| |
A Bayesian View of Some Fundamental Problems in Statistical Signal
Processing
Patrick J. Wolfe
Harvard University
Many problems in science and engineering can be reduced in essence to
the underlying statistical task of regression/classification. In this
talk I will concentrate on the former aspect and outline some important
problems in signal processing that I hope may be of interest to the
statistical community. While engineering has traditionally borrowed
from statistics, I hope to encourage more interaction by demonstrating
some ways in which applications can serve to motivate new statistical
theory and methodology. In particular, much recent work concerns itself
with Bayesian probabilistic modeling. Regularization of some sort, the
solution of ill-posed inverse problems, and optimal (or maybe just
practical) estimation and decision-making under uncertainty are
ubiquitous tasks. I will illustrate these types of problems with
examples of my own research into the modeling of audio time series, in
which Markov chain Monte Carlo methods are used to obtain point
estimates for inference. This area provides a convenient test bed for
more generally applicable techniques, and also serves to convey a sense
of the requirements of typical signal processing problems.
|