Bayes Parameter Estimation (BPE) tutorial

                                                A slecture by ECE student Haiguang Wen

                       Partially based on the ECE662 lecture material of Prof. Mireille Boutin.

 What will you learn from this slecture?

• Basic knowledge of Bayes parameter estimation
• An example to illustrate the concept and properties of BPE
• The effect of sample size on the posterior
• The effect of prior on the posterior

Introduction

Bayes parameter estimation (BPE) is a widely used technique for estimating the probability density function of random variables with unknown parameters. Suppose that we have an observable random variable X for an experiment and its distribution depends on unknown parameter θ taking values in a parameter space Θ. The probability density function of X for a given value of θ is denoted by p(x|θ ). It should be noted that the random variable X and the parameter θ can be vector-valued. Now we obtain a set of independent observations or samples S = {x1,x2,...,xn} from an experiment. Our goal is to compute p(x|S) which is as close as we can come to obtain the unknown p(x), the probability density function of X.