By Robert Hogg, Elliot A. Tanis

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Extra resources for Instructor's Solutions Manual: Probability and Statistical Inference, Seventh Edition

Example text

Ani. In the Forbes case, for instance, the set of supposed facts asserted is not {‘Forbes did it’, ‘Forbes did it’} ¼ {‘Forbes did it’}, which is a singleton, but h‘Forbes did it’, ‘Forbes did it’i, which is not. Since the latter is not a singleton, Rescher’s Principle is not applicable. Applying Lewis’s congruence deﬁnition, moreover, gives exactly the desired result: assuming the one element of this ordered set as given premiss raises the probability of the other; indeed it raises it to 1. The latter fact can even be taken in support of ascribing to Lewis acceptance of (3): full agreement is not just coherent; it is very coherent.

The coherence of a system of beliefs is decreased in proportion to the presence of unexplained anomalies in the believed content of the system. While this account has many merits, it is also unclear on several crucial points. For one, how are we to measure the number and strength of inferential connections? How can we assess whether subsystems are ‘relatively unconnected’ or not? What is the connection between coherence as an absolute notion (see the ﬁrst criterion) and coherence as a matter of degree (see the other criteria)?

5, the posterior joint probability of what is agreed upon depends (1) on the number n of equally probable suspects or equivalently the prior probability of the agreed proposition and (2) on the credibility i that each report has, taken in isolation. e. provided the credibility parameter i is held ﬁxed. Suppose for instance that we ﬁx i at 2=10. 861. Later we will consider other witness scenarios where we do not have this simple relationship between the prior and the posterior. However, it will still be true that the latter depends on the former, albeit in more complex ways.