To the best of our knowledge, Norbert Wiener never actually applied Bayes' theorem in a published work; yet he perceived the logical necessity of its use as soon as one builds beyond the sampling distributions involved in his own statistical work. In the present chapter we examine some of the consequences of failing to use Bayesian methods in some very simple problems, where the paradoxes of Chapter 15 never arise.

In Chapter 16 we noted that the orthodox objections to Bayesian methods were always philosophical or ideological in nature, never examining the actual results that they give, and we expressed astonishment that mathematically competent persons would use such arguments. In order to give a fair comparison, we need to adopt the opposite tactic here, and concentrate on the demonstrable facts that orthodoxians never mention. Since Bayesian methods have been so egregiously misrepresented in the orthodox literature throughout our lifetimes, we must lean over backwards to avoid misrepresenting orthodox methods now; whenever an orthodox method does yield a satisfactory result in some problem, we shall acknowledge that fact, and we shall not deplore its use merely on ideological grounds.