A Student’s Guide to Bayesian Statistics

Supported by a wealth of learning features, exercises, and visual elements as well as online video tutorials and interactive simulations, this book is the first student-focused introduction to Bayesian statistics.

Without sacrificing technical integrity for the sake of simplicity, the author draws upon accessible, student-friendly language to provide approachable instruction perfectly aimed at statistics and Bayesian newcomers. Through a logical structure that introduces and builds upon key concepts in a gradual way and slowly acclimatizes students to using R and Stan software, the book covers:

• An introduction to probability and Bayesian inference
• Understanding Bayes’ rule
• Nuts and bolts of Bayesian analytic methods
• Computational Bayes and real-world Bayesian analysis
• Regression analysis and hierarchical methods

This unique guide will help students develop the statistical confidence and skills to put the Bayesian formula into practice, from the basic concepts of statistical inference to complex applications of analyses.

Table of Contents

Chapter 1 How Best To Use This Book
Part I An Introduction to Bayesian Inference
Chapter 2 The Subjective Worlds Of Frequentist And Bayesian Statistics
Chapter 3 Probability – The Nuts And Bolts Of Bayesian Inference

Part II Understanding the Bayesian Formula
Chapter 4 Likelihoods
Chapter 5 Priors
Chapter 6 The Devil Is In The Denominator
Chapter 7 The Posterior – The Goal Of Bayesian Inference

Part III Analytic Bayesian Methods
Chapter 8 An Introduction To Distributions For The Mathematically Uninclined
Chapter 9 Conjugate Priors
Chapter 10 Evaluation Of Model Fit And Hypothesis Testing
Chapter 11 Making Bayesian Analysis Objective?

Part IV A practical guide to doing real-life Bayesian analysis: computational Bayes
Chapter 12 Leaving Conjugates Behind: Markov Chain Monte Carlo
Chapter 13 Random Walk Metropolis
Chapter 14 Gibbs Sampling
Chapter 15 Hamiltonian Monte Carlo
Chapter 16 Stan

Part V Hierarchical models and regression
Chapter 17 Hierarchical Models
Chapter 18 Linear Regression Models
Chapter 19 Generalised Linear Models And Other Animals