BabyGate - Palin's supposed "fake" pregnancy

Some are speculating that Palin's "son" Trig is really the child of Palin's daughter Bristol. These speculators think that perhaps Sarah Palin faked her pregnancy to protect her daughter. The evidence supporting babygate consists of photos of Sarah taken just before Trig was born in which Sarah doesn't seem pregnant, and Sarah's busy schedule just before Trig was born which doesn't seem consistent with the limited stamina of a woman about to give birth.

But because Trig has Down Syndrome probability analysis indicates that the baby is almost certainly Sarah's. As a 44 year old there was a 1 in 52 chance that Sarah Palin would have a baby with Down Syndrome. In contrast, as a 17 year old Bristol had only a 1 in 1654 chance of having a Down Syndrome baby.

Let's do some Bayesian math. Imagine a strange lottery takes place. 90% of the time under this lottery Sarah will have a baby and raise it herself. The other 10% of the time Bristol will have a child and Sarah will pretend that the child is hers. So given just this information there is a 10% chance that the baby is Bristol's. But now pretend that someone tells you the baby has Down Syndrome. If I have done my Bayesian calculations correctly then the chances of the baby being Bristol's falls to .35%.

So this means that if we initially assume there is a 10% chance that the baby is Bristol's (which is surely much, much too high) the chance of the baby being Bristol's drops to .35% after we learn that the baby has Down Syndrome.

The above analysis is not complete because it ignores some information such as the relative probabilities of Bristol and Sarah having a baby and the chance that Sarah would agree to be McCain's running mate given that she is hiding the fact that Trig is not hers.

If, however, Trig really is Sarah's grandson, then Sarah becomes an even BETTER running mate for McCain because the hypothetical deception hurt no one but shows Sarah's devotion to her children.