COMPUTATIONAL RESEARCH in BOSTON and BEYOND (CRIBB)

Many problems arising in science and engineering are effectively ones of statistical inference, and in all but the simplest cases the associated models may not admit analytical solutions. In this talk I will describe simulation-based Monte Carlo methods for inference, in particular two important classes of algorithms for stochastic computation: a batch methodology known as Markov chain Monte Carlo and an on-line one termed sequential Monte Carlo. Many interpretations are possible, but I shall frame my discussion in terms of the Bayesian paradigm, whereby all inference stems from a description of the (posterior) probability distribution associated with a given model after having observed the data in question. I will illustrate these simulation methodologies with examples of my own research into statistical audio signal processing, in which case they are used to obtain point estimates of salient parameters. This application area is not only interesting and important in its own right, but also provides a convenient test bed for more generally applicable techniques of time series modeling.