Bayesian Analysis with Python

Cover
 Copyright
 Credits
 About the Author
 About the Reviewer
 www.PacktPub.com
 Table of Contents
 Preface
 Chapter 1: Thinking Probabilistically --
A Bayesian Inference Primer
 Statistics as a form of modeling
 Exploratory data analysis
 Inferential statistics
 Probabilities and uncertainty
 Probability distributions
 Bayes' theorem and statistical inference
 Single parameter inference
 The coin-flipping problem
 The general model
 Choosing the likelihood
 Choosing the prior
 Getting the posterior
 Computing and plotting the posterior
 Influence of the prior and how to choose one. Communicating a Bayesian analysisModel notation and visualization
 Summarizing the posterior
 Highest posterior density
 Posterior predictive checks
 Installing the necessary Python packages
 Summary
 Exercises
 Chapter 2: Programming Probabilistically --
A PyMC3 Primer
 Probabilistic programming
 Inference engines
 Non-Markovian methods
 Markovian methods
 PyMC3 introduction
 Coin-flipping, the computational approach
 Model specification
 Pushing the inference button
 Diagnosing the sampling process
 Summarizing the posterior
 Posterior-based decisions
 ROPE
 Loss functions
 Summary. Keep readingExercises
 Chapter 3: Juggling with Multi-Parametric and Hierarchical Models
 Nuisance parameters and marginalized distributions
 Gaussians, Gaussians, Gaussians everywhere
 Gaussian inferences
 Robust inferences
 Student's t-distribution
 Comparing groups
 The tips dataset
 Cohen's d
 Probability of superiority
 Hierarchical models
 Shrinkage
 Summary
 Keep reading
 Exercises
 Chapter 4: Understanding and Predicting Data with Linear Regression Models
 Simple linear regression
 The machine learning connection
 The core of linear regression models. Linear models and high autocorrelationModifying the data before running
 Changing the sampling method
 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 variablesAdding interactions
 The GLM module
 Summary
 Keep reading
 Exercises
 Chapter 5: Classifying Outcomes with Logistic Regression
 Logistic regression
 The logistic model
 The iris dataset
 The logistic model applied to the iris dataset
 Making predictions
 Multiple logistic regression
 The boundary decision
 Implementing the model
 Dealing with correlated variables
 Dealing with unbalanced classes
 How do we solve this problem?
 Interpreting the coefficients of a logistic regression
 Generalized linear models
 Softmax regression or multinomial logistic regression.