Title Page Copyright and Credits Bayesian Analysis with Python Second Edition Dedication About Packt Why subscribe? Packt.com Foreword Contributors About the author About the reviewer Packt is searching for authors like you Preface Who this book is for What this book covers To get the most out of this book Download the example code files Download the color images Conventions used Get in touch Reviews Thinking Probabilistically Statistics, models, and this book's approach Working with data Bayesian modeling Probability theory Interpreting probabilities Defining probabilities Probability distributions Independently and identically distributed variables Bayes' theorem Single-parameter inference The coin-flipping problem The general model Choosing the likelihood Choosing the prior Getting the posterior Computing and plotting the posterior The influence of the prior and how to choose one Communicating a Bayesian analysis Model notation and visualization Summarizing the posterior Highest-posterior density Posterior predictive checks Summary Exercises Programming Probabilistically Probabilistic programming PyMC3 primer Flipping coins the PyMC3 way Model specification Pushing the inference button Summarizing the posterior Posterior-based decisions ROPE Loss functions Gaussians all the way down Gaussian inferences Robust inferences Student's t-distribution Groups comparison Cohen's d Probability of superiority The tips dataset Hierarchical models Shrinkage One more example Summary Exercises Modeling with Linear Regression Simple linear regression The machine learning connection The core of the linear regression models Linear models and high autocorrelation Modifying the data before running Interpreting and visualizing the posterior Pearson correlation coefficient Pearson coefficient from a multivariate Gaussian Robust linear regression Hierarchical linear regression Correlation, causation, and the messiness of life Polynomial regression Interpreting the parameters of a polynomial regression Polynomial regression – the ultimate model? Multiple linear regression Confounding variables and redundant variables Multicollinearity or when the correlation is too high Masking effect variables Adding interactions Variable variance Summary Exercises Generalizing Linear Models Generalized linear models Logistic regression The logistic model The Iris dataset The logistic model applied to the iris dataset Multiple logistic regression The boundary decision Implementing the model Interpreting the coefficients of a logistic regression Dealing with correlated variables Dealing with unbalanced classes Softmax regression Discriminative and generative models Poisson regression Poisson distribution The zero-inflated Poisson model Poisson regression and ZIP regression Robust logistic regression The GLM module Summary Exercises Model Comparison Posterior predictive checks Occam's razor – simplicity and accuracy Too many parameters leads to overfitting Too few parameters leads to underfitting The balance between simplicity and accuracy Predictive accuracy measures Cross-validation Information criteria Log-likelihood and deviance Akaike information criterion Widely applicable Information Criterion Pareto smoothed importance sampling leave-one-out cross-validation Other Information Criteria Model comparison with PyMC3 A note on the reliability of WAIC and LOO computations Model averaging Bayes factors Some remarks Computing Bayes factors Common problems when computing Bayes factors Using Sequential Monte Carlo to compute Bayes factors Bayes factors and Information Criteria Regularizing priors WAIC in depth Entropy Kullback-Leibler divergence Summary Exercises Mixture Models Mixture models Finite mixture models The categorical distribution The Dirichlet distribution Non-identifiability of mixture models How to choose K Mixture models and clustering Non-finite mixture model Dirichlet process Continuous mixtures Beta-binomial and negative binomial The Student's t-distribution Summary Exercises Gaussian Processes Linear models and non-linear data Modeling functions Multivariate Gaussians and functions Covariance functions and kernels Gaussian processes Gaussian process regression Regression with spatial autocorrelation Gaussian process classification Cox processes The coal-mining disasters The redwood dataset Summary Exercises Inference Engines Inference engines Non-Markovian methods Grid computing Quadratic method Variational methods Automatic differentiation variational inference Markovian methods Monte Carlo Markov chain Metropolis-Hastings Hamiltonian Monte Carlo Sequential Monte Carlo Diagnosing the samples Convergence Monte Carlo error Autocorrelation Effective sample sizes Divergences Non-centered parameterization Summary Exercises Where To Go Next? Other Books You May Enjoy Leave a review - let other readers know what you think