Mathematical Foundations for Signal Processing, Communications, and Networking

Chapter 12  Monte Carlo Methods for Statistical Signal Processing

Xiaodong Wang^‡

^‡ Columbia University, New York, USA

12.1    Introduction

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. However, most problems encountered in applied research require non-Gaussian and/or nonlinear models in order to correctly account for the observed data. In these cases, it is typically impossible to obtain the required statistical estimates of interest, e.g., maximum likelihood, conditional expectation, in ...