Maximum a posteriori probability estimate (MAP)

Suppose we have a hypothesis space $H$ and we want to pick the best hypothesis given some data $D$. Further more suppose we have prior belief about the likelihood of each hypothesis represented by a probability distribution over $H$. The maximum a posteriori probability estimate is

$$h_{MAP} = \mbox{arg}\max_{h \in H} \ \mathbb{P}[D \ \vert \ h] \ \mathbb{P}[h].$$