In several previous discussions we inserted parenthetic remarks to the effect that ‘there is still an essential point missing here, which will be supplied when we take up decision theory’. However, in postponing the topic until now, we have not deprived the reader of a needed technical tool, because the solution of the decision problem was, from our viewpoint, so immediate and intuitive that we did not need to invoke any underlying formal theory.

Inference vs. decision

The situation of appraising inference vs. decision arose as soon as we started applying probability theory to our first problem. When we illustrated the use of Bayes' theorem by sequential testing in Chapter 4, we noted that there is nothing in probability theory per se which could tell us where to put the critical levels at which the robot changes its decision: whether to accept the batch, reject it, or make another test. The location of these critical levels obviously depends in some way on value judgments as well as on probabilities; what are the consequences of making wrong decisions, and what are the costs of making further tests?