Examples of Bayesian Inference

6 Examples of Bayesian Inference Example. Gaussian Random Variable 

Consider a Gaussian random variable X with mean fx and variance. These two parameters are unknown and they are the uncertain parameters for identification. Independent measurements of the random variable X are available T = x, X2. x so the likelihood function is given by  

To obtain the joint posterior PDF, it requires only the values of Yln=i 

Similarly, the most probable value (mode) for the variance parameter can be obtained by solving 9/(/u, a T), C) da = 0  

by observing Equation (2.39), the conditional PDF p a p, T , C) follows the inverse Gamma distribution, denoted by IG(a, P)  

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