[FRIAM] Bayes Rules and Base Rates Count

[David Eric Smith]

Yes, while the clip was a nice explanation about Bayesian updating, the narrator’s statement that we need to make assumptions about prevalence seem to me like they send the viewer on a wrong turn.

It’s just an affine transform.  If you know the sensitivity and the selectivity of your test (which presumably you get from the design process before you deploy it), then the fraction of test-positives and test-negatives is just a linear function of the fraction of true-positives and true-negatives, +/- sampling noise.  In a large sample, the noise can be pushed down as a fraction of the mean.

So the test-positives and test-negatives do not equal the true-positives and true-negatives, but the former are an invertible function of the latter.  This is a simplification of a binary variable, I think.  But I haven’t taken a minute to go looking for a range of examples to show where non-invertibility starts.  I imagine again all this was largely worked out between 1500 and 1700, and is in basic stats textbooks.

I think everything I have said above is right.  I did take a minute to just write out the decomposition in terms of priors, likelihoods, and posteriors on a sheet of paper, and the linear function sits there and looks at me, so I don’t think I am spouting off the cuff.

Anyway,

Eric



> On May 1, 2020, at 8:39 AM, Tom Johnson <tom at jtjohnson.com> wrote:
> 
> Good explanation.  But it always comes back to the basic question: What are the methods and data informing our assumptions about prevalence, at this moment, in a population?  Or am I wrong?
> Tom
>  
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> On Wed, Apr 29, 2020 at 4:03 PM George Duncan <gtduncan at gmail.com <mailto:gtduncan at gmail.com>> wrote:
> Here's an easy numerical example of why conditional probabilities as employed in Bayes Rule are important:
> https://www.youtube.com/watch?v=x5FfTjJtV3E&feature=share <https://nam05.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3Dx5FfTjJtV3E%26feature%3Dshare&data=02%7C01%7Ckelsey%40edc.pitt.edu%7Cd4539c648e544adc9a3608d7ec422ca0%7C9ef9f489e0a04eeb87cc3a526112fd0d%7C1%7C1%7C637237641268432573&sdata=sSVCqTqIkvlnbjX%2BoUoUxdPdt%2FolTIHHw%2FZiJzCgCMk%3D&reserved=0> 
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