Final Answer:
The MAP estimate of h is obtained as hˆmap = arg max h fh|y,x, and the ML estimate is hˆml = arg max h fy|x,h.
Step-by-step explanation:
In the given scenario, the Maximum A Posteriori (MAP) estimate of the parameter h is derived by maximizing the conditional probability distribution fh|y,x, given the observed vectors y and x.
Simultaneously, the Maximum Likelihood (ML) estimate is determined by maximizing the likelihood function fy|x,h with respect to the parameter h. These estimates provide statistical inferences about the parameter h based on the observed data y and x.
Understanding the mathematical expressions for MAP and ML estimates involves the application of probability distributions and statistical independence assumptions among the variables h, x, and z. The Laplacian distribution for h, Gaussian distributions for x and z, and their independence play crucial roles in formulating these estimates.