This book is concerned with the processing of signals that have been sampled and digitized. The authors present algorithms for the optimization, random simulation, and numerical integration of probability densities for applications of Bayesian inference to signal processing. In particular, methods are developed for the computation of marginal densities and evidence, and are applied to previously intractable problems either involving large numbers of parameters or where the signal model is of a complex form. The emphasis is on the applications of these methods notably to the restoration of digital audio recordings and biomedical data. After a chapter which sets out the main principles of Bayesian inference applied to signal processing, subsequent chapters cover numerical approaches to these techniques, the use of Markov chain Monte Carlo methods, the identification of abrupt changes in data using the Bayesian piecewise linear model, and identifying missing samples in digital audio signals.