William M. Briggs

Statistician to the Stars!

The Hierarchy Of Models: From Causal (Best) To Statistical (Worst)


There is a hierarchy of models in the sense they offer insight into the thing modeled. The order of importance is: causal, deterministic, probabilistic, statistical. Most models use mixtures of these elements.

All models have this form: a set of premises, which include any number of facts, truths, supposeds, data, and such forth, and a proposition of interest, which is the thing being modeled conditional on those premises.

A classic—or perhaps better, as you’ll agree, classical—causal model “Socrates is mortal” given “All men are mortal and Socrates is a man.” The model predicts Socrates will die because of the nature of all men. It is man’s nature to die, and Socrates (and you, dear reader) are among the race of men. We know all men are mortal from the necessarily limited sample of observations of past men, and from the induction of these dead men to the entire race.

Causal models give insight into or make use of the nature, the universal essence, of the thing of interest. Causal models require universals; they also require induction because we know the validity of all universals, natures, essences, through a type of induction.

Deterministic models are common in mathematics and are usually stated in a form such that the proposition of interest is a function of premises, like this: y = f(x). The “x” is placeholder for any number of premises. An example of a functional form of a deterministic model is y = a + bx3, which shows there are three explicit premises, the “a”, “b”, and x3, and one implicit, which is the form or arrangement of these premises. This equation might give the numerical level of some thing as a function of a, b, and x. It says, “Given a, b, and x, y will certainly be at a + bx3.” The equation determines y, but doesn’t explain the essence of the cause.

Some causal models may be put in equation form, but not all deterministic models are also causal. The equation given applies to a black box with two readouts, a “y” and “x”, and a dial is discovered to change the “x”. The formula is induced based on rotating the dial and noting the values of y and x. Only in the weakest sense can we say we have discovered the essence of the machine: we don’t even know what the values imply. Interestingly (and obviously to mathematical readers), more than one equation can be found to fit the same data (premises), which is also proof we have not learned the nature of the machine.

Probabilistic models abound. Given “This is a two-state object and only one state of s1 or s2 may show at any time”, the probability “The object is in state s1” is 1/2. Note carefully that no such real object need exist; and neither must real objects exist for causal or deterministic models, as should be obvious.

There isn’t any understanding of essence or nature of this object in this probability model: we don’t know the workings. If we did, we’d have a deterministic or causal model. The probability is thus only a measure of our state of knowledge of the truth of the proposition and not of the essence of object. Probability models are silent on cause.

The last and least are statistical models. These are always ad hoc and conflate probability and decision or mistake probability with essence. Statistical models are a prominent cause of the vast amount of over-certainty which plagues science.

Statistical models purport to say that x causes y, or that x is “linked to” y, through the mechanism of hypothesis testing, via frequentist p-values or Bayesian Bayes factors, but though x may really be a cause of y, or x really may be linked to y in some essential way, the statistical judgment that these conditions are so is always a fallacy.

Hypothesis testing conflates decision with probability; nothing in any hypothesis test gives the desired probability “Given x, what is the probability of y”; instead, testing says, based on ad hoc criteria, x and y are mysteriously related (“linked”) or that x causes y. These inferences are never valid. The importance of this logical truth cannot be overstated. This why so many statistical models report false results. (A reminder that a logical argument can be invalid but still have a true conclusion; the conclusion is just true for other reasons than the stated argument.)

Lastly, statistical models purport to report “effect size”, which is a measure of the importance of x on y. This “effect size” always either false or an assertion given far too much confidence (I used this word in its plain-English sense). Effect sizes say something about a premise inside x (a parameter or parameters) and not x itself, hence they are always over-certain. This form of over-certainty is eliminated by moving to a probability model.

More about this topic in the must-read get-it-now don’t-do-another-analysis-without-reading-it Uncertainty: The Soul of Modeling, Probability & Statistics.

“All Religions Want Peace”: The Pope, Propaganda & The Expected Lie


There is a kind of propaganda that everybody knows is propaganda, but which involves statements which everybody expects a personage to make. Call it Expected Lies.

So that when a fellow who used to be President was asked if his latest already-well-known dalliance was true, he wagged his finger and said no. As he was expected to. Nobody (above a certain intelligence) believed it, but because the lie was expected, those on his political side were expected to support it, which they did (at first) in a desultory fashion. The Expected Lie is after all one of the reasons why we have taboos on self-incrimination.

This is a silly but illustrative example. Why did this fellow tell the lie? Because, simply, if he told the truth he would have had to act on that truth. So that if he said, “Yes, I did it and often, and once with a cigar” there was little recourse left to him but to resign. A drastic action, one filled with portents and consequence. The Expected Lie brings freedom from acting.

Nothing more than this explains the endless stream of nothing-to-see-heres we get from European leaders after the latest killing by Muslims in the name of Islam. We are told the Expected Lie in many forms: “This is not true Islam (even though the Muslim attackers swear that it is)”, “All Muslims are not terrorists (a truth but non sequitur)”, “We don’t know the reason for the murders (despite the sworn testimony of cowardly killers)”, “The slaughter was sparked by racism (false, and even if true no excuse for wanton murder)”, “The rapes of children and their cover-up were not unusual (a hell-condemning perposterosity)”, “Immigration is good and will continue (even though all of history shows forced mixing of cultures leads to violence)”, and so on.

Nobody believes any of these Expected Lies, nor are we meant to. Yet there is something in all of us that screams, “Why can’t these bloody liars tell the truth!” They cannot because, as with the serially offending President, admitting the truth must needs lead to action. And the action called for cannot be countenanced by these leaders.

At the least would be the public recognition that Equality and Diversity are false gods. Religions as deeply held as these are not given up over a few deaths. Better would be the ejection of Muslims from once-Christian countries, but that would not only cause leaders to admit the superiority of Christianity over Islam, but again it would force them to say Equality and Diversity are wrong. (I’ll soon have more to say on the freedom of religion.) At the most would be war: Crusade against Jihad.

None of these actions are palatable; none will be taken. The Expected Lies therefore must continue.

God bless Pope Francis. He was on yet another plane and as is his wont he spoke without even notes on his cuff. He admitted the world was at war, but he clarified what he meant by war:

“When I speak of war, I talk about it seriously, but it’s not a war of religion. It’s a war for money, for resources, for nature, for dominion. This is the war,” Pope Francis told journalists on his July 27 flight from Rome to Krakow.

“Could one think of a religious war? No. All religions want peace. Others want war,” he said. “Is that clear?”

No, your holiness, it is not clear. Blessed be the peacemaker, but Our Lord also said, “Think not that I am come to send peace on earth: I came not to send peace, but a sword.” While Christianity desires peace, war, like the poor, is something we recognize we will always have with us.

The Pope’s propaganda isn’t believed, and isn’t expected to be believed. Did not the holy Quran say (sura 2 at 191) “And kill them wherever you find them, and turn them out from where they have turned you out” and (sura 9 at 5) “So when the sacred months have passed away, then slay the idolaters wherever you find them, and take them captive and besiege them and lie in wait for them in every ambush…”, and more beside? Did those religions which offered human sacrifice desire peace?

What’s puzzling here are the actions expected were the Pope to tell the truth instead of the Expected Lie. One would be the admission that Christianity is superior to Islam. Is the Pope reluctant to make this claim? The Pope may calculate that his opinion is so weighty that the secular leaders of Europe (and elsewhere) would have to openly agree with him, thus leading to the consequences noted above. But does Pope Francis really believe he is so important in the post-Christian West?

I leave this question with you, dear reader.

Computers Can Find Future Criminals? Why, Computers Can Do Anything!

There is a belief—a persistent and beguiling, yet false belief—that a formula exists that can predict anything. This formula will differ, it is thought, by the thing predicted, and it is certain that once the formula is fed into a computer, the future is ours to see.

You might have guessed that our experience with, at the least, quantum mechanics and chaos would have beat this notion out of our heads. But you would have been wrong. (Philosophical note: I do not claim that the future is unforeseeable by any means, but I do claim that the standard, mathematical, mechanistic view of the universe is an unproductive route for augury.)

For a symptom of over-confidence, take this example provided by reader Michael Kubat:

Before his sentence, the judge in the case received an automatically generated risk score that determined Loomis was likely to commit violent crimes in the future.

There are no such things as risk scores; they don’t exist, at least not in the sense implied by this sentence, which is taken from the article “This Guy Trains Computers to Find Future Criminals” at Bloomberg. Just like you don’t have “a probability” of being stung by a bee or hit by lightning, you do not have a risk or chance or probability that you’ll break the law.

Why? All probability, all risk, all chance is conditional. In order to have “a” probability, probability itself would have to be unconditional. Put it this way. You have “a” height, which though the units it’s expressed in are relative, is real and measurable (though even height is dependent on conditions; think of measuring yourself near a black hole, where your stature would be diminished).

Here’s another example. What’s “the” probability of drawing the Jack of Hearts? There isn’t one. There is if you assume the conditions there are fifty-two cards in a deck, just one of which is the Jack of Hearts and when drawn only one card will show. But if you change the conditions to there are twenty-two cards, etc., the probability changes (and dramatically).

All this means that it’s possible to predict this Loomis will commit a crime, but only conditional on some ad hoc model. Bloomberg says:

Risk scores, generated by algorithms, are an increasingly common factor in sentencing. Computers crunch data—arrests, type of crime committed, and demographic information—and a risk rating is generated. The idea is to create a guide that’s less likely to be subject to unconscious biases, the mood of a judge, or other human shortcomings.

Algorithms are done on computers!

The “unconscious bias” so fretted about won’t be present in the judge who relies on an ad hoc model, but it will exist in the ad hoc model, or the creators of that model. What happens is that everybody thinks the algorithm is unbiased, but this is simply impossible. The bias are the conditions, and conditions must exist for any algorithm to exist.

Richard Berk from the University of Pennsylvania, “a shortish, bald guy” and statistician, is one of the folks pushing the false view of model prowess. “Berk wants to predict at the moment of birth whether people will commit a crime by their 18th birthday, based on factors such as environment and the history of a new child’s parents.”

Of course, he can make such predictions; anybody can. You can, based on patterns in the scatter from your Fruit Loops. Whether these predictions have any skill (a word I used in its technical sense) is another matter entirely. Bloomberg rightly says Berk’s models “makes people uncomfortable”, which they should. The danger is that they’ll be assumed to be better than they are because they were made by Science on Bias-Free Computers using Machine Learning. Machines that can learn!

Accuracy? “Berk says that in his own work, between 29 percent and 38 percent of predictions about whether someone is low-risk end up being wrong.” Is this from prediction of entirely new data, or from the model fit? A guess is the later. Anyway, these dismal accuracies are not from at-birth predictions, but are contemporaneous. Predictably (get it?), Berk says “focusing on accuracy misses the point”. Yeah, sure it does. Here’s the frightening bit:

When it comes to crime, sometimes the best answers aren’t the most statistically precise ones. Just like weathermen err on the side of predicting rain because no one wants to get caught without an umbrella, court systems want technology that intentionally overpredicts the risk that any individual is a crime risk.

No no no no no no no no no! No. No. Rubbish. Rot. Nonsense.

What is always wanted is, given the conditions (i.e. the model), the actual probability of the event. No two people make the same decisions based on the weather report, and any shading of the probability one way or the other is, in effect, making the decision for somebody. Same goes for predicting pre-crime, where the decisions are (usually) more consequential. Accuracy always matters.

I have much more on these subjects in Uncertainty: The Soul of Modeling, Probability & Statistics.

Jumping Jackers Organize Demonstration For Peace


On a grassy knoll inside Central Park at the People’s Climate March, a group of demonstrators, keen on enlightening the world, had set up in plain view (see my original report) and readied themselves for their spectacle.

Some eight or dozen people, half men, half women, all roughly thirty years old, were doing jumping jacks. Hup two three ourp! A smaller group was demonstrating squat thrusts—down! up! down! up!—while a third bunch were showing arm curls with tree branches evidently foraged from the park. Unh unh unh!

This athletic show was meant to convince people to be one with Mother Earth, to be one with the Universe, to be one with each other. Or something like that.

No, wait. It wasn’t weight lifting or old-fashioned calisthenics. I mis-remembered. It was yoga. Well, they’re easy to mix up, right? Each are forms of exercise, conduits for health and that kind of thing. Isn’t that so?

We’re seeing a lot of this lately. People cropping up, flexing their musculature in an effort to twist the space-time continuum to align the vibrations (it’s always vibrations), to be in spiritual resonance, and to cause bystanders to fall under the spell of these vibrations and travel along the same world-line to the final destination of Full Enlightenment.

Item Turkish protesters hold mass yoga demo (video). This was in 2013. From the description: “Protesters who have been occupying Istanbul’s Gezi park for six days in an effort to save it from the bulldozers take to mass yoga as a new form of protest.”

A women in the video said, “I felt Peace. I felt Peace. I mean, I’m like I’m not sleeping and you know there’s this craziness and you feel you’re really upset but I was at peace today. It was nice.” Another man (pictured above), looking like the Director in some California corp “Oohhmmed” silently and said nothing.

Item At the Republican Convention in Cleveland came many protesters. According to one news report:

…To the northwest, brightly colored characters dressed like monochrome dervishes twirled in silence. To the northeast, a row of five figures wearing black from head to toe engaged in slow-motion yoga.

It was a typical scene this week in Cleveland’s Public Square, the 10-acre park where demonstrators, media, and above all police congregated while delegates duked it out at the Republican National Convention.

Item At that same event, a magazine devoted to celebrity tittle tattle spoke of “an ambidextrous beatnik doing yoga in a Black Lives Matter tee in front of sign that proclaims ‘Pro-police Anti-brutality.'”

Item In Vancouver two “two pro-pot activist groups” went to war with one another. Organizer “Jeremiah Vandermeer says it’s when police told them they could set up on the front steps of the art gallery, that things turned ugly.”

“We didn’t set up a stage, we were just going to go up the Art Gallery stairs.”

“Well there’s another group of activists who are very aggressive and they actually physically assaulted me twice, one of them ran at me with a rolled-up yoga mat sideways, wacked me in the side of the head, like battering rammed me.”

Yoga mats as physical as well as spiritual weapons!

Item The Yoga of Protest Politics: How to Bring Yogic Principles into the Upcoming Election Season by white guy Josh Schrei.

How do we reconcile the yogic teachings on inner calm with the anxiety we feel at the state of the world? How do we quiet our mind when… Trump? [ellipsis original] And should we quiet it at all? Isn’t our outrage at the current situation a catalyst for change? Shouldn’t we be out in the streets and in the back alleys of the Twitterverse calling for a better world? Or would that be decidedly “un-yogic” of us?

Schrei tells us “Guess what? Yogis protest.”

There are so many more such items that they represent a trend. Not only in the public display of provocative or hideous clothing (as the body of the wearer is fit or not) known as “yoga pants”, or in the danger of sliding under the sway of bizarre religious figures (such as with Dahn), but in the return to something like an old-fashioned kind of paganism.

These protesters really do think, like those doing jumping jacks or stretching before the game really don’t think, that their pretzel-bending is manipulating “elements” and that these manipulations will cause spiritual changes in others. But unlike paganism in the good old days, the only gods yoga-ists recognize, besides the universe itself or Mother Earth, is themselves. Interesting, no?

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