Bayes factors¶

In bayes factor we compare 2 hypothesis by comparing they marginal likelihoods:

\[BF_{1,0} \triangleq \frac{p(D|M_1)}{p(D|M_2)} = \frac{p(M_1|D)}{p(M_0|D)} / \frac{p(M_1)}{p(M_0)} \]

If we assume that \(p(M_0) = p(M_1) = 0.5\) than the equation simplifies to:

\[p(M_0|D) = \frac{1}{BF_{1,0} +1 }\]

Now we can use this ration, to say which model is better or worse, and by how much.

Computing¶

We frame them as hierachical models.