joseph_c comments on E.T. Jaynes Probability Theory: The logic of Science I

[joseph_c]

$$\frac{P(H\mid DX)}{P(\overline{H}\mid DX)}=\frac{\frac{P(D\mid HX)P(H\mid X)}{P(D\mid X)}}{\frac{P(D\mid \overline{H}X)P(\overline{H}H\mid X)}{P(D\mid X)}}$$$$O(H\mid DX)=O(H\mid X)\frac{P(D\mid HX)}{P(D\mid \overline{H}X)}$$

The trick here is that both equations contain $P(D\mid H)$ which is the hardest to calculate, and that number drops out when we divide the equations.

You have a couple typos here. The first centered equation should not have a $P(\bar H H | X)$ but instead have $P(\bar H | X)$, and the inline expression should be $P(D | X)$, not $P(D | H)$.

[Gunnar_Zarncke]

Also, the second $P(intact∣orc,X)$ should be $P(intact∣goblin,X)$