图书简介

Chapter 1: How to best use this book \\ The purpose of this book \\ Who is this book for? \\ Pre-requisites \\ Book outline \\ Route planner - suggested journeys through Bayesland \\ Video \\ Problem sets \\ Code \\ R and Stan \\ Why don’t more people use Bayesian statistics? \\ What are the tangible (non-academic) benefits of Bayesian statistics? \\ Part I: An introduction to Bayesian inference \\ Chapter 2: The subjective worlds of Frequentist and Bayesian statistics \\ Bayes’ rule - allowing us to go from the effect back to its cause \\ The purpose of statistical inference \\ The world according to Frequentists \\ The world according to Bayesians \\ Do parameters actually exist and have a point value? \\ Frequentist and Bayesian inference \\ Bayesian inference via Bayes’ rule \\ Implicit versus Explicit subjectivity \\ Chapter 3: Probability - the nuts and bolts of Bayesian inference \\ Probability distributions: helping us explicitly state our ignorance \\ Independence \\ Central Limit Theorems \\ A derivation of Bayes’ rule \\ The Bayesian inference process from the Bayesian formula \\ Part II: Understanding the Bayesian formula \\ Chapter 4: Likelihoods \\ What is a likelihood? \\ Why use ‘likelihood’ rather than ‘probability’? \\ What are models and why do we need them? \\ How to choose an appropriate likelihood? \\ Exchangeability vs random sampling \\ Maximum likelihood - a short introduction \\ Chapter 5: Priors \\ What are priors, and what do they represent? \\ The explicit subjectivity of priors \\ Combining a prior and likelihood to form a posterior \\ Constructing priors \\ A strong model is less sensitive to prior choice \\ Chapter 6: The devil’s in the denominator \\ An introduction to the denominator \\ The difficulty with the denominator \\ How to dispense with the difficulty: Bayesian computation \\ Chapter 7: The posterior - the goal of Bayesian inference \\ Expressing parameter uncertainty in posteriors \\ Bayesian statistics: updating our pre-data uncertainty \\ The intuition behind Bayes’ rule for inference \\ Point parameter estimates \\ Intervals of uncertainty \\ From posterior to predictions by sampling \\ Part III: Analytic Bayesian methods \\ Chapter 8: An introduction to distributions for the mathematically-un-inclined \\ The interrelation among distributions \\ Sampling distributions for likelihoods \\ Prior distributions \\ How to choose a likelihood \\ Table of common likelihoods, their uses, and reasonable priors \\ Distributions of distributions, and mixtures - link to website, and relevance \\ Chapter 9: Conjugate priors and their place in Bayesian analysis \\ What is a conjugate prior and why are they useful? \\ Gamma-poisson example \\ Normal example: giraffe height \\ Table of conjugate priors \\ The lessons and limits of a conjugate analysis \\ Chapter 10: Evaluation of model fit and hypothesis testing \\ Posterior predictive checks \\ Why do we call it a p value? \\ Statistics measuring predictive accuracy: AIC, Deviance, WAIC and LOO-CV \\ Marginal likelihoods and Bayes factors \\ Choosing one model, or a number? \\ Sensitivity analysis \\ Chapter 11: Making Bayesian analysis objective? \\ The illusion of the ’uninformative’ uniform prior \\ Jeffreys’ priors \\ Reference priors \\ Empirical Bayes \\ A move towards weakly informative priors \\ Part IV: A practical guide to doing real life Bayesian analysis: Computational Bayes \\ Chapter 12: Leaving conjugates behind: Markov Chain Monte Carlo \\ The difficulty with real life Bayesian inference \\ Discrete approximation to continuous posteriors \\ The posterior through quadrature \\ Integrating using independent samples: an introduction to Monte Carlo \\ Why is independent sampling easier said than done? \\ Ideal sampling from a posterior using only the un-normalised posterior \\ Moving from independent to dependent sampling \\ What’s the catch with dependent samplers? \\ Chapter 13: Random Walk Metropolis \\ Sustainable fishing \\ Prospecting for gold \\ Defining the Metropolis algorithm \\ When does Metropolis work? \\ Efficiency of convergence: the importance of choosing the right proposal scale \\ Metropolis-Hastings \\ Judging convergence \\ Effective sample size revisited \\ Chapter 14: Gibbs sampling \\ Back to prospecting for gold \\ Defining the Gibbs algorithm \\ Gibbs’ earth: the intuition behind the Gibbs algorithm \\ The benefits and problems with Gibbs and Random Walk Metropolis \\ A change of parameters to speed up exploration \\ Chapter 15: Hamiltonian Monte Carlo \\ Hamiltonian Monte Carlo as a sledge \\ NLP space \\ Solving for the sledge motion over NLP space \\ How to shove the sledge \\ The acceptance probability of HMC \\ The complete Hamiltonian Monte Carlo algorithm \\ The performance of HMC versus Random Walk Metropolis and Gibbs \\ Optimal step length of HMC: introducing the “No U-Turn Sampler” \\ Chapter 16: Stan \\ Why Stan, and how to get it \\ Getting setup with Stan using RStan \\ Our first words in Stan \\ Essential Stan reading \\ What to do when things go wrong \\ How to get further help \\ Part V: Hierarchical models and regression \\ Chapter 17: Hierarchical models \\ The spectrum from fully-pooled to heterogeneous \\ Non-centered parameterisations in hierarchical models \\ Case study: Forecasting the EU referendum result \\ The importance of fake data simulation for complex models \\ Chapter 18: Linear regression models \\ Example: high school test scores in England \\ Pooled model \\ Interactions \\ Heterogeneous coefficient model \\ Hierarchical model \\ Incorporating LEA-level data \\ Chapter 19: Generalised linear models and other animals \\ Example: electoral participation in European countries \\ Discrete parameter models in Stan

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