Bayesian Analysis with Python
Osvaldo Martin更新时间：2021-08-20 10:14:06
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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
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更新时间：2021-08-20 10:14:06