6.4.16

PRIORS AND POSTERIORS

Here's a Heterodox Academy post on the usefulness of constructing stylized facts, or stereotypes.

"Stereotype" is a loaded word, often conflated with "prejudice."  Thus, the careful researcher uses them carefully.
For some time now, the term stereotype has connoted one aspect of prejudice, and this linkage between stereotyping and prejudice isn’t altogether unfair. Most people can recall at least one instance when someone applied a stereotype to them, assuming something that was untrue, unflattering, and unfair. Nonetheless, there is another side to stereotypes—it can be rational to apply them when they’re generally true.
A more formal way of dealing with the distinction between a prejudice and a stereotype is to think of a prejudice as a possibly naive prior belief (and that becomes particularly fraught in the social sciences, where being wary of strangers is an inherited and evolutionary stable strategy) while a stereotype can either be a prior confirmed by evidence, or a prior updated or discarded on the basis of evidence.

Yes, that can get mathematical, but all the intuition appears in the first sentence of the following passage.
Taking a step back, we widely accept that the process of having beliefs about the world, interacting with it, and then updating these beliefs is a fundamental component of learning.

Well, computing the posterior from the prior with Bayes' theorem is simply a mathematical formulation of updating your beliefs. In fact, these ideas are at the core of Bayesian statistics, so it's well worth your time becoming familiar with the mechanics of working with them.
Thus when the boutique multiculturalists let some people act badly and call it authenticity, the resulting outcome actually confirms the very prejudices the Diversity Weenies would like to root out.  Why are they allowed to do things that we're not allowed to do?

Perhaps, as a first step, the Diversity Weenies ought to understand the logical basis of both central tendencies, which are a big part of social science, and confirmed stereotypes, which is a more pejorative way of describing a central tendency.
To my knowledge, no critic of stereotype accuracy research has leveled the same criticisms against social science in general even though the parallels are clear. In a number of social sciences, this is how you make a generalizable scientific claim. First, you advance a hypothesis. “Men are taller than women” is a good example. Second, you conjure an opponent, the null hypothesis. In this case, the null is: “Men and women are equally tall.” Third, you collect and measure a large sample of women and men and test for an average difference in height. You then plug that average difference into a formula that tells you whether it’s likely you would have found that difference if your opponent (the null hypothesis) were right.
There's more to it than "plug in" and a careful researcher must be conscious of the margin of error and the power of his test.  But the productive way to deal with pejoratives is in a logical way. Back to Heterodox Academy.
If we can develop imperfect but reasonably good conventions for what constitutes a valid scientific finding, we can also develop imperfect but reasonably good conventions for what constitutes stereotype accuracy. Establishing these conventions can also spur research to establish which stereotypes are inaccurate. The “how do we measure it” school doesn’t note that if we simply give up on accuracy measurement, we have to give up on both accuracy and inaccuracy. When only stereotype accuracy is held to a higher standard, that’s an indication of political bias. In a fairer world, we would treat both scientific validity and stereotype accuracy similarly—as problems that have pragmatic though imperfect solutions.
Simpler, still, though, and more pragmatic, to treat generalizations of any kind, whether given the status of stylized fact or of stereotype, as supported tolerably well by evidence, or not.

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