<html><head><meta http-equiv="Content-Type" content="text/html; charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class="">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.<div class=""><br class=""></div><div class="">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.</div><div class=""><br class=""></div><div class="">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.</div><div class=""><br class=""></div><div class="">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.</div><div class=""><br class=""></div><div class="">Anyway,</div><div class=""><br class=""></div><div class="">Eric</div><div class=""><br class=""></div><div class=""><br class=""><div><br class=""><blockquote type="cite" class=""><div class="">On May 1, 2020, at 8:39 AM, Tom Johnson <<a href="mailto:tom@jtjohnson.com" class="">tom@jtjohnson.com</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><div dir="ltr" class="">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?<div class="">Tom<br class=""><div class=""> <br clear="all" class=""><div class=""><div dir="ltr" class="gmail_signature" data-smartmail="gmail_signature"><div dir="ltr" class=""><div class=""><div dir="ltr" class=""><div class=""><div dir="ltr" class=""><div class=""><div dir="ltr" class=""><div class=""><div dir="ltr" class=""><div class=""><div dir="ltr" class=""><div class=""><div dir="ltr" class=""><div class=""><br class="">============================================<br class="">Tom Johnson - <a href="mailto:tom@jtjohnson.com" target="_blank" class="">tom@jtjohnson.com</a><br class="">Institute for Analytic Journalism -- Santa Fe, NM USA<br class="">505.577.6482(c) 505.473.9646(h)<br class=""><a href="http://nmfog.org/" target="_blank" class=""><b class=""><font color="#0b5394" class="">NM Foundation for Open Government</font></b></a><br class=""><b class=""><font color="#0000ff" class="">Check out <a href="https://www.facebook.com/pages/Its-The-Peoples-Data/1599854626919671" target="_blank" class="">It's The People's Data</a></font></b> </div><div class="">============================================</div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div><br class=""></div></div></div><br class=""><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Wed, Apr 29, 2020 at 4:03 PM George Duncan <<a href="mailto:gtduncan@gmail.com" class="">gtduncan@gmail.com</a>> wrote:<br class=""></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr" class=""><div class="gmail_default" style="font-family:tahoma,sans-serif;font-size:large">Here's an easy numerical example of why conditional probabilities as employed in Bayes Rule are important:</div><div class="gmail_default" style="font-family:tahoma,sans-serif;font-size:large"><a href="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" style="font-family:Arial,Helvetica,sans-serif;font-size:small" target="_blank" class="">https://www.youtube.com/watch?v=x5FfTjJtV3E&feature=share</a> </div><div class="gmail_default" style="font-family:tahoma,sans-serif;font-size:large"> <br class=""></div><div class=""><div dir="ltr" class=""><div dir="ltr" class=""><div class=""><div dir="ltr" class=""><div class=""><div dir="ltr" class=""><div dir="ltr" class=""><div dir="ltr" class=""><div dir="ltr" class=""><div class="">George Duncan</div><div class="">Emeritus Professor of Statistics, Carnegie Mellon University<br class=""><a href="http://georgeduncanart.com/" target="_blank" class="">georgeduncanart.com</a></div><div class="">See posts on Facebook, Twitter, and Instagram</div>
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<div class=""> <br class="">My art theme: Dynamic exposition of the tension between matrix order and luminous chaos.<br class=""></div><div class=""><br class=""></div><div class=""><h1 style="letter-spacing:-0.02em;margin:0px" class=""><font size="2" face="arial, helvetica, sans-serif" style="font-weight:normal" class="">"Attempt what is not certain. Certainty may or may not come later. It may then be a valuable delusion."</font></h1><div class=""><span style="font-size:small;letter-spacing:-0.02em;line-height:1.125em" class=""><font face="arial, helvetica, sans-serif" class="">From "Notes to myself on beginning a painting" by Richard Diebenkorn. </font></span></div><table width="85%" style="color:rgb(93,86,81);font-family:Helvetica;font-size:18px;margin:auto;border-collapse:collapse" class=""><tbody class=""><tr class=""><td style="text-align:center" class=""><p style="margin-top:4px;margin-bottom:12px" class=""><font size="2" class="">"It's that knife-edge of uncertainty where we come alive to our truest power." Joanna Macy.</font></p></td></tr><tr class=""><td valign="top" style="font-size:13px;text-transform:uppercase" class=""><p style="margin-top:0px;margin-bottom:27px;color:rgb(146,146,146);text-align:center" class=""><br class=""></p></td></tr></tbody></table></div></div></div></div></div></div></div></div></div></div></div></div>
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