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Preface | |
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List of examples | |
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Introduction | |
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What are Bayesian methods? | |
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What do we mean by 'health-care evaluation'? | |
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A Bayesian approach to evaluation | |
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The aim of this book and the intended audience | |
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Structure of the book | |
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Basic Concepts from Traditional Statistical Analysis | |
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Probability | |
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What is probability? | |
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Odds and log-odds | |
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Bayes theorem for simple events | |
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Random variables, parameters and likelihood | |
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Random variables and their distributions | |
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Expectation, variance, covariance and correlation | |
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Parametric distributions and conditional independence | |
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Likelihoods | |
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The normal distribution | |
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Normal likelihoods | |
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Normal approximations for binary data | |
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Normal likelihoods for survival data | |
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Normal likelihoods for count responses | |
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Normal likelihoods for continuous responses | |
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Classical inference | |
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A catalogue of useful distributions | |
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Binomial and Bernoulli | |
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Poisson | |
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Beta | |
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Uniform | |
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Gamma | |
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Root-inverse-gamma | |
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Half-normal | |
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Log-normal | |
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Student's t | |
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Bivariate normal | |
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Key points | |
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Exercises | |
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An Overview of the Bayesian Approach | |
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Subjectivity and context | |
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Bayes theorem for two hypotheses | |
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Comparing simple hypotheses: likelihood ratios and Bayes factors | |
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Exchangeability and parametric modelling | |
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Bayes theorem for general quantities | |
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Bayesian analysis with binary data | |
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Binary data with a discrete prior distribution | |
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Conjugate analysis for binary data | |
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Bayesian analysis with normal distributions | |
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Point estimation, interval estimation and interval hypotheses | |
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The prior distribution | |
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How to use Bayes theorem to interpret trial results | |
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The 'credibility' of significant trial results | |
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Sequential use of Bayes theorem | |
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Predictions | |
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Predictions in the Bayesian framework | |
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Predictions for binary data | |
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Predictions for normal data | |
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Decision-making | |
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Design | |
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Use of historical data | |
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Multiplicity, exchangeability and hierarchical models | |
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Dealing with nuisance parameters | |
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Alternative methods for eliminating nuisance parameters | |
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Profile likelihood in a hierarchical model | |
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Computational issues | |
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Monte Carlo methods | |
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Markov chain Monte Carlo methods | |
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WinBUGS | |
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Schools of Bayesians | |
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A Bayesian checklist | |
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Further reading | |
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Key points | |
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Exercises | |
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Comparison of Alternative Approaches to Inference | |
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A structure for alternative approaches | |
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Conventional statistical methods used in health-care evaluation | |
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The likelihood principle, sequential analysis and types of error | |
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The likelihood principle | |
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Sequential analysis | |
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Type I and Type II error | |
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P-values and Bayes factors | |
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Criticism of P-values | |
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Bayes factors as an alternative to P-values: simple hypotheses | |
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Bayes factors as an alternative to P-values: composite hypotheses | |
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Bayes factors in preference studies | |
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Lindley's paradox | |
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Key points | |
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Exercises | |
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Prior Distributions | |
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Introduction | |
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Elicitation of opinion: a brief review | |
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Background to elicitation | |
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Elicitation techniques | |
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Elicitation from multiple experts | |
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Critique of prior elicitation | |