Fuzzy MLE and Fisher Information Analogue?

Stephen Paul King (stephenk1@home.com)
Mon, 10 May 1999 15:38:18 +0200 (MET DST)

Hi all,

> Subject:
> Re: Fisher information
> Date:
> Wed, 5 May 1999 10:53:19 -0400
> From:
> "Christopher Brown" <cbrown@chem1.chem.dal.ca>
> To:
> <stephenk1@home.com>

>> I have assembled a link page on Fisher information and have a
>>definition: "The Fisher Information about a parameter is defined to
>>be \theta the expectation of the second derivative of the
>>loglikelihood."
>>http://members.home.net/stephenk1/Outlaw/fisherinfo.html
>> But I am still needing an intuitive grasp of that it means. :)

>In short, when you estimate a parameter, you estimate it's value usually by taking
>the estimate of the parameter to be the maximum likelihood value. So we get an
>estimated parameter value, and we know it's uncertain. Imagine it as a normal
>distribution, the center of which is our estimate, and the variance of which is the
>uncertainty we have in the location of our estimate. The Fischer Information
>essentially describes how sharp that normal distribution is around our estimate.
>More Fischer Information roughly implies a more informative estimate (i.e. tighter
>spread around the MLE).

>Hope it helps,
>CDB

Is there a fuzzy logical version of this, e.g. the MLE and the
consequent definition of the Fisher Information? Also, is there a way
to parametrize the sharpness of the fuzzy normal distribution, perhaps
as a function of the \theta parameter?

Kindest regards,

Stephen

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