them all....215 The bikes model, Bambi's version....219 Polynomial regression....222 Splines....224 Distributional models....227 Categorical predictors....229 Categorical penguins....229 Relation to hierarchical models....232 Interactions....233 Interpreting models with Bambi....236 Variable selection....238 Projection predictive inference....240 Projection predictive with Kulprit....241 Summary....246 Exercises....247 Chapter 7: Mixture Models....250 Understanding mixture models....251 Finite mixture models....253 The Categorical distribution....255 The Dirichlet distribution....255 Chemical mixture....256 The non-identifiability of mixture models....258 How to choose K....260 Zero-Inflated and hurdle models....263 Zero-Inflated Poisson regression....264 Hurdle models....266 Mixture models and clustering....269 Non-finite mixture model....270 Dirichlet process....270 Continuous mixtures....276 Some common distributions are mixtures....276 Summary....277 Exercises....279 Chapter 8: Gaussian Processes....282 Linear models and non-linear data....283 Modeling functions....284 Multivariate Gaussians and functions....286 Covariance functions and kernels....287 Gaussian processes....290 Gaussian process regression....291 Gaussian process regression with PyMC....291 Setting priors for the length scale....295 Gaussian process classification....296 GPs for space flu....299 Cox processes....300 Coal mining disasters....301 Red wood....303 Regression with spatial autocorrelation....306 Hilbert space GPs....311 HSGP with Bambi....314 Summary....315 Exercises....316 Chapter 9: Bayesian Additive Regression Trees....318 Decision trees....319 BART models....321 Bartian penguins....322 Partial dependence plots....324 Individual conditional plots....325 Variable selection with BART....326 Distributional BART models....329 Constant and linear response....331 Choosing the number of trees....333 Summary....334 Exercises....334 Chapter 10: Inference Engines....336 Inference engines....337 The grid method....338 Quadratic method....341 Markovian methods....343 Monte Carlo....343 Markov chain....345 Metropolis-Hastings....346 Hamiltonian Monte Carlo....351 Sequential Monte Carlo....353 Diagnosing the samples....356 Convergence....357 Trace plot....357 Rank plot....359 , (R hat)....360 Effective Sample Size (ESS)....362 Monte Carlo standard error....364 Divergences....365 Keep calm and keep trying....367 Summary....368 Exercises....369 Chapter 11: Where to Go Next....372 Other Books You May Enjoy....383 Index....388