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This is a follow-up question to one I asked on Math.SE:

What are the measurement units of Fisher information? (Dimensional Analysis)

When doing calculations with Fisher information in practice, does one report the values of the Fisher information in terms of the units of the parameter being estimated? Or does one treat it like a dimensionless quantity?

I only know about Fisher information from a theoretical context so far, but I am not sure how I would go about using it in research and what type of quantity I should treat it as.

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    $\begingroup$ I'm confused about what you're asking here: given that it's not, in general, a dimensionless quantity (as explained in the accepted answer at math.stackexchange.com/q/1892907/59351) what exactly would it mean to "treat it like" one? Reporting the maximum-likelihood estimate of & Fisher information (or anything derived from it) for the rate parameter of an exponential distribution, say, without mentioning that the distribution is of time-to-event data in seconds would of course be useless. $\endgroup$ – Scortchi - Reinstate Monica Aug 19 '16 at 9:23
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    $\begingroup$ @Scortchi your comment is basically what I am looking for in an answer "reporting... without mentioning that the distribution is of time-to-event data in [units] would of course be useless". I suspected that, but it wasn't obvious me to that this would be the case, i.e. I would struggle to justify the "of course" part. Perhaps this is more an issue of confidence on my part than of genuine confusion, however. $\endgroup$ – Chill2Macht Aug 19 '16 at 19:16
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    $\begingroup$ @Scortchi, let me know if you decide converting your comment into an answer. Apparently, it solved OP's question. Tks. $\endgroup$ – Andre Silva Sep 19 '16 at 16:21
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Partially answered in comments:

I'm confused about what you're asking here: given that it's not, in general, a dimensionless quantity (as explained in the accepted answer at https://math.stackexchange.com/questions/1892907/what-are-the-measurement-units-of-fisher-information-dimensional-analysis) what exactly would it mean to "treat it like" one? Reporting the maximum-likelihood estimate of & Fisher information (or anything derived from it) for the rate parameter of an exponential distribution, say, without mentioning that the distribution is of time-to-event data in seconds would of course be useless. – Scortchi

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    $\begingroup$ I asked this question three years ago, so to be honest I don't remember what my exact reasoning/motivation was for doing so at the time. Right now I agree with you more than me from three years ago, if that means anything. $\endgroup$ – Chill2Macht Jan 30 '19 at 18:13

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