Robust Stochastic Predictive Analysis and Bayesian Updating

Speaker:
Jim Beck, Ph.D.
Engineering and Applied ScienceCaltechAbstractA general framework and some corresponding computational tools will be described for stochastic predictive analysis of a system that treats modeling uncertainties in the input-output relationship as well as input uncertainty. The essential modeling ingredient is a Bayesian model class, which consists of a set of stochastic predictive models (e.g. stochastic state-space models) and a prior probability distribution over this set of models that gives a measure of the relative plausibility of each of the models. Here, we utilize the Cox-Jaynes derivation of the probability axioms based on an interpreting probability P(b|c) as a quantification of the plausibility of statement b given the conditioning information in statement c. Prior robust predictive analysis for a given model class involves using the prior-weighted predictions of all the stochastic predictive models, as prescribed by the theorem of total probability. If system data is available to provide additional information, Bayes' Theorem can be used to update the probability distribution over the set of predictive models and then a posterior robust predictive analysis can be performed. To evaluate the multi-dimensional integrals involved in the robust analysis, analytical approximations and stochastic simulation methods, such as Gibbs Sampler and Metropolis-Hastings algorithms, will be described, along with their strengths and limitations. Illustrative examples will be given. If a set of candidate Bayesian model classes is prescribed, then a "super-robust" posterior predictive analysis can be performed (i.e. model class averaging) where Bayes' Theorem is used at the level of all the model classes rather than within a specific model class. This leads to a rigorous approach to model class selection where only the more probable (i.e. plausible) model classes are used to perform the predictive analysis. Illustrative examples will be given, including the problem of the best selection of possible terms in a regression equation for earthquake ground-motion attenuation; the best model class in a set of possible probabilistic Support Vector Machines, which leads to the Relevance Vector Machine; and the optimal number of modes for a linear model of a dynamic system based on dynamic test data.

Location: Kaprielian Hall (KAP) - rialian Hall, Room 203

Audiences: Everyone Is Invited

Contact: Evangeline Reyes