In this Chapter we deﬁne the two methods of parameter estimation which are used in this text, namely, marginal posterior mean and joint maximum a posteriori estimators. Typically these estimators are found by integration and diﬀerentiation to arrive at explicit equations for their computation. There are often instances where explicit closed form equations are not possible. In these instances, numerical integration and maximization estimation procedures are required. The typical explicit integration and diﬀerentiation procedures are discussed as are the numerical estimation procedures used. The numerical estimation procedures are Gibbs sampling for sampling based marginal posterior means and the iterated conditional modes algorithm (ICM) for joint maximum posterior (joint posterior modal) estimates.