Bayes’ Theorem: Deceptively Simple

Bayes' Theorem, in classic form

Good ol’ Bayes’ Theorem. Have you even wondered where it comes from, though? If you don’t know probability, there doesn’t seem to be any obvious logic to it. Once you’ve had it explained to you, though, it seems blindingly obvious and almost tautological. I know of a couple of good explainers, such as E.T. Jaynes’ Probability Theory, but just for fun I challenged myself to re-derive the Theorem from scratch. Took me about twenty minutes; if you’d like to try, stop reading here and try working it out yourself.

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Model Failure

This may be hard to believe, but I’m not about to talk about Bayesian modeling nor CompSci. Nope, I got dragged into an argument over implicit bias with a science-loving “skeptic,” and a few people mobbed me over the “model minority.”

Asian-Americans, like Jews, are indeed a problem for the “social-justice” brigade. I mean, how on earth have both ethnic groups done so well in such a profoundly racist society? How have bigoted white people allowed these minorities to do so well — even to the point of earning more, on average, than whites? Asian-Americans, for example, have been subject to some of the most brutal oppression, racial hatred, and open discrimination over the years. In the late 19th century, as most worked in hard labor, they were subject to lynchings and violence across the American West and laws that prohibited their employment. They were banned from immigrating to the U.S. in 1924. Japanese-American citizens were forced into internment camps during the Second World War, and subjected to hideous, racist propaganda after Pearl Harbor. Yet, today, Asian-Americans are among the most prosperous, well-educated, and successful ethnic groups in America. What gives?

What gives is simple demographics. Take it away, Jeff Guo of the Washington Post: [Read more…]

This Rings A Bell

Heavyweight tech investor and FDA-critic Peter Thiel is among conservative funders and American researchers backing an offshore herpes vaccine trial that blatantly flouts US safety regulations, according to a Monday report by Kaiser Health News.

The vaccine—a live but weakened herpes virus—was first tested in a 17-person trial on the Caribbean Island of St. Kitts without federal oversight or the standard human safety requirement of an institutional review board (IRB) approval. Biomedical researchers and experts have sharply rebuked the lack of safety oversight and slammed the poor quality of the data collected, which has been rejected from scientific publication. However, investors and those running the trial say it is a direct challenge to what they see as innovation-stifling regulations by the Food and Drug Administration.

It was around that point in Beth Mole’s article for Ars Technica that I got a sense of deja-vu. A quick Google search confirmed it was more than a feeling:

Biomedical research, then, promises vast increases in life, health, and flourishing. Just imagine how much happier you would be if a prematurely deceased loved one were alive, or a debilitated one were vigorous — and multiply that good by several billion, in perpetuity. Given this potential bonanza, the primary moral goal for today’s bioethics can be summarized in a single sentence.

Get out of the way.

A truly ethical bioethics should not bog down research in red tape, moratoria, or threats of prosecution based on nebulous but sweeping principles such as “dignity,” “sacredness,” or “social justice.” Nor should it thwart research that has likely benefits now or in the near future by sowing panic about speculative harms in the distant future.

That was an ill-informed opinion of Steven Pinker from two years ago. I took it to task back then, but I wonder if Pinker has changed his mind in the intervening years. I checked his Twitter feed, and came away empty. Stick a pin in that one, it may become interesting.

Sex Around the World

Oh, Jerry Coyne. I’m amused with his defense of a sex binary…

In Drosophila and humans, the two species with which I’m most familiar, the behavior, appearance, and primary and secondary sex characteristics are determined almost completely by whether the chromosomal constitution is male (XY) or female (XX).

… since, like most such “scientific” defenses, he immediately turns around and shoots it in the foot.

Yes, there are a few exceptions, like AIS, but the various forms of that syndrome occur between 1 in every 20,000 to 1 in only 130,000 births.  Is that “too many examples” to all0w us to say that biological sex is not connected with chromosomes? If you look at all cases of intersexuality that occur in people with XX or XY chromosomes (we’re not counting XOs or XXYs or other cases of abnormal chromosomal number), the frequency of exceptions is far less than 1%. That means that, in humans as in flies, there is almost a complete correlation between primary/secondary sex characteristics and chromosome constitution.

Ah yes, chromosomes determine human sex except in the 0.05% to 1.7% of cases where they don’t. Brilliant logic, that.

But it’s easy to get trapped by your filter bubble. The internet is a lot bigger than North America, after all, and other places have their own view of sex. Take Sweden, for instance, where it’s  government policy to avoid teaching gender stereotypes. One kindergarten made headlines not too long ago by declaring itself “gender-neutral.” As the founder put it,

00:10:10,909 –> 00:11:03,329
I’m going to show you what we call the “whole life spectra.” We tend to divide this life spectra into two pieces, one for boys and one for girls. More often pink is for girls, and blue is for boys. When we call a boy “cool” and “strong,” and to girls we more often say that they should be “helpful,” “nice,” “cute,” we have different expectations [for how they behave]. We take away this border, and we don’t separate into “boyish” and “girlish,”  we give the whole life spectra to everyone. So we are not limiting, we are just adding. We are not changing the children, we are changing our own thoughts.

That video is worth watching, as it follows around two gender non-conforming kids with an intersex “ma-pa.” The few bigots on screen seem right out of 1984, claiming that expanding or eliminating gender stereotypes somehow constrains kids in some mysterious fashion. Every kid, in contrast, is either at ease with gender role fluidity or made uncomfortable when asked to label their gender.

But even Sweden appears behind the curve when contrasted with the Khawaja Sira of South Asia.

For centuries, South Asia has had its own Khawaja Sira or third gender culture. The community, identifying as neither male nor female, are believed by many to be “God’s chosen people,” with special powers to bless and curse anyone they choose. The acceptance of Khawaja Sira people in Pakistan has been held up internationally as a symbol of tolerance, established long before Europe and America had even the slightest semblance of a transgender rights movement.

But the acceptance of people defining their own gender in Pakistan is much more complicated. The term transgender refers to someone whose gender identify differs from their birth sex. This notion is yet to take root in Pakistan and the transgender rights movement is only beginning to assert itself formally. Now, some third gender people in Pakistan say the modern transgender identity is threatening their ancient third gender culture.

The problem is that the Khawaja Sira are allowed to exist within South Asian culture because they renounce both male and female gender roles, thus don’t challenge either. Trans* people, on the other hand, reject the role assigned to the Khawaja Sira and invoke the male or female one instead. This upsets every gender’s apple cart. It doesn’t help either that the Khawaja Sira in Pakistan have recently fallen onto hard times, facing increasing bigotry and hate; the increasing number of trans* people feels like an invasion of “Western” ideals, at a time when their community is ill-equipped to cope.

But do you remember hearing about Oyasiqur Rhaman, the atheist blogger murdered in Bangladesh? His murderers were outed by a courageous “hijra,” which is similar in meaning to “Khawaja Sira” but not quite the same.

Transgender people occupy an unusual social stratum in South Asia, where conservative societies still consider same-sex intercourse to be a crime but also allow the existence of a third gender — a well-established category that dates back to the age of the “Kama Sutra.” Nepal, Pakistan, Bangladesh and India have all legally recognized the existence of a third gender, including on passports and other official documents.

In India, in fact, “kinnar” freely mixes gender identity with non-binary sex. Compare and contrast this with Mexico’s “muxes,” who are called a third gender but in practice act more like trans* women, and Balkan sworn virgins who are more like trans* men. There’s no intersex component to the latter two, so lumping everybody under the banner of “third gender” or “transgender” is quite misleading.

Our binary view of sex and gender seem terribly archaic (which is ironic, as it may be a recent invention). It should not be controversial in North America to have a non-conforming parent or be raised in a genderless environment, yet it is. We could learn a thing or two from the rest of the world, especially when it comes to sex.

“Science Is Endangered by Statistical Misunderstanding”

He’s baaaaaack. I’ve linked to David Colquhoun’s previous paper on p-values,[1] but I’ve since learned he’s about to publish a sequel.

Despite decades of warnings, many areas of science still insist on labelling a result of P < 0.05 as “significant”.   This practice must account for a substantial part of the lack of reproducibility in some areas of science. And this is before you get to the many other well-known problems, like multiple comparisons, lack of randomisation and P-hacking. Science is endangered by statistical misunderstanding, and by university presidents and research funders who impose perverse incentives on scientists. [2]

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P-values are Bullshit, 1942 edition

I keep an eye out for old criticisms of null hypothesis significance testing. There’s just something fascinating about reading this…

In this paper, I wish to examine a dogma of inferential procedure which, for psychologists at least, has attained the status of a religious conviction. The dogma to be scrutinized is the “null-hypothesis significance test” orthodoxy that passing statistical judgment on a scientific hypothesis by means of experimental observation is a decision procedure wherein one rejects or accepts a null hypothesis according to whether or not the value of a sample statistic yielded by an experiment falls within a certain predetermined “rejection region” of its possible values. The thesis to be advanced is that despite the awesome pre-eminence this method has attained in our experimental journals and textbooks of applied statistics, it is based upon a fundamental misunderstanding of the nature of rational inference, and is seldom if ever appropriate to the aims of scientific research. This is not a particularly original view—traditional null-hypothesis procedure has already been superceded in modern statistical theory by a variety of more satisfactory inferential techniques. But the perceptual defenses of psychologists are particularly efficient when dealing with matters of methodology, and so the statistical folkways of a more primitive past continue to dominate the local scene.[1]

… then realising it dates from 1960. So far I’ve spotted five waves of criticism: Jerzy Neyman and Egon Peterson head the first, dating from roughly 1928 to 1945; a number of authors such as the above-quoted Rozeboom formed a second wave between roughly 1960 and 1970; Jacob Cohen kicked off a third wave around 1990, which maybe lasted until his death in 1998; John Ioannidis spearheaded another wave in 2005, though this died out even quicker; and finally the “replication crisis” that kicked off in 2011 and is still ongoing as I type this.

I do like to search for papers outside of those waves, however, just to verify the partition. This one doesn’t qualify, but it’s pretty cool nonetheless.

Berkson, Joseph. “Tests of Significance Considered as Evidence.” Journal of the American Statistical Association 1942;37:325-35. International Journal of Epidemiology, vol. 32, no. 5, 2003, pp. 687.

For instance, they point to a specific example drawn from Ronald Fisher himself. The latter delves into a chart of eye facet frequency in Drosophila melanogaster, at various temperatures, and extracts some means. Conducting an ANOVA test, Fisher states “deviations from linear regression are evidently larger than would be expected, if the regression were really linear, from the variations within the arrays,” then concludes “There can therefore be no question of the statistical significance of the deviations from the straight line.”

Berkson’s response is to graph the dataset.eye facets vs. temperature, Drosophila Melangaster, graphed and fit to a line. From Fisher (1938).

The middle points look like outliers, but it’s pretty obvious we’re dealing with a linear relationship. That Fisher’s tests reject linearity is a blow against using them.

Jacob Cohen made a very strong argument against Fisherian frequentism in 1994, the “permanent illusion,” which he attributes to a paper by Gerd Gigerenzer in 1993.[3][4] I can’t find any evidence Gigerenzer actually named it that, but it doesn’t matter; Berkson scoops both of them by a whopping 51 years, then extends the argument.

Suppose I said, “Albinos are very rare in human populations, only one in fifty thousand. Therefore, if you have taken a random sample of 100 from a population and found in it an albino, the population is not human.” This is a similar argument but if it were given, I believe the rational retort would be, “If the population is not human, what is it?” A question would be asked that demands an affirmative answer. In the hull hypothesis schema we are trying only to nullify something: “The null hypothesis is never proved or established but is possibly disproved in the course of experimentation.” But ordinarily evidence does not take this form. With the corpus delicti in front of you, you do not say, “Here is evidence against the hypothesis that no one is dead.” You say, “Evidently someone has been murdered.”[5]

This hints at Berkson’s way out of the p-value mess: ditch falsification and allow evidence in favour of hypotheses. They point to another example or two to shore up their case, but can’t extend this intuition to a mathematical description of how this would work with p-values. A pity, but it was for the best.

[1] Rozeboom, William W. “The fallacy of the null-hypothesis significance test.” Psychological bulletin 57.5 (1960): 416.

[2] Berkson, Joseph. “Tests of Significance Considered as Evidence.” Journal of the American Statistical Association 1942;37:325-35. International Journal of Epidemiology, vol. 32, no. 5, 2003, pp. 687.

[3] Cohen, Jacob. “The Earth is Round (p < .05).” American Psychologist, vol. 49, no. 12, 1994, pp. 997-1003.

[4] Gigerenzer, Gerd. “The superego, the ego, and the id in statistical reasoning.” A handbook for data analysis in the behavioral sciences: Methodological issues (1993): 311-339.

[5] Berkson (1942), pg. 326.

A Flurry of Science

“Think about being able to do all these experiments on the ground, from airplanes, from balloons, with citizen scientists. It’s pretty breathtaking,” said Lika Guhathakurta, an astrophysicist at NASA. Guhathakurta will shepherd dozens of scientific projects on Aug. 21, including polarized images of the corona, which help scientists measure its temperature; measurements of Earth’s ionosphere — the charged layer of the atmosphere that gives us auroras; spatial disturbances in the atmosphere caused by heat changes; and a whole lot more. (You can get involved, too. With an app called GLOBE Observer and a thermometer, you can collect data during the eclipse and submit it to NASA. And Google and the University of California, Berkeley, are asking for video and images, which they’ll stitch together into an “Eclipse Megamovie.”) Other scientists will be studying animals — creatures as small as grasshoppers and as big as hippos have been documented reacting to eclipses — and us, too. Humans are sure to have a wide range of responses, as we have since time immemorial.

I’ll admit, this comes as a bit of a shock to me. I thought that coronagraphs permitted really good science provided a scientist could grab some funding. Not so, though.

… coronagraphs usually block more of the sun than astronomers would like. Typically, a coronagraph covers an area around 1.4 times the radius of the sun, obscuring arguably the most important region — the one closest to the sun’s surface.

“That is sort of the missing link, the region where space weather is formed, where the corona gets heated, where the solar wind gets accelerated. … So that’s where we want observations to be pristine,” Guhathakurta said.

Which means that my US readers have an excellent opportunity to do some citizen science in exactly three weeks (well, 21 days and 11 minutes from when I post this). In addition to the above links, Space.com has a good rundown of how to safely observe the eclipse and NASA has tonnes more charts and info.

And remember, a solar eclipse was once considered a bad omen for a king or ruler.

Objectively Biased

Enjoyed that inspirational break? Good, because it’s back to Depresso Land.

Astronomy and planetary science, as the fields concerned with celestial objects and processes, help shift human attention outward. Gazing at the stars is an accessible introduction to science, one that gets many young children dreaming of being an astronaut, astronomer, or planetary scientist one day. […]

At the same time, the accessibility and inclusive atmosphere within science, including astronomy and planetary science, has been called into question. Science syllabi use gendered language that not only can show women as incompetent but also normalizes masculine behaviors, belief systems, and priorities [Bejerano and Bartosh, 2015]. Several studies of Science, Technology, Engineering, and Mathematics (STEM) fields have found implicit bias, or the bias in judgment resulting from implicit attitudes that operates below cognitive awareness, related to both gender and race limits opportunities in mentorship [Milkman et al., 2015], hiring [Moss-Racusin et al., 2012], and opportunities in the classroom [Eddy et al., 2014, 2015; Grunspan et al., 2016], as well as workplace conflict [Williams et al., 2016] and experiences that map onto stereotypes of scientists’ racial-ethnic identification [Williams et al., 2014, 2016]. Women of color faculty in STEM are also more likely to experience the dominant culture of their disciplines as outsiders, with their views validated less than the dominant group [Rios and Stewart, 2015]. Further, the number of women of color science faculty has recently decreased, even while the number of white women science faculty has increased [Armstrong and Jovanovic, 2015]. These marginalities are further compounded by power differentials, as women of color are more likely to be junior in rank compared to those with majority identities [National Science Foundation (NSF), 2015].[1]

That much was known; left without examination, though was the extent that this sexism hits on a personal level. Now we have a study that covers that, and whoamygawd:

Women were more likely than men to observe remarks that they interpreted as racist, sexist, that one was not feminine or masculine enough, or disparaging someone’s physical abilities or mental abilities (Table 3, see supporting information Table S1 for all analyses). Women were also significantly more likely than men to report that they experienced both verbal and physical harassment because of their gender. When asked if they had ever felt physically unsafe in their current position, more women than men reported that they felt unsafe as a result of their gender (30% versus 2%, p < 0.001). Finally, women were also more likely than men to report skipping at least one class, meeting, fieldwork, or other professional event per month because they felt unsafe (13% versus 3%, p = 0.01). […]

Respondents of color were significantly more likely than white respondents to observe remarks that were racist (from peers and others, p = 0.0001 and 0.023) or homophobic (from supervisors, p < 0.0001, Table 4, see supporting information Table S2 for all analyses). Respondents of color were also significantly more likely than white respondents to report that they experienced both verbal and physical harassment because of their race. When asked if they had ever felt physically unsafe in their current position, more respondents of color reported they felt unsafe as a result of their race (24% versus 1%, p < 0.001). Respondents of color and white respondents reported similar frequencies of skipped classes, meetings, fieldwork, or other professional events per month because they felt unsafe (15% versus 9%, p = 0.08).[1]

There’s more bad news, and thankfully the paper is open-access so you can wallow in it yourself. Suffice to say, not only does this establish sexism and racism is pervasive within astronomy, there’s strong reason to suspect its killing careers.

An even stronger portrait emerges if we include the LGBTQA+ community. This relates to physics, rather than astronomy, but

About 15% of LGBT men, 25% of LGBT women, 30% of gender-nonconforming individuals characterized the overall climate of their department or division as “uncomfortable” or “very uncomfortable.” Also, 30% of trans individual regardless of gender identity characterized the overall climate of their department or division as “uncomfortable” or “very uncomfortable.” […]

Over 40% of climate survey respondents agreed with the statement, “Employees are expected to not act too gay,” and about 45% disagreed with the statement, “Coworkers are as likely to ask nice, interested questions about same-sex relationships as they are about heterosexual relationships.” […]

More than 20% of climate survey respondents reported experiencing exclusionary behavior in the past year, while about 40% reported observing exclusionary behavior due to gender, gender expression, gender identity, sexual orientation, or sexual identity. These numbers were significantly higher (49% and 60% respectively) for trans respondents. […]

Over one-third of climate survey respondents considered leaving their workplace or school in the past year.[2]

That last line is important; we’re excluding people from working in the sciences for reasons that have nothing to do with competence. This has to change, and as always awareness of the problem is the first step.

[1] Clancy, Kathryn B. H., Katharine M. N. Lee, Erica M. Rodgers, and Christina Richey. “Double Jeopardy in Astronomy and Planetary Science: Women of Color Face Greater Risks of Gendered and Racial Harassment.” Journal of Geophysical Research: Planets, n.d., 2017JE005256. doi:10.1002/2017JE005256.

[2] Atherton, T. J., R. S. Barthelemy, W. Deconinck, M. L. Falk, S. Garmon, E. Long, M. Plisch, E. H. Simmons, and K. Reeves. “LGBT Climate in Physics: Building an Inclusive Community.” American Physical Society, College Park, MD, 2016.

Bookmark This One

Not this one, mind, but this one from Shiv.

So, without further ado, let’s dive into the latest candy-glossed hate piece to make waves in feminist discourse: “I am not a ‘cis’ Woman, I am a Woman and that Matters.”

Hands down, it’s the best counter-argument to the “E” in TERF that I’ve read.

I mean, hey, it’s taken a good ~2,400 words but now we can answer the question, “why is it wrong for cis women to have some spaces just for them to feel safe in a world where they don’t?”

It’s not wrong to want safety. However, the motivations for this trans-free “women only” space…

  1. Perpetrate rape culture by overstating stranger danger;
  2. Perpetrate rape culture by obscuring the actual tactics of serial predators;
  3. Assumes trans women are as likely to be violent as cis men, which is factually incorrect;
  4. Assumes violence is an essential property of certain persons, which is also factually incorrect–not to mention the rhetorical flourish liberally employed by white supremacists;

…all of which are complaints which have nothing to do with “trying to take away cis women’s safety.”

And all of those prior 2,400 words are well-cited and argued. I do two minor nitpicks, but the first only strengthens the argument. The second:

Please note, I have not once accused Broustra of being transphobic in this piece, nor will I.

I’ll go two steps farther. Broustra denies gender identity, via calling for the explicit exclusion of trans* women in “women-only” spaces; she shows a familiarity with TERF culture, through her Xeroxing of their ideas and arguments; and as a bonus, she is actively working to exclude trans* women, because she is campaigning for her point of view in a public forum. In my books, that makes her a TERF.

That first? I’ll post it over on Shiv’s piece as a comment, when I get a chance. So go read and bookmark her post!

Squirting Right

Ever heard of the Sea Squirt? It’s a memorable creature.

What’s most fascinating about the sea squirt is that, almost as soon as it stops moving, its brain is absorbed by its body. Being permanently attached to a home makes the sea squirt’s spinal cord and the neurons that control locomotion superfluous. Once the sea squirt becomes stationary, it literally eats its own brain.

This tells us something important: brainpower is strongly related to movement. If you don’t go anywhere, you don’t need that much computational power between your ears.

While there are those like Sean Hannity who are reliable cheerleaders for all things President Trump, much of the conservative news media is now less pro-Trump than it is anti-anti-Trump. The distinction is important, because anti-anti-Trumpism has become the new safe space for the right. […]

For the anti-anti-Trump pundit, whatever the allegation against Mr. Trump, whatever his blunders or foibles, the other side is always worse.

But the real heart of anti-anti-Trumpism is the delight in the frustration and anger of his opponents. Mr. Trump’s base is unlikely to hold him either to promises or tangible achievements, because conservative politics is now less about ideas or accomplishments than it is about making the right enemies cry out in anguish.

There’s been a remarkable shift in US politics. The Right-wing has largely become the “anti-Left:” whatever the Left is in favor of, the Right opposes. This has some advantages, like making it easy to leverage fear and removing the possibility of contradiction. Truth and feelings become synonymous.

[NEWT] GINGRICH: The current view is that liberals have a whole set of statistics that theoretically may be right, but it’s not where human beings are.

CAMEROTA: But what you’re saying is, but hold on Mr. Speaker because you’re saying liberals use these numbers, they use this sort of magic math. These are the FBI statistics. They’re not a liberal organization. They’re a crime-fighting organization.

GINGRICH: No, but what I said is equally true. People feel more threatened.

CAMEROTA: Feel it, yes. They feel it, but the facts don’t support it.

GINGRICH: As a political candidate, I’ll go with how people feel and I’ll let you go with the theoriticians.

But if you define yourself as the opposite of something else, other people define your position for you. If you cannot contradict yourself, you do not have to waste time and energy searching for contradictions. In the intellectual sphere, you drift under the power of others, and otherwise cannot be moved.

If you cannot move, why do you need a brain? No wait, let me rephrase that: why do you need to think? There’s no need to teach critical thought, and plenty of reason to oppose it. Intellectuals become the enemy, experts the target of scorn. This makes you easily manipulated. Hucksters flock in to take advantage of you.

It doesn’t have to be this way. Conservatives used to hold to specific positions in US politics, some of which were progressive. Should any Republicans or conservatives wander onto this post, I implore you: think, before you glue yourself down and lose that ability.