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Math Help - Challenging problem comparing categories...

  1. #1
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    Question Challenging problem comparing categories...

    Hi all,

    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 ?

    Any suggestions?
    Thanks in advance!
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  2. #2
    Senior Member MaxJasper's Avatar
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    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.
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  3. #3
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    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
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