## Sunday, November 15, 2009

### Bayes and models.

This is me talking to the pumpkin (aka thinking aloud).

I have two models.
One is that everything is noise, and has a discrete distribution over a grid.
One is that there's a pattern and predicts the future location of an event.

Bayes says the posterior probability of the model is:
P(M|E) = P(E|M)P(M) / P(E)
where
P(E) = P(E)P(M) + P(E)P(!M)

Ahhh. I realise my mistake. P(E) is not the ideal probability of the event, but the much more restricted 'probably of event in the space the P(E|M) is measured '.

In my case, where the distance between the predicted location and a movement event is being considered, the underlying distribution is the expected distance to a movement events, independent of the model.

I.e. Have no model. Just measure the expected distance from random points to movement events to build the model. Then seperately build the same model specifically for known model conforming events. That generates P(E) and P(E|M).

Doh. For some reason that took a very long to sink in.