Convergence of Bayesian posterior distributions

With comparing the model of determining the true price of a product to determining the proportion of black balls in a bottom less, rotating urn, it is seen that as long as the ratio of black balls converge to the true proportion, the Bayesian updating method for the rth moment will converge to the true proportion raised to the rth power. Thus the posterior distributions converge to unit mass at the true proportion. With the knowledge of convergence a theory for speeding up the convergence rate for the Bayesian updating method was tested.