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.