Dynamic Inference

Abstract

SummaryWe consider a model for dynamic uncertain processes. The underlying statistical parameters of a stochastic process that produces observable outputs are themselves allowed to change at times generated by another stochastic process. We would like to make probability assignments to future outputs of the process, given only the past outputs. We develop the inferential relations for the case where the changes of parameters are governed by a renewal process, and where the process that generates observables depends only on its present parameters. We illustrate these results using an example with a Bernoulli observable distribution, a beta parameter distribution, and a geometric distribution for the time between parameter changes. Possible applications of the general class of dynamic inferences models range from marketing to antisubmarine warfare.