An Introduction to Monte Carlo Methods for Bayesian Data Analysis

Often it is natural to describe a signal processing or dynamical modeling problem in terms of probability distributions, and in particular tin Bayesian terms, where the unknown parameters are taken to be random variables and their distributions are updated by applying Bayes’ theorem to gave the distributions of the parameters conditional on the data. In the past, it was not possible to handle many non-trivial problems in this way because the distributions seldom took tractable forms. Considerable progress has been made in recent years in applying Monte Carla methods to overcome this, and in this chapter we describe some of the new results that have made a full Bayesian approach to signal processing tractable as well as powerful.

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