Temporal Reasoning with Probabilities

This paper explores the use of probabilistic graphical modelling to represent and reason about temporal knowledge. The idea is that of representing concepts and variables involved diagramatically, by means of a directed graph, called an influence diagram (/D), designed to capture probabilistic dependencies between those variables. Statistical models of progression in time, such as semi­ Marko� prociSses, can be tra11Slated inlo 'pieces' of influence diagram, and then embedded inlo large influence diagrams represenling bodies of knowledge. In this way, we can include statistical modelling of time inlo expert systems. Stochastic simulation (Monte Carlo) approaches are proposed for probability propagation on the obtained diagrams. In particular, a combination of two techniques, known as 'Gibbs salmpling' and rorward sampling' , is discussed.