Chapter 12 – Bayesian approaches

Publisher Summary The Bayesian approach is unique in that it treats the problem as an inference problem, and incorporates prior information in both the signal model and the prior probabilities of the model parameters. Bayes' theorem can be used as a mathematical tool to update the state of knowledge about the problem prior to making observations to a posterior state of knowledge after making observations. Source separation methods based on the Bayesian approach and the incorporation of prior information have demonstrated successful results in real-world problems in situations where classical blind source separation methods have failed. This chapter discusses the application of Bayesian methods to the two data types commonplace in source separation, namely time-series and digital images, and presents how the Bayesian methodology readily enables one to extend these methods to source localization and characterization. An important step in any source separation method is the appropriate modeling of the sources. Whichever model is selected, it will depend on a set of parameters, which are typically called hyperparameters as they are extra parameters needed to describe model parameters.

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