Bayesian Analysis with Python电子书

Title Page

Copyright and Credits

Bayesian Analysis with Python Second Edition

Dedication

About Packt

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Packt.com

Foreword

Contributors

About the author

About the reviewer

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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?

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