Simulation Approaches for Calculations in Directed Graphical Models
Abstract
In formulating models for a complex system graphical representation is an effective tool. When the components of the system are viewed as random variables, directed graphical models detail the nature of the dependence among them. Moreover, if for each variable the conditional distribution is provided according to the graph, the joint distribution is uniquely determined. Natural questions arise about the static behavior of the system under such specification as well as its response to information (observed levels of some of the variables). Answers to these questions require the ability to calculate arbitrary marginal and conditional distributions. In complex cases (high dimensional structures) such calculations require high dimensional integrations and/or summations. Most of the work to date has taken advantage of properties of directed graphs to facilitate exact calculations but is limited with regard to distributional assumptions and feasible system size. Monte Carlo methods for such calculations can accommodate much larger system size with arbitrary dependence structure and distributional forms yielding approximations which can be as accurate as desired. It is the objective of this paper to detail such methodology. An illustration is provided using a diagnostic system for congenital heart disease in neonates.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 12, 1993
- Accession Number
- ADA274825
Entities
People
- Alan E. Gelfand
- Constantin T. Yiannoutsos
Organizations
- Stanford University