Markov chain Monte Carlo methods with applications to signal processing

The last five years have witnessed a really significant increase in the awareness of numerical Bayesian methods, both in Statistics and in Signal Processing. It is now clear that many problems that could only be addressed using ad hoc methods, because of their complexity, can now be solved and these solutions can be applied to almost all areas of data and signal processing. Bayesian methods have been popular for decades. However, various approximations have been required in order to make progress because most of the integrations required within the framework have no analytical solutions apart from some simple models which usually involve Gaussian and linearity assumptions. This explains why sub-optimal, ad hoc approximations have been developed. The aim of this paper is to set out the foundations upon which modern numerical Bayesian methods are based, give one application to missing data in audio restoration and then give references to application areas that can be addressed. (C) 2001 Elsevier Science B.V. All rights reserved.