The Bayes’ Rule formalization is okay as far as it goes. However, I worry that this sort of analysis may be less informative than your post makes it appear.
For one thing, Bayes’ Rule requires subjective probabilities for various sorts of events you may observe. If these subjective probabilities are not reasonable, then Bayes’ rule will not give reasonable results.
For eaxmple, if Iran is actually continuing its nuclear development program at present, do you think it is likely that a Western intelligence source within the program could produce documents showing that the program had been suspended in 2003? This supposedly is one of the justifications for the current NIE assessment about the Iranian nuclear program. Bayesian analysis doesn’t remove the dispute; it merely shifts it to the assignment of subjective probabilities.
Setting aside the issue of subjective proabilities, Bayesian analysis of the sort you describe will provide a rational process for changing your mind _provided that_ the amount of information you have about the question increases over time. There is a formal mathematical idea underlying this, but the practical requirement is that the separate tests and assessments you do should be independent of one another.
If the intelligence you recieve is provided by different teams of analysts working off of different sets of data, this gives you some confidence that your information is increasing. However, if your intelligence is provided by the same people using the same information sources, then maybe you are getting little new information at all.
The problems I see in these sorts of intelligence questions come back to these two issues: How reasonable are our rules of thumb for assessing the behavior of our adversaries? How much information do we really have? Bringing Bayes’ Rule answers neither question, and may distract analysts from answering these background questions.
