William M. Briggs

Statistician to the Stars!

Author: Briggs (page 3 of 536)

Predicting Doom—Guest Post by Thomas Galli

Some treatments are more efficacious than others.

Some treatments are more efficacious than others.

I am not a statistics wizard; an engineer, I value the predictive power of statistics. Indeed, if one can precisely control variables in the design of an experiment, statistics-based prediction of future material properties is remarkably accurate. The joy of predicting end strength for a new carbon nanotube concrete mix design in minutes versus days melts the heart of this engineer.

This predictive power has a foreboding downside. It attaches to other projections, including those used by the medical profession to forecast life after diagnosis with late-stage cancer. Unfortunately, I have first-hand experience with this. I was granted but 6 months of remaining life nearly 11 years ago! My doom was predicted with certainty, and for a while, I believed it.

In the dwell time between treatments, I searched for methods used to generate projections of doom. Each patient’s type, stage, age, ethnicity and race were reported to the National Cancer Institute upon diagnosis. Deaths were also reported but not the cause of death. Nothing was captured on complicating health problems like cardio-pulmonary disease, diabetes or other life-threatening diseases. The predictive data set appeared slim.

My battle turned while mindlessly searching web pages of the American Cancer Society. Ammunition in the form of a powerful essay from the noted evolutionary biologist Stephen Jay Gould—“The Median Isn’t The Message”—contained the words: “…leads us to view statistical measures of central tendency wrongly, indeed opposite to the appropriate interpretation in our actual world of variation, shadings, and continua.”

The statistician seeks to aggregate and explain. I’d forgotten that I was in a “world of variation,” was but one data point in about 1.4 million Americans diagnosed in 2004. I might be “the one” on the right-shifted curve prohibiting intersection with the x-axis.

There was one benefit from my encounter with predictive doom. I found hope—something no statistician can aggregate or explain.

Gould survived 20 years beyond his late-stage, nearly always statistically fatal, abdominal cancer diagnosis. Ironically, he passed after contracting another form of unrelated cancer. A distinguished scientist, Gould eloquently described the limits of science and statistics by suggesting that “a sanguine personality” might be the best prescription for success against cancer. There is always hope, with high confidence.

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Editor’s Note I have long been interested in working with physicians who routinely make end-of-life prognoses. The concepts of rating such judgments are no different than, say, judging how well climate models predict future temperatures. I mean predictions should be rated on their difficulty. I haven’t yet discovered docs willing to conduct these experiments, but if anybody happens to know somebody, let me know.

Nonpolitical Images Evoke Neural Predictors Of Political Ideology?

From the paper.

From the paper.

The study

Another day, another dreary study purporting to show that the brains of “conservatives” are different than those of “liberals.”

This one hooked up to an electrical phrenology device (fMRI) 83 people1 and had them look at disgusting pictures (still shots from The View?) and other sorts of pictures and then rate them “using a nine-point Likert scale”. I’ve asked this before, but on a scale of -2 to 52.7, how good are these faux numerical scales at quantifying things like disgust or pleasantness? Never mind.

The peer-reviewed paper is by Read Montague and a slew of others in Current Biology, and has the same name sans question mark as today’s post.

To discover “conservatives”, “liberals”, and “moderates” questions were asked about how strongly participants supported items like “Biblical truth” (do no liberals believe this?) and “Foreign aide”. These were scored, the scores separated, and the results assumed infallible. Yes, really. There is no indication—which is to say, no indication—the uncertainty from these arbitrary questions arbitrarily scored and arbitrarily busted up was carried through in any analyses. But since everybody makes this mistake, we shouldn’t question it.

Anyway, the main result is no result. The three “groups did not significantly differ in subjective ratings of disgusting, threatening, or pleasant pictures”. Also turned out that “there were no significant group differences on [other] self-report measures”.

End of story? No, sir. Scientists do not let the absence of wee p-values discourage them. Out came the “penalized regression method called the elastic net” applied to the fMRI data. The theory was that even though there were no real differences in behavior, maybe the brains were different after all, which is a strange thing to think given there were no real differences in behavior. I hope my repeating that isn’t annoying.

Is this a good point to remind us the fMRI data are not pictures of the brain but are themselves output of models and heuristics (“Functional data were first spike-corrected to reduce the impact of artifacts using AFNI’s 3dDespike”, etc., etc.) which themselves are subject to uncertainty which should be carried forward in any analysis but which usually aren’t, and weren’t here? If not, let me know when is.

The analysis

I hesitate to describe the authors did next not because it’s difficult, but because I don’t think anybody will believe it. I will first remind us that we are to again lament that most statistical practice is designed around model fit, which tell the world how closely a model fits to the data at hand, and that the more models tried the better success of discovering one which fits.

The authors showed each person sets of neutral (whatever the hell that is), pleasant, threatening, and disgusting photos. There weren’t any reported differences in fMRI manipulated data between people seeing these images in the three different groups.

Next up was to form “contrasts”, which was to sort of difference the fMRI manipulated data from times when people looked at disgusting, threatening, and pleasant images against so-called neutral images. These same differences were applied to averages between “conservative” and “liberals.” The “moderates”, sad folks, were thereafter forgotten.

Incidentally, the types of people in the “conservative” and “liberal” groups were not the same: “liberals” averaged 33 years old, 39% female; “conservatives” 27 years old, 61% female. Might these biological differences account for differences in fMRI manipulated data? The authors admit (in supplementary material) that “religiousness”, age, and sex “were significantly correlated with political attitudes”. But they put this down to “false alarms” and carried on.

Now came generalized linear models—we still haven’t reached the elastic net—where for each individual “a temporal high-pass filter (128s) and order 1 temporal autocorrelation (AR(1)) was assumed”. And “The onsets for each picture subcondition (core/contamination disgust, animal reminder disgust, actual threat, no actual threat, social pleasure, nonsocial pleasure) and fixation crosses were convolved with a canonical hemodynamic response function…using a delta function of zero duration”, etc.

And that wasn’t all. “Six head motion parameters were also included in the first level GLM as covariates.” So were age and sex. Uh oh. Then they “separately examined the maps of [Disgusting – Neutral], [Threatening – Neutral], and [Pleasant – Neutral] contrasts”. Then some t-tests and some other things.

Result? “The contrasts with threatening or pleasant pictures revealed no regions surviving multiple corrections. However, in the [Disgusting > Neutral] contrast, the Conservative group showed greater activity than the Liberal group in several regions” (hint: amygdala! amygdala!). Yet, sadly, “No regions survived correction for multiple comparisons for the
[Liberal group > Conservative group] comparison.”

Another no result. So back to the computer and the “penalized logistic regression analysis”, a.k.a. “elastic net”.

“First, we extracted a map of the [Disgust > Neutral] contrast for each participant. Then, we applied an a priori mask, which was generated from the Neurosynth website”. Then they “obtained the union of meta-analytic (positively correlated and both forward and reverse inference) maps of ‘Emotion’ and ‘Attention'” and then finally formed up all the voxels into a matrix and submitted all to the “elastic net.”

That creature is so cumbrous I don’t dare describe it. But it was, in the end, fit to the “individual scores on a standard political ideology assay” and, mirabile dictu, the model fit was reasonable. But only for those time disgusting images were viewed (and leaving out “moderates”). Would young females dislike disgusting images more than older males? Just asking.

The true test: How well does their model predict political attitudes for people not used to fit the model? [INSERT CRICKET CHIRPS HERE]

The End

The authors conclude “Neuroscience has started to provide rich information about the neurophysiological processes underlying political behavior.” No, it hasn’t. It is true that a spate of flawed papers are appearing, each borrowing the mistakes of the other. Yet the authors don’t even blush when the say “Our results have important implications for the links between biology, emotions, political ideology, and human nature more fundamentally.”

Here’s where it gets scary, folks. They suggest “people are born with certain dispositions and traits that influence the formation of their political beliefs”. This seems trivially true; after all, some of us are men and some women, and that difference means a lot. But the differences the authors means refer to flawed ad hoc idiotically scaled questionnaires. How long until some bright academic produces “the” list of questions which separate the sheep from goats?

Next: “A wide range of brain regions contributed to the prediction of political ideology (Figure 3A), including those known from past work to be involved in the processing and interoception of disgust and other stimuli with negative affective valence, but also those involved in more basic aspects of attentive sensory processing”.

The mistake here is to assume we are our brains, slaves to them somehow, that these curious organs can make us do what they like, and that we have little to say about it. The lack of philosophical training tells again.

Nowhere do these authors (or any other that I have seen) betray any lack of confidence in their convoluted analyses. It seems as if—I’m just guessing—that all these authors think that because their analyses are complex they are therefore right. We need a name for this fallacy.

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1In supplementary material the authors say 12 people were removed from the analysis, but it’s not clear if these were before or after the 83.

Thanks to Rexx Shelton, Robert, and one anonymous reader for suggesting this topic.

Nothing Is Distributed: So-Called Random Variables Do Not Follow Distributions

Wow is this wrong, but common, common.

Wow is this wrong, but common, common.

People say “random” variables “behave” in a certain way as if they have a life of their own. To behave is to act, to be caused, to react. This is reification, perhaps caused by the beauty of the mathematics where, literally, the equations undergo biogenesis. The behavior of these “random” creatures is expressed in language about “distributions.” We hear, “Many things are normally (gamma, Weibull, etc., etc.) distributed”, “Y is binomial”, “Height is normally distributed”, “Independent identically distributed random variables”.

I have seen someone write, “[Click here to] see a normal distribution being created by random chance!” Wolfram MathWorld writes, “A statistical distribution in which the variates occur with probabilities asymptotically matching their ‘true’ underlying statistical distribution is said to be random.” Examples abound.

All of this is wrong and indicates magical thinking. It is to assume murky, occult causes are at work, pushing variables this way and that so that they behave properly. To say about a proposition X that “X is normal” is to ascribe to X a hidden power to be “normal” (or “uniform” or whatever). It is to say that dark forces exist which cause X to be normal, that X somehow knows the values it can take and with what frequency.

This is false. We are only privileged to say things like this: “Give this-and-such set of premises, the probability X takes this value equals that”, where “that” is a deduced value implied by the premises. Probability is a matter of ascribable or quantifiable uncertainty, a logical relation between accepted premises and some specified proposition, and nothing more.

Let S = “Sally’s grade point average is x”. Suppose we have the premise G = “The grade point average will be some number in this set”, where the set is specified. Given our knowledge that people take only a finite number of classes and are graded on a numeric scale, this set will be some discrete collection of numbers from, say, 0 to 4; the number of members of this set will be some finite integer n. Call the numbers of this set g_1, g_2,…, g_n.

The probability of S given G does not exist. This is because x is not a number; it is a mere placeholder, an indication of where to put the number once we have one in mind. It is at this point the mistake is usually made of saying x has some “distribution”. Nearly all researchers say or assume “GPA is normal”; they will say “x is normally distributed.” Now if this is shorthand for “The uncertainty I have in the value of x is quantified by a normal distribution” the shorthand is sensible—but unwarranted. There are no premises which allow us to deduce this conclusion. This is pure subjective probability (and liable to be a rotten approximation).

When they say “x is normally distributed” they imply that x is itself “alive” in some way, that there are forces “out there” that make, i.e. cause, x to take values according to a normal distribution; that maybe even the central limit theorem lurks and causes the individual grades which comprise the GPA to take certain values.

This is all incoherent. Each and every grade Sally received was caused, almost surely by a myriad of things, probably too many for us to track. But suppose each grade was caused by one thing and the same thing. If we knew this cause, we would know the value of x; x would be deduced from our knowledge of the cause. And the same is true if each grade were caused by two known things; we could deduce x. But since each grade is almost surely the result of hundreds, maybe thousands—maybe more!—causes, we cannot deduce the GPA. The causes are unknown, but they are not random in any mystical sense, where randomness has causative powers.

What can we say in this case? Here is something we deduce: Pr(x = g_1 | G) = Pr(x = g_2 | G), where x = g_1 is shorthand for S = “Sally’s GPA is g_1″ (don’t forget this!). This equation results from the so-called symmetry of individual constants, a logical principle. The probabilities are equivalent to G = “We have a device which can take any of n states, g_1, …, g_n, and which must take one state.” From the principle we deduce Pr(x = g_i | G) = 1/n.

“Briggs, you fool. That makes GPAs of 0 just as likely as 4. That isn’t possible.”

Is it not? I see you haven’t taught at a large state university. Anyway, the probabilities deduced are correct. What you are doing in your question is adding to G. You are saying to yourself something like “Pr(g_n | G & What I know about typical grades)” which I insist is not equal to Pr(g_n | G). Either way, x does not “have” a distribution.

Homework 1: discover instances of abuse. Homework 2: What’s wrong with the phrase “independent identically distributed random variables”? Hint: a lot.

Universities? Nuke ‘em From Orbit. It’s The Only Way To Be Sure.

Harvard, meeting its fate.

Harvard, meeting its fate.

ALERT: My spam checker is on the fritz. Many comments going directly to moderation. Please be patient.

What do you do with a cancer? Right. Only one thing: kill it. Poison it, radiate it, cut it out. Make it dead. And with extreme prejudice.

If not, what happens?

Right. It grows. It crowds out healthy cells, choking the life out of them. Left unkilled, what happens? Right again. The cancer weakens then destroys its host. It kills itself too, the malignancy, but if it could think, it would, as it gazed contemptuously at the death which surrounds it, take pleasure in being the last thing standing. Right you are. This is what evil does.

Sorry. I should have began this story with a Trigger Warning in case a college professor or her student accidentally read it and became traumatized for life.

Check your privilege: Trigger Warnings are a farce, a contemptible asinine idiotic burlesque. Anybody who is not insane knows this—and that is still most of us. But our knowing this, our laughter and ridicule and our exposing this and every other form of nonsense created by universities, is not stopping this cancer from spreading.

Wendy Kaminer, not realizing the forces of destruction she herself helped loose years ago, ventured recently to Smith College to tell the little darlings enrolled in that cocoon that freedom of expression in universities is to be cherished. She quoted from The Adventures of Huckleberry Finn to prove that none would expire on hearing forbidden words.

Kaminer was naive. The cancer reacted violently to the medicine.

The event—and Ms. Kaminer’s words—prompted blowback from Smith undergraduates, recent alumnae and some faculty members. One member of the audience posted an audio recording and transcript of the discussion, preceded by what has come to be known in the academic world as a “trigger warning”:

“Trigger/Content Warnings: Racism/racial slurs, abelist slurs, anti-Semitic language, anti-Muslim/Islamophobic language, anti-immigrant language, sexist/misogynistic slurs, references to race-based violence.”

Abelist. The cancer has invaded more systems than you know.

The president of Smith, the dear, probably distracted by budgeting, forgot her primary duty to the cancer was to rebuke and renounce Kaminer. And so the cancer attacked her—and won.

In a Sept. 29 letter responding to the Smith community, she apologized to students and faculty who were “hurt” and made to feel “unsafe” by Ms. Kaminer’s comments in defense of free speech.

Time for Smith to go.

Time for others, too. “Lincoln University president Robert Jennings told an auditorium of female students in September that there had been three false rape accusations during the previous semester.” Poor Jennings. He had no idea the extent of disease on his own campus.

Jennings said what is true: “[false] allegations can ruin a young man’s life and urged them not to put themselves in a situation where they would be ‘trying to explain something that really needs no explanation.'” Mistake. Jennings was made to apologize—to women. What for?

Does it matter? It does not. Lincoln University is among the walking dead.

Need we bring up Larry Summers? How about the innumerable times infected students or their intellectual epigone watchers charged stages, created incidents, or chased away the uninfected in order to protect their precious ears from Truth? Must we re-display the innumerable speech codes which banned “hurtful” words?

Every cancer has a cause, and in this case the carcinogen was and is Equality. Never was there a more pernicious and malevolent idea. As everybody knows, Equality is inevitable spawn of Democracy. This is why there is at present no cure for it. It is why something more radical is called for.

It was Equality that led to the quota system in universities and the creation of Studies departments, staffed by representative members of whatever Grievance Group moaned the loudest. Administrators thought that this form of appeasement would isolate the cancer, keep it in plain view and controlled.

How quaint. Any doctor could have told them cancers don’t work that way. It wasn’t long before quotas spread to other departments. Then came the multifarious budget-sink Offices of Diversity and Indignation. Then came quotas for the students themselves. Then came the rigorous enforcement of ideology.

All pretense that universities were places to study Truth, Beauty, The Good, What Is Man were abandoned, except (partially) in so-called STEM fields, where students find false refuge in believing the answer to any question is “Science!” But we need only say “Global Warming” or “Amygdala” to know that the rot has infected these semi-redoubts as well.

The charge is Corrupting the Youth. If we are save our young from becoming temperamental sniveling thumb-sucking snot-nosed molly-coddled tantrum-throwing ignorant know-nothing cowardly narcissistic brats, we must eliminate their exposure to grasping avaricious hateful lazy gossiping caustic vindictive grievance-mongering race-bating sex-obsessed privileged cultural leeches.

Since there isn’t enough hemlock to go around, nuking the cancer from space will do—though kinetic weapons would make a cheap alternative. It’s the only way to be sure.

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