In this chapter we motivate the philosophy of Bayesian processing from a probabilistic perspective. We show the coupling between model-based signal processing (MBSP) incorporating the a priori knowledge of the underlying processes and the Bayesian framework for specifying the distribution required to develop the processors. The idea of the sampling approach evolving from Monte Carlo (MC) and Markov chain Monte Carlo (MCMC) methods is introduced as a powerful methodology for simulating the behavior of complex dynamic processes and extracting the embedded information required. The main idea is to present the proper perspective for the subsequent chapters and construct a solid foundation for solving signal processing problems.
1.2 BAYESIAN SIGNAL PROCESSING
The development of Bayesian signal processing has evolved in a manner proportional to the evolution of high performance/high throughput computers. This evolution has led from theoretically appealing methods to pragmatic implementations capable of providing reasonable solutions for nonlinear and highly multi-modal (multiple distribution peaks) problems. In order to fully comprehend the Bayesian perspective, especially for signal processing applications, we must be able to separate our thinking and in a sense think more abstractly about probability distributions without worrying about how these representations can be “applied” to realistic processing problems. Our motivation is to first present the ...