Preface
1
Quick start
1.1
Popular methods may fail
1.2
Model uncertainty
1.3
Are computations always hard?
1.4
Logistic regression
1.5
Non-linear effects via Generalized Additive Models (GAMs)
2
Bayesian model selection and averaging
2.1
A simplest example
2.2
Bayesian model selection
2.3
Bayesian model averaging
2.4
Prediction problems
2.5
Prior on models
2.5.1
Binomial prior
2.5.2
Beta-Binomial prior
2.5.3
Complexity prior
2.5.4
A simple example
2.6
Prior on coefficients
2.6.1
Jeffreys-Lindley-Bartlett paradox
2.6.2
Non-local priors
2.6.3
Heavy-tails and finite sample consistency
2.6.4
Objective Bayes
2.7
Exercises
2.8
Exercise solutions
3
Bayesian computation
3.1
Marginal likelihoods and model-specific posteriors
3.2
Model search
3.3
MCMC basics
3.4
Gibbs sampling
3.5
Locally-informed proposals
3.6
Hamiltonian Monte Carlo
3.7
Exercises
4
L0 criteria
4.1
Basics
4.2
Theoretical considerations
4.3
Model search
4.3.1
Optimization methods
4.3.2
MCMC
4.4
Exercises
5
Generalized linear models
5.1
Prior on coefficients
5.2
Approximating the marginal likelihood
5.3
MCMC model search
5.4
Assessing MCMC convergence
6
Generalized additive models
7
Empirical Bayes for transfer learning
8
Survival data
9
Gaussian graphical models
10
Gaussian mixture models
High-dimensional model choice. A hands-on take
8
Survival data
To be added.