Introduction to “Cuts in Bayesian graphical models” by M. Plummer

Cuts in Bayesian graphical models

The cut function defined by theOpenBUGS software is described as a “valve” that prevents feedback in Bayesian graphical models. It is shown that theMCMC algorithm applied by OpenBUGS in the presence of a cut function does not converge to a well-defined limiting distribution. However, it may be improved by using tempered transitions. The cut algorithm is compared with multiple imputation as a go...

Introduction to Graphical Models, Hidden Markov Models and Bayesian Networks

Introduction to Graphical Models

Two real-valued or vector-valued random variables X, Y are independent for probability measure P (written: X ⊥ Y [P ]) if for all sets A and B, P[X ∈ A, Y ∈ B] = P[X ∈ A] · P[Y ∈ B]. For jointly discrete or jointly continuous random variables this is equivalent to factoring of the joint probability mass function or probability density function, respectively. The variables X and Y are conditiona...

Introduction to Probabilistic Graphical Models

9.1 Naive Bayes 9.1.

An introduction to graphical models

Graphical models are a marriage between probability theory and graph theory. They provide a natural tool for dealing with two problems that occur throughout applied mathematics and engineering – uncertainty and complexity – and in particular they are playing an increasingly important role in the design and analysis of machine learning algorithms. Fundamental to the idea of a graphical model is ...