I have kind of a tricky problem ... hope someone can help me!
Suppose a couple of ethologists checked the probability distributions of categories of bear in some areas (let's say 50), for example:
brown black polar grizzly other area 1 0.11 0.23 0.00 0.49 0.17 area 2 0.51 0.00 0.00 0.39 0.10 area 3 0.06 0.00 0.94 0.00 0.00 ... ... ... ... ... ... area 50 0.30 0.18 0.02 0.19 0.31
The distributions within a category are not necessarily normal (e.g. the polar bear).
Now a remote system tracks a single bear, across a limited number of areas (let's say 4). The system doesn't know which kind of bear it is, so it is unknown to which category it belongs beforehand.
Is there a way to determine the probability and certainty (confidence) the bear will belong to a category, given the areas the bear is found in?
To clarify the reasoning: consider three adjacent areas. The left area has a high occurrence of brown bears, the right area a high occurrence of black bears and the middle area both black and brown are equally distributed. Suppose a bear moves around only in the middle and right areas, it would seem the probability that bear is a black bear increases. But how to calculate this?
I was first thinking of using a Wilcoxon Signed test for each category combination, or should I use Fisher's exact test... and some post-hoc test ?
Thanks in advance!