What Should Philosophers Of Statistics Do?

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D.G. Mayo looking scholarly.

A while back, far longer than it should have been, D.G. Mayo asked me to stop by her place and comment on a couple of posts. But laziness and excessive travel (primarily laziness) have kept me from doing so. This ungentlemanly behavior is partly corrected today.

Mayo bills herself as a “Frequentist in Exile”, a self-imposed state given her worry that subjective Bayesians have taken over most of the slots reserved for philosophers of statistics. She quotes from D.R. Cox, “arguments for this personalistic theory were so persuasive that anything to any extent inconsistent with that theory should be discarded” for an example the trouble frequentists are having.

Frequentist philosophers, mark you. Frequentists in practice outweigh Bayesians by at least an order of magnitude. P-values rain from the skies in both academics and in civilian life. And just try and teach an introductory statistics course which begins with or emphasizes Bayes and not frequentism and see where it gets you. Don’t guess: I’ll tell you. It gets you an invitation to take the first bus out of town. At least you can always run a blog where you beg for jobs (have any? See my Hire Me page).

But comparing miseries gets us nowhere. Let’s look at agreements.

Mayo is my sister in the mistrust of subjectivism. What an awful philosophy! What a distasteful way to found probability! “What’s probability? I’m glad you asked, Student. Truth is what gives you a special frisson, a shiver deep inside. If you want to know the probability, you must first tell me how you feel. Probability is completely personal. Your probability and my probability make us what we are.” Oh please.

Then again, I’m with Cox when he wants to jettison frequentism. Frequencies are the result of and may inorm probability, but they are not probabilities themselves.

There is a third way, which is so-called objectivism, all explained here: Subjective Versus Objective Bayes (Versus Frequentism). There are also fourth, and fifth, and etc. ways, all of which Mayo (if I read her right) and I don’t love. These for a long winter evening.

Mayo:

Nowadays, while the foundations of statistics are being considered anew by many statisticians, philosophers of statistics are almost nowhere to be found. Arguments given for some very popular slogans (mostly by non-philosophers), are too readily taken on faith as canon by others, and are repeated as gospel. Examples are easily found: all models are false, no models are falsifiable, everything is subjective, or equally subjective and objective, and the only properly epistemological use of probability is to supply posterior probabilities for quantifying actual or rational degrees of belief.

Amen and amen. All models are not false, and what a strange thing to believe: “Don’t trust me, I’m the statistician—what I just told you is false.” Of course some models are falsifiable: any time a model says X is impossible (as in impossible; a probability of epsilon is not impossible) and X happens, then the model is falsified; but if the model says the probability of X is epsilon and X happens, the model is not falsified.

Everything is not subjective: is the phrase “everything is subjective” subjective? I.e. true for thee but not or me? And everything can’t be equally subjective and objective: woe betide you if you know a truth but reject it for a feeling.

And “the only properly epistemological use of probability is to supply posterior probabilities…” isn’t quite right. That statement is only mostly true, which means it is sometimes false. It is false when there is no “posterior”, when we are “at the priori”, to coin a phrase. See the series linked above.

I’ll let Mayo have the last (and best) word.

There is a valid question as to whether it is the philosopher of X’s responsibility to solve philosophical problems in domain X; and the answer will surely depend on the field. But in statistical science—itself sometimes regarded as “applied philosophy of science,”—I say the answer is, emphatically, yes! Their failure to do so has left them out of one of the most interesting periods in the areas of statistical science as well as machine learning.


Never Say “Caused By Chance”

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Why does everybody blame me?

Why does everybody blame me?

One of the services of this blog is grammatical guidance. In that spirit, here are phrases which should be forbidden, and will be once I am in charge (all highlights mine):

  • “If our actions are caused by chance…” (source)
  • “How can you tell whether this deviation was due to chance?” (source)
  • “A difference among samples that is due to random variation (chance) is called sampling error.” (source)
  • “In normal English, ‘significant’ means important, while in Statistics ‘significant’ means probably true (not due to chance).” (source)
  • “Such alternative explanations may be due to the effects of chance (random error)…” (source
  • “The difference between two groups is statistically significant if it can not be explained by chance alone.” (source)
  • “A significance test will help us decide if the observed difference between two sample proportions is the result of pure chance…” (source)

We needn’t continue; the gist is clear.

Chance is not a cause; it is not a physical thing; it cannot be operative; it is not a measurable property. If you think it is, I challenge you to collect a bucket of it and bring it our way. If that is too much to carry, make it a thimbleful. Or tell us how it can be seen, felt, heard, smelt (yes, smelt), or touched. Or show us just how, by what precise mechanism, the property of chance carries out its nefarious duties.

Saying events are “due to chance” is a holdover from the days when if a cause was unknown it was ascribed to fairies, pixies, or spirits. It’s the same now, except that chance is sort of vague mystical entity, a dangerous creature not to be stared at, nor sought. Its presence can be felt; it is just as real as any vaporous apparition, and as vexing as a poltergeist. Chance is always destructive of knowledge in a demonically playful way, operating always behind a cloak. It never sleeps.

It’s true that the old (and not yet deceased) frequentist view of probability requires chance (or Chance) to be real; probability is (somehow) created in the wake of Chance. Chance is the being, to a frequentist, which fiddles with the coin as it is spinning, causing it to land heads. Busy man, Chance. Think of all those quarks it has to spin.

But even Bayesians who should know better use the same words. A guess is that this is so because Bayesians were first trained as frequentists and that it is difficult to leave behind fully a bad upbringing. If true, the solution is to eschew frequentist training—which should be done in any case.

What is real definition of chance? Since probability (also not real) is just a measure of uncertainty, chance is a synonym for unknown cause. Try it in the sentences above and you’ll see that they usually become tautological or nonsensical.

“How can you tell whether this deviation was caused by something unknown?” Well, it’s when we don’t know what the cause was. “The difference between two groups is statistically significant if it can not be explained by a cause we don’t know about.” Say that three times fast. “A difference among samples that is due to an unknown cause is called sampling error.” This one works, except for the unfortunate word error, which implies a mistake has been made.

Chance always means “I don’t know how that happened.” This does not imply that somebody doesn’t know why it happened, thought that could be true sometimes (e.g. quantum effects). Coin flips are great examples. Most times the initial conditions are of such complexity that predicting the outcome is too difficult, especially for most civilians. But the measurements can be done. The same flip which for one man is “random”, i.e. “caused by chance”, i.e. “caused by he knows not what”, is for the next man perfectly predictable.

Incidentally, my favorite bad example in today’s list is the one which begins “In normal English…” signaling that in statistics we will be using abnormal language. Too true. The unintentional additional hilarity of getting the (frequentist) theory wrong, I leave you to work out for yourself.


Update In comments some expressed a habit of saying “by chance”. Break it. To say a thing comes to be (known) by something is to say it either caused by it, or is part of the cause of it. Webster by: “With, as means, way, process, etc.; through means of; with aid of; through; through the act or agency of” Chance.

If pressed for a cause, admit ignorance up to the point of probability and then say, “But my uncertainty in the thing is expressed by this & such probability.”

Example 1: Something caused the coin to land heads; I don’t enough to say what; but given the evidence we discussed, the probability of a heads is 1/2.

Example 2: Something caused the observed minor differences between patient groups; I don’t know what; but given the evidence of the study, the probability of a difference is only 1/2.

George Weigel’s Evangelical Catholicism, A Brief Review

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Evangelical Catholicism: Deep Reform in the 21st-Century Church, George Weigel.

The Good Old Days may never have existed, but surely there were better days. Worse days, too. It is also not certain that these days are the best or worst days, nor is there any guarantee that only delights or horrors await us in the future.

Yet it’s hard to find anybody involved in the Church, and even those outside of it, who isn’t keen on reform. However it is now, most suspect, isn’t ideal. Things need fixing. Traditionalists desire antiquarianism and imagine “that the remedy for chaos and confusion…is a return to the Baltimore Catechism” without realizing “that the cultural circumstances in which [it reigned] no longer obtain.” Progressives suffer from “Catholic Presentitis—a lust for ‘relevance’ according to post-modern culture and intellectual canons”.

Weigel spanks both traditionalists and progressives and makes himself seen to be doing it early so that neither side can dismiss his pleas as partisan. But it’s clear that except for gently needling some ate up (that’s some military lingo for you) Lefrebvrist’s, “much more consequential” is the “psychological schism on the left (in which large numbers of Catholics have ceased to believe and process what the Catholic Church believes and professes, but have remained formally, or canonically, within the Church’s boundaries).” This is particularly so in Catholic academia where the game appears to be denying dogma in the cleverest way possible.

Weigel has directions for polishing every facet of ecclesiastical life, from catechism classes to pope picking. Some rubbing is gentle (“consider younger men for the office of bishop”, replace “trashy liturgical hymns”), some require more elbow grease (correcting the liturgical calendar to avoid “biblical insanity” and to insist butts are placed in pews when required), to still others which need (to complete the overworked metaphor) harsh rasps (insistence on celibacy, forbidding men “oriented” towards males the priesthood to avoid future abuse scandals, and to start talking like you believed what you were saying).

About that last requirement, here is a quick quiz. What is the common thread among these phrases, all in common use?

  • “Catholics believe abortion is wrong.”
  • “The Church teaches that Jesus was both man and God.”
  • “According to the catechism, salvation can only be found in the Church.”
  • “The Pope agrees that marriage is only between one man, one woman.”

None of these proposition contain a definite claim of truth. It might be true that “Catholics believe abortion is wrong” but it does not follow from this that abortion is wrong. Neither does it follow that marriage can only be one-biological-man, one-biological-woman because the Pope likes it.

If one wants to claim that abortion is wrong, then the best way to do it is to state, “Abortion is wrong.” That is clear, distinct, and unambiguous. If somebody asks why, it can be proved by saying (for example) “Abortion is the killing on an innocent human life and the killing of an innocent human life is wrong.” The basis for the argument is set.

If you want to claim the divinity of Jesus, then say so shorty. If it is true that salvation can only be had via the Church (i.e. the Body of Christ), then say it plainly—especially from the pulpit and in the seminaries. “It is not a truth for Catholics only, or for Christians only, but a truth that demands of its very nature to be shared with everyone.”

The central reason for the Great Divide, Weigel suggests, starts with the split on the gnostic line: knowable reality versus pleasant stories. “The most prominent example [of] the New Gnosticism is the sexual revolution, which sexualizes everything while concurrently insisting that maleness and femaleness are social constructs—not givens that reveal deep truths about the human condition”. This will ring true to any close observer. But if this is so—if sexuality is a social construct—one wonders where the social constructs arose. What were their templates? Nature? Biology? These can’t be so: they are denied. Skip it.

Weigel is a Big Name, so it’s likely his book will at least be noticed (but perhaps not read) by the Powers. Whether it’s heeded is anybody’s guess.

The Consensus On Global Cooling

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Look at that irreversible, plunging trend!

Look at that irreversible, plunging trend!

It is an interesting exercise to read press reports of the Consensus. The Consensus as was, not as is. The Consensus as of 1975, when the sky was literally going to fall, frozen into a giant blue cube and killing, oh, just about everything.

Reader Jim Fedako sent in the 28 April 1975 Newsweek article “Our Cooling World” by Peter Gwynne. The hyperbole then is the same as now: “serious political implications for just about every nation on earth,” “The drop in food production could begin quite soon,” “devastating outbreak of tornadoes”, “national boundaries make it impossible for starving peoples to migrate from their devastated fields,” and so forth.

Nothing but dead, dying, and soon-to-be suffering everywhere, with subtle lamentations for the (as-yet?) non-existent one-world government (“national boundaries…”). Given the similarity with news reports of today, it suggests activists have a limited palate of horrors and hobgoblins with which to terrorize, trotted out with depressing regularity. All that was missing were threats of sea-level rise. Why were there no reports then of an increase in beach property? Ocean water would have been sucked up in glaciers, see.

It was a Consensus, incidentally. “Meteorologists disagree about the cause and extent of the cooling trend…But they are almost unanimous in the view that the trend will reduce agricultural productivity for the rest of the century.” Note “almost unanimous”, which equaled ninety-seven or so percent of meteorologists—here curiously defined as people expert in weather and agriculture.

The distinctions between the old Consensus and the new one? The old Consensus was formed by meteorologists; now it’s climatologists. Though most are true believers, meteorologists are now among the prominent defectors from the current Consensus. Why? In 1975 climatology was only beginning to be a separate field, complete with their own grants (i.e. money from government), conferences in exotic locations, and journals in which to publish papers few would read.

Then, scientists were not agreed why the world was nearing a “tipping point”; that frightening term had not yet been invented, or it wasn’t in wide-spread use. They did however say that something had to be done, by which then as now meant government should increase in size and power. Makes sense: Consensus-holders depend on government for their salaries, and larger government means fatter and surer paychecks. For both, it didn’t and doesn’t matter what the government does, as long as they act in the name of the Consensus.

The older Consensus was only pretty sure that what was causing the planetary sickness was humanity. The new Consensus is morally certain of it. Both groups were convinced that whatever good happened to the planet was due to Nature, and that whatever bad happened was our fault. Scientific imagination has thus not advanced beyond paganism.

Members of the current Consensus say there is a dramatic distinction between them and the holders of the old Consensus: current scientists say that now—here and now—they know more than did the members of the old Consensus. This is true: they do know more.

But the certainty scientists in both Consensuses held in their prognosticative abilities is the same. Scientists know much more about (say) clouds now, but the folks of 1975 were convinced that what they knew was sufficient to forecast a trial by ice, just as scientists now insist it will be a gauntlet of fire.

Concentrating on the differences of knowledge is wrong, because it doesn’t answer the main question: Do they know enough? We had their word on it in 1975, just as we have sworn Congressional testimony today. Clearly, we cannot use ardency as a measure of truth. Neither is the apoplexy resulting from departures from the Consensus any guide. The very public exasperation against “deniers” is not convincing, and is not evidence, that the current forecasts are any better than the old.

A citizen is well justified to think: “Scientists were so sure before, and claim to be so again. But they were wrong before. Therefore it is rational to suppose they might be wrong again. Only a zealot would disagree. Plus, the dire threats of starvation and so forth are just the same then as now. So which is it? Is it a cooler world or a hotter one which spells death? And just what is the ideal, to-be-desired-for-all-time climate? Exactly now, please.”