Structural learning of Bayesian Networks

1. Bayesian Networks

1.1. Joint distribution

1.2. Conditional distributions

1.2.1. P( X_i | Pa( X_i ) )

1.2.1.1. Distribution known

1.2.1.2. Parameters \Phi to be obtained

1.3. Bayes' theorem

1.4. Marginal likelihood

1.4.1. p( X | G )

1.4.1.1. Heckerman et al. 1995

1.4.1.2. Dirichlet distribution

1.5. Posterior distribution

1.5.1. P( G | X )

2. Structural learning

2.1. Markov Chain Monte Carlo

2.1.1. Metropolis-Hastings

2.1.1.1. Proposal distribution

2.1.1.1.1. Q( G'; G )

2.1.1.2. Acceptance probability

2.1.2. Stationary distribution

2.2. Informative priors

2.2.1. Locally informative priors

2.2.2. Prior based proposals