Challenging problem comparing categories...

Hi all,

I have kind of a tricky problem:confused: ... 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 ?

Any suggestions?

Thanks in advance!

Re: Challenging problem comparing categories...

1-You can normalize each row of this table so that sum of prob values=1 for each row.

2-Confidence intervals are based on probabilities already on the table

3-There are more advanced methods that instead of this table you can have probabilities contour maps on a real 2D map so that movement of bears and finding probabilities can be examined more easily.

Re: Challenging problem comparing categories...

@MaxJasper...eh... thanks I guess.

1 - obviously, this is already the case

2 - obviously, for bear types in an area. not for the unknown bear across areas

3 - probabilities contour maps are an excellent answer to something I didn't ask