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1.1
1.2 Definition of statistical models
1.3 Bayes theorem
1.4 Model-based Bayesian inference
1.5
Introduction: Bayesian modeling in the 2 1 st century
Inference using conjugate prior distributions
1.5.6 Other conjugate prior distributions
1.5.7 Illustrative examples
Inference for the Poisson rate of count data
Inference for the success probability of binomial data
Inference for the mean of normal data with known variance
Inference for the mean and variance of normal data
Inference for normal regression models
1.6 Nonconjugate analysis
Problems
2 Markov Chain Monte Carlo Algorithms in Bayesian Inference
2.1 Simulation, Monte Carlo integration, and their implementation in
Bayesian inference
Markov chain Monte Carlo methods
2.2.1 The algorithm
2.2.2 Terminology and implementation details
2.3 Popular MCMC algorithms
2.3.1 The Metropolis-Hastings algorithm
2.3.2 Componentwise Metropolis-Hastings
2.3.3 The Gibbs sampler
2.3.4 Metropolis within Gibbs
2.3.5 The slice Gibbs sampler
2.3.6
2.2
A simple example using the slice sampler
11.1 Prior predictive distributions as measures of model comparison: Posterior
model odds and Bayes factors
1 1.2 Sensitivity of the posterior model probabilities: The Lindley-Bartlett
paradox
1 1.3 Computation of the marginal likelihood
1 1.3.1 Approximations based on the normal distribution
11.3.2 Sampling from the prior: A naive Monte Carlo estimator
11.3.3 Sampling from the posterior: The harmonic mean estimator
11.3.4 Importance sampling estimators
11.3.5 Bridge sampling estimators
11.3.6 Chib’s marginal likelihood estimator
11.3.7 Additional details and further reading
11.4 Computation of the marginal likelihood using WinBUGS
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