A Student’s Guide to Bayesian Statistics. (2018)

• Record Type: Book
• Further Information: Note: Ben Lambert.
• Authors: Lambert, Ben
• Contents: 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;
• Edition: 1st
• Publisher Details: London : SAGE Publications Ltd
• Publication Date: 2018
• Extent: 1 online resource (512 pages)
• Languages: English
• ISBNs: 9781526418289; 1526418282
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.