I am ultimately trying to perform a regression task - for this example, let's say I'm trying to determine the height (in pixels) of a person in an image. However, rather than doing regression, I am solving this problem by hypothesising a few different possible heights (e.g. by detecting parts of the image that look like 'head' and 'feet') and then finding which hypothesis is the most likely. For want of a better term, I am calling this 'classification for regression'.
I am using training data to learn a classifier, and my question is how the likelihood and prior can be used in this context.
In my mind, there are several pieces of information that can be levered:
Goodness of fit of the hypotheses. In this case, this might be how much the detected feet look like feet and how much the detected heads look like heads
Overall likelihood of matching. e.g. how much does the bit between the detected feet and head look like a body.
Relation to prior knowledge about body size. Assuming absolute sizes are known, this could be a normal distribution over the range of peoples' heights.
Which of these pieces of information is a prior, and which can be used to infer the likelihood? (1) and (2) seem to be likelihood data, while (3) seems to be a prior, but why not use (3) as part of the likelihood?
Are there any more general points and tips for this sort of task?