Pattern Recognition, 4th Edition

2.5.3. Bayesian Inference

Both methods considered in the preceding subsections compute a specific estimate of the unknown parameter vector θ. In the current method, a different path is adopted. Given the set X of the N training vectors and the a priori information about the pdf p(θ), the goal is to compute the conditional pdf p(x|X). After all, this is what we actually need to know. To this end, and making use of known identities from our statistics basics, we have the following set of relations at our disposal:(2.70)with(2.71)(2.72)The conditional ...