ABSTRACT
This chapter provides a simple yet complete review of these methods in a signal processing context. It describes generic Monte Carlo methods which can be used to perform statistical inference in both batch and sequential contexts. The chapter illustrates their applications in solving inference problems found in digital communications and bioinformatics. In many problems encountered in signal processing, it is possible to describe accurately the underlying statistical model using probability distributions. Statistical inference can then theoretically be performed based on the relevant likelihood function or posterior distribution in a Bayesian framework. A standard approach consists of making model simplifications or crude analytic approximations in order to obtain algorithms that can be easily implemented. With the recent availability of high-powered computers, numerical simulation based approaches can now be considered and the full complexity of real problems can be addressed. The classical methods are often either not precise and robust enough or are too complex to implement.
