1.1
Probability axioms
1.2
Random variables
1.3
Probability distributions
1.4
Expectation and variance
1.5
Joint and conditional probabilities
1.6
Law of total probability
1.7
Independence
2.1
Bayes' theorem
2.2
Inverse probability
2.3
Updating beliefs
2.4
Bayesian networks
2.5
Applications in machine learning
2.6
Applications in medical diagnosis
3.1
Informative priors
3.2
Non-informative priors
3.3
Conjugate priors
3.4
Jeffreys priors
3.5
Empirical Bayes methods
4.1
Definition and properties
4.2
Maximum likelihood estimation
4.3
Likelihood principle
4.4
Likelihood ratio tests
5.1
Derivation of posterior distributions
5.2
Posterior predictive distributions
5.3
Credible intervals
5.4
Highest posterior density regions
6.1
Point estimation
6.2
Interval estimation
6.3
Hypothesis testing
6.4
Model comparison
6.5
Prediction
7.1
Monte Carlo integration
7.2
Metropolis-Hastings algorithm
7.3
Gibbs sampling
7.4
Hamiltonian Monte Carlo
7.5
Diagnostics and convergence assessment
8.1
Multilevel models
8.2
Random effects models
8.3
Shrinkage and pooling
8.4
Hyperparameters
8.5
Applications in social sciences
9.1
Bayes factors
9.2
Posterior odds
9.3
Model selection criteria
9.4
Multiple hypothesis testing
10.1
Loss functions
10.2
Risk and expected utility
10.3
Optimal decision rules
10.4
Sequential decision making
11.1
Model comparison methods
11.2
Bayesian information criterion
11.3
Deviance information criterion
11.4
Bayesian model averaging
12.1
Bayesian software packages
12.2
BUGS and JAGS
12.3
Stan
12.4
PyMC
12.5
R packages for Bayesian analysis