Graphical Models, Bayesian Belief Networks, Gibbs sampler

by Shruti Gupta for RooStats

Various fields including high speed statistical physics, bio-informatics, speech processing and others involve the use of huge models of variables linked in complex ways. Probabilistic Graphical Models provide a general methodology for solving these problems. Bayesian networks, are one class of these models. The present document proposes a full methodology to implement these networks and sampling techniques and integrate them with RooStats. The aim is to equip RooStats with a new statistical tool, in the form of these Bayesian Belief Networks, in order to reduce the complexity being faced in the existing methods. The document suggests a method to construct these networks efficiently from given data and probability density functions as currently represented in RooStats., according to: An Algorithm for Bayesian Belief Network Construction from Data depending on present probability density functions, a method to store them , and lastly, implementations of a sampling algorithm to further use these networks. The sampling algorithm I propose to implement as a part of the project: Adaptive Importance Sampling, AIS-BN algorithm.