Good Math Bad Math has an excellent piece on the misunderstandings of Bayes which underlie recent credit problems.
As he points out, “the whole system of ratings and insurance for mortgage (and other) bonds is based on probability computations of how likely it is for the underlying loans to default”; but most calculations assume that the default rates of loans are independent of each other. In fact, except for individual cases of bad luck, the probability of one loan defaulting is closely linked to the probability of another – for instance many defaults are caused by interest rate rises affecting floating rate loans, and clearly the interest rate rise is the same for everyone.
So if the probability fo default on any one junk loan is 10%, the probability of default on two is not 10% times 10%, but in some circumstances 10%.
Oddly enough I was thinking yesterday about Stepen Unwins use of Bayes to “prove” the existence of God. Human reasoning is a strange thing. We can prove what we want to believe, and disprove what we dont. Making billions of dollars skews evidential criteria.