Abstract:
Graphical models have been an area of active research since the beginning of the twentieth century. Graphical models have wide scope of ap- plicability in various scientic elds. This paper presents applications of graph- ical models with a focus on Bayesian networks. An exploration on the basics of graph theory and probability theory which tie together to form graphical models is outlined. Markov properties, graph decompositions, and their im- plications to inference are discussed. An algorithmic software for graphical models, Netica is used to demonstrate an inference problem in medical di- agnostics. We address instances where parameters in the model are unknown, through maximum likelihood method if analytically feasible, but numerical and Markov Chain Monte Carlo methods are warranted otherwise.
