William M. Briggs

Statistician to the Stars!

The IPCC’s And McKitrick’s “Hiatus” Time Series Models

Several readers asked me to look at Ross McKitrick’s paper “HAC-Robust Measurement of the Duration of a Trendless Subsample in a Global Climate Time Series”, which is receiving the usual internet peer-reviewing (here, here, and here).

Before we begin, it is absolutely crucial that you understand the following point: both the IPCC (you know I mean the people and groups which contribute to it) and McKitrick have produced time series models.

Many people and groups have created time series models of the temperature, including the rank amateurs who attended the People’s Climate March. The latter model is, in essence, “The End Is Nigh”. This is simplistic, yes, and stupid certainly, but it is still a time series model.

Now we know, without error, that the IPCC’s time series model stinks. That it should not be trusted. That decisions should not be made based on its forecasts. That it is, somewhere, in error.

How do we know this? Because it has consistently and for many, many years said temperatures would be high when in reality they were low (relative to the predictions). People who refuse to see this are reality deniers.

Because the IPCC’s model said temperatures would be high these past eighteen or so years, when in reality the temperature bounced around but did nothing special, the IPCC has taken to calling reality a “pause” or “hiatus”. Everybody must understand that this “hiatus” is model-relative. It has nothing to do with reality. Reality doesn’t know squat about the IPCC’s model. The reality versus the model-relative “hiatus” is how we know the IPCC’s model stinks.

If the IPCC’s model did not stink, it would have predicted the reality we saw. It did not predict it. Therefore the model stinks. The debate really is over.

Now where the IPCC’s model goes wrong is a mystery. Could be it represents deep ocean circulation badly; could be that cloud parameterizations are poor. Could be a combination of things. It’s not our job to figure that out. The burden is solely on the IPCC to identify and fix what’s busted.

Enter McKitrick, who has his own model (or models; but for shorthand, I’ll speak of one). McKitrick’s model is a standard econometric model, which uses the Dickey-Fuller test (economists are always using the Dickey-Fuller test; I just like to say, “Dickey-Fuller test”; try it).

Is McKitrick’s model any good? There is no reason to think so. (Sorry, Ross.) It’s just a simplistic set of equations which is scarcely likely to capture the complexity of the atmosphere. If McKitrick’s model should be trusted, there is one test it could take to prove it. The same test the IPCC took—and failed.

McKitrick needs to use his creation to predict data he has never before seen. He hasn’t done that; and in fairness, he hasn’t had time. We need to wait a decade or so to see whether his model’s predictions have skill. But in a decade, I predict nobody will care.

The objection will be raised: but McKitrick’s model was built not to make predictions but to measure how long the “hiatus” was.

We needed a model for that? No, sir. We did not. We could just use our eyes. We need no model of any kind. We just take reality as she comes. To show you how easy it is to fool yourself with time series, here’s Figure 1 from McKitrick’s paper:

McKitrick's Figure 1.

McKitrick’s Figure 1.

It shows “Globally-averaged HadCRUT4 surface temperature anomalies, January 1850 to April 2014. Dark line is lowess smoothed with bandwidth parameter = 0.09.” Let’s don’t argue about the dots, i.e. the temperature, a.k.a. reality, which really should have accompanying error bounds. Let’s just assume that the dots were the reality, full stop.

The black line is a chimera, a distraction, put there to fool the eye into believing the author has discovered some underlying “signal” in the reality. Well, he might have done. But if he has, he should be able pass the reality test mentioned above. Unfortunately, you can’t make forecasts with that kind of black line. The black line is not what happened! To say it is is to commit the Deadly Sin of Reification.

We must take reality as she is. All we need is a working definition of trend. Easy, right? No, sir. Not really. See this post. But skip all that and call a trend, “Over any ten year period, the temperature increased more than it decreased.” That’s one possible definition of trend.

Accepting that definition (but feel free to make up your own, using the post as a guide), there is no trend in the last two decades. But then there are many other periods sine 1850 without trends. So maybe bump up the time window to 20 years. Still no trend in the latter years.

And so on. No model is needed. None. We just look. There is no need for “statistical significance”, or any other pseudo-quantification.

Listen: make sure you get this. It doesn’t even matter if the IPCC or McKitrick perfectly predicted reality. We still do not need their models to see whether there was a trend. A trend only depends on (1) its definition, and (2) reality.

Update Ken below discovered this gem, which shows Richard Feynman destroying the IPCC’s global warming models.

The Rise Of Bayes

The man himself.

Thanks to reader Frank Kristeller we learn that the far left New York Times yesterday ran an article by F.D. Flam praising the rise of Bayesian statistics: The Odds, Continually Updated.

The replacement of frequentist statistics is, if true, moderately cheering news. And Bayes is the next step in the removal of magical and loose thinking from statistics. But far from the destination. That, I argue, is logical probability, which you can think of as Bayes sans scientism and subjectivism.

However, baby steps:

Bayesian statistics are rippling through everything from physics to cancer research, ecology to psychology. Enthusiasts say they are allowing scientists to solve problems that would have been considered impossible just 20 years ago. And lately, they have been thrust into an intense debate over the reliability of research results.

Nothing like a little hyperbole, eh? I don’t think our frequentist friends would agree they couldn’t solve the same problems as Bayesians. And of course they can. But so can storefront psychics solve problems. What we’re after is good solutions.

Flam got this right:

But the current debate is about how scientists turn data into knowledge, evidence and predictions. Concern has been growing in recent years that some fields are not doing a very good job at this sort of inference. In 2012, for example, a team at the biotech company Amgen announced that they’d analyzed 53 cancer studies and found it could not replicate 47 of them.

This is what happens when you base your decisions on p-values, little mystical numbers which remove the responsibility of thinking. P-values aren’t the only scourge, of course, willful transgressive thinking (especially in fields like sociology) and false quantification are just as, and probably even more, degrading.

False quantification? That’s when numbers are put to non-numerical things, just so statistics can have a go at them. Express your agreement with that statement on a Likert scale from 1 to 5.


“Statistics sounds like this dry, technical subject, but it draws on deep philosophical debates about the nature of reality,” said the Princeton University astrophysicist Edwin Turner, who has witnessed a widespread conversion to Bayesian thinking in his field over the last 15 years.

This is true. But just try to get people to believe it! Most academics, even their Bayesian variety, feel the foundations are fixed, that most or all that need be known about our primary premises is already known. Not true. Philosophy in a statistician’s education is put last, if at all. The error here is to assume probability is only a branch of mathematics.

One downside of Bayesian statistics is that it requires prior information — and often scientists need to start with a guess or estimate. Assigning numbers to subjective judgments is “like fingernails on a chalkboard,” said physicist Kyle Cranmer, who helped develop a frequentist technique to identify the latest new subatomic particle — the Higgs boson.

This isn’t really so. The problem here is blind parameterization, which is the assigning of probability models for the sake of convenience without understanding where the parameters of those models arise. This is an area of research that most statisticians are completely unaware of, so used are they to taking the parameters as a given. Logical probability removes the subjectivism and arbitrary quantification here, so that the true state of knowledge at the beginning of a problem is optimally stated.

Others say that in confronting the so-called replication crisis, the best cure for misleading findings is not Bayesian statistics, but good frequentist ones. It was frequentist statistics that allowed people to uncover all the problems with irreproducible research in the first place, said Deborah Mayo, a philosopher of science at Virginia Tech. The technique was developed to distinguish real effects from chance, and to prevent scientists from fooling themselves.

Mayo (our friend) is wrong. It was the discordance between scientists’ commonsensical knowledge of causality and the official statistical results that allowed us to see the mistakes. Statisticians do causality very, very badly. Indeed, frequentism is based on a fallacy of mixing up ontology (what is) with epistemology (our knowledge of what might be). Bayes does slightly better, but errs but introducing arbitrary subjective opinion.

Uri Simonsohn…exposed common statistical shenanigans in his field — logical leaps, unjustified conclusions, and various forms of unconscious and conscious cheating.

He said he had looked into Bayesian statistics and concluded that if people misused or misunderstood one system, they would do just as badly with the other. Bayesian statistics, in short, can’t save us from bad science.

Simonsohn (whom I don’t know) is right, mostly. The problems are deep. But you notice he left out p-values.

Flam missed that resistance to Bayes is still strong in many traditional fields, like medicine, where p-values are demanded. Still, that Bayes is becoming more available is good. But since we’re at the start and let’s try and do it right, and not, say, re-introduce old notions (like p-values!) into new theory.

A Wandering Mind Is An Unhappy Mind?


The gentleman who runs Shadow To Light asked me to take a look at a paper which Sam Harris approvingly quoted. The 2010 peer-reviewed one-page paper shares today’s title (sans question mark) and was written by Matthew A. Killingsworth and Daniel T. Gilbert, appearing in Science.

The pair are from Harvard which allowed them, it appears, to garner national attention for their project, which asked people to log onto the website TrackYourHappiness.org. The website boasts itself as “a new scientific research project that investigates what makes life worth living.”

Which is an immediate failure in the narrow sense that science must remain forever mute on what makes life worth living. That is the task of religion, philosophy, literature, and other arts. Saying science can tell us means the billions of people who lived before (say) 1500 had no clue why they were happy or sad. But never mind.

The 5,000 or so participants had to have a (surprise) iPhone, which was in part given over to alerting holders, via text message or email, from 1 to 3 times a day, to answer several questions, including in what activity were they engaging, whether their “minds” were “wandering”, and how numerically happy they were.

How long after receiving these messages it took participants to answer I couldn’t discover—perhaps their minds were wandering when they were received?—but since some people reported engaging in sexual intercourse and others in driving, it might have been appreciable. But perhaps iPhone users are more dedicated to their hand machines than I suspect?

Anyway, everybody was contacted from between 1 and 39, average 8, times; compliance was about 83%, meaning not everybody responded to every message.

The authors say, “Unlike other animals, human beings spend a lot of time thinking about what is not going on around them,” which is true. That is because humans are rational beings, which implies having wander-capable minds, and other animals do not. Yet somehow from this the authors conclude:

Although this ability is a remarkable evolutionary achievement that allows people to learn, reason, and plan, it may have an emotional cost. Many philosophical and religious traditions teach that happiness is to be found by living in the moment, and practitioners are trained to resist mind wandering and “to be here now.” These traditions suggest that a wandering mind is an unhappy mind. Are they right?

Living in the moment? If your mind is always “in the moment”, how does it escape into the next moment and have more than one thought? Skip it.

The authors claim to to have “solved” the problem of sampling people’s thoughts with their iPhone app. And that was to ask participants “How are you feeling right now?” (from 0 to 100) and “Are you thinking about something other than what you’re currently doing?” Such as letting the traffic before you dissolve and instead think about designing an internet survey? Or not paying attention to the television commercial (several participants claimed to be watching TV) and thinking about something more pleasant?

Now comes the wee p-values. “[M]ultilevel regression revealed that people were less happy when their minds were wandering than when they were not”, confirmed, as said, by a wee p-value. Further, and in the category of Who Knew?: “people’s minds were more likely to wander to pleasant topics (42.5% of samples) than to unpleasant topics (26.5% of samples) or neutral topics (31% of samples)”.

But wasn’t it just the case that when faced with dull or familiar topics, participants’ minds would wander? And wouldn’t whether their minds wandered into happy or sad places depend on the (unsampled) nature of what urgent matters were pressing down on participants’ minds, and don’t negative matters cause us to consider them more urgently than positive ones?

They say no. “[T]ime-lag analyses strongly suggested that mind wandering in our sample was generally the cause, and not merely the consequence, of unhappiness.” Time-lag analysis? In supplementary material, they say: “We used multilevel regression to determine whether there was a relationship between happiness in given sample (T) and mind-wandering in the previous sample (T-1) and/or the next sample (T+1).” The conclusion of which was

…we found a strong negative relationship between mind-wandering at T-1 and happiness at T, but no relationship between mind-wandering at T+1 and happiness at T. In other words, a person’s happiness was strongly related to whether they had been mind-wandering in the previous sample, but was unrelated to whether they were mind-wandering in the next sample.

This is a silly statistical procedure, of course. The times were not constant, the things thought about where not constant or controlled for, and then consider some samples came from previous days. And also that quantifying happiness on a numerical scale, as often as it is done, is absurd. Is my “50” the same as yours? Is my “50” the same as my “50” yesterday?

The problem with this study is the same as that with “big data”, incidentally. The ability to collect massive amounts of “data”, most of it highly suspect, does not bring about an increase in intelligence.

Update On religions not wanting your mind to wander, listen to this speech by Peter Kreeft, starting about here.

Summary Against Modern Thought: God Is Not A Body. Part III

This may be proved in three ways. The first...

This may be proved in three ways. The first…

See the first post in this series for an explanation and guide of our tour of Summa Contra Gentiles. All posts are under the category SAMT.

Previous post.

This is the last part proving God is not a body (more proofs, that is; we have already had several), a proposition which in unfamiliar to moderns and therefore not under much dispute, except for the steady stream of demiurges put forth by modern atheists as misconceptions of who or what God is. Yet I see that we’re growing weary of this subtopic, and so we’ll finish it today, and in a circumscribed fashion. I’ll also keep my footnotes to a minimum. Don’t forget we already know the Unmoved Mover, God, is outside time, i.e. is eternal. There are a lot of infinities involving God, and today we meet some of them. Next week, we start on a new and essential topic, that God is His own essence.

Chapter 20: That God is not a body

13That the power of the first mover is infinite is proved thus. No finite power can cause movement in an infinite time. Now the power of the first mover causes movement in an infinite time, since the first movement is eternal. Therefore the power of the first mover is infinite.i

The first proposition is proved thus. If any finite power of a body causes movement in infinite time, a part of that body having a part of that power, will cause movement during less time, since the greater power a thing has, for so much the longer time will it be able to continue a movement, and thus the aforesaid part will cause movement in finite time, and a greater part will be able to cause movement during more time. And thus always according as we increase the power of the mover, we increase the time in the same proportion. But if this increase be made a certain number of times we shall come to the quantity of the whole or even go beyond it. Therefore the increase also on the part of the time will reach the quantity of time wherein the whole causes movement. And yet the time wherein the whole causes movement was supposed to be infinite. Consequently a finite time will measure an infinite time: which is impossible…ii

16The second objection is that, although a body be divided, it is possible for a power of a body not to be divided when the body is divided, thus the rational soul is not divided when the body is divided.iii

17To this we reply that by the above argument it is not proved that God is not united to the body as the rational soul is united to the human body, but that He is not a power residing in a body, as a material power which is divided when the body is divided. Wherefore it is also said of the human intellect that it is neither a body nor a power in a body.[11] That God is not united to the body as its soul, is another question.[12]

18The third objection is that if the power of every body is finite, as is proved in the above process; and if a finite power cannot make its effect to endure an infinite time; it will follow that no body can endure an infinite time: and consequently that a heavenly body will be necessarily corrupted. Some reply to this that a heavenly body in respect of its own power is defectible, but acquires everlastingness from another that has infinite power. Apparently Plato approves of this solution, for he represents God as speaking of the heavenly bodies as follows: By your nature ye are corruptible, but by My will incorruptible, because My will is greater than your necessity.[13]iv

19But the Commentator refutes this solution in 11 Metaph. For it is impossible, according to him, that what in itself may possibly not be, should acquire everlastingness of being from another: since it would follow that the corruptible is changed into incorruptibility; and this, in his opinion, is impossible. Wherefore he replies after this fashion: that in a heavenly body whatever power there is, is finite, and yet it does not follow that it has all power; for, according to Aristotle (8 Metaph.)[14] the potentiality to (be) somewhere is in a heavenly body, but not the potentiality to be. And thus it does not follow that it has a potentiality to not-be.

It must be observed, however, that this reply of the Commentator is insufficient.v Because, although it be granted that in a heavenly body there is no quasi-potentiality to be, which potentiality is that of matter, there is nevertheless in it a quasi-active potentiality, which is the power of being: since Aristotle says explicitly in 1 Coeli et Mundi,[15] that the heaven has the power to be always. Hence it is better to reply that since power implies relation to act, we should judge of power according to the mode of the act. Now movement by its very nature has quantity and extension, wherefore its infinite duration requires that the moving power should be infinite. On the other hand being has no quantitative extension, especially in a thing whose being is invariable, such as the heaven. Hence it does not follow that the power of being a finite body is infinite though its duration be infinite: because it matters not whether that power make a thing to last for an instant or for an infinite time, since that invariable being is not affected by time except accidentally…

28Again. No movement that tends towards an end which passes from potentiality to actuality, can be perpetual: since, when it arrives at actuality, the movement ceases. If therefore the first movement is perpetual, it must be towards an end which is always and in every way actual. Now such is neither a body nor a power residing in a body; because these are all movable either per se or accidentally. Therefore the end of the first movement is not a body nor a power residing in a body. Now the end of the first movement is the first mover, which moves as the object of desire:[21] and that is God. Therefore God is neither a body nor a power residing in a body…vi

31Hereby is refuted the error of the early natural philosophers,[23] who admitted none but material causes, such as fire, water and the like, and consequently asserted that the first principles of things were bodies, and called them gods. Among these also there were some who held that the causes of movement were sympathy and antipathy: and these again are refuted by the above arguments. For since according to them sympathy and antipathy are in bodies, it would follow that the first principles of movement are forces residing in a body. They also asserted that God was composed of the four elements and sympathy: from which we gather that they held God to be a heavenly body. Among the ancients Anaxagoras alone came near to the truth, since he affirmed that all things are moved by an intellect.

32By this truth, moreover, those heathens are refuted who maintained that the very elements of the world, and the forces residing in them, are gods; for instance the sun, moon, earth, water and so forth, being led astray by the errors of the philosophers mentioned above.vii


i[Comment updated to fix stupid typo.] Don’t forget to review what these terms mean. The first movement is not some movement that caused the universe to start on its way in the dim dark past. It is the movement that starts all other movements, and we have seen that it must take no time. Again, I ask you to review Chapter 13. And Chapter 17, which proves God is not made of matter, and Chapter 15, which proves God is eternal. These are all premises here.

iiThis is not as bad as it looks when you first scan it. Read it. Two objections answered about conditionals and divided bodies are skipped.

iiiThe first time we hear the soul is immaterial! See also the next point, at that word “united.” This is only a hint of what is to come in other books of STG. Book One is all God all the time. Do not become a Descartesian over this one small word.

iv“For the sword outwears its sheath…And the soul wears out the breast.”

vSo much for slavishly following his predecessor!

viThis is pretty, but you must have Chapter 13 assimilated before you understand what he’s talking about. For instance, movement is actualization of a potential, and some actual power must actualize the potential. Potentials are powerless. (There’s a new business slogan for you.)

viiThe two-paragraph passage has interest in itself, as philosophical history, but is also proof that progress can be and is had in philosophy and theology, just like in science. Decay and distraction, again just in like science, also happen. Theology is thus, in the same sense as science, self correcting.

[11] Cf. Bk. II., ch. lvi.
[12] Cf. Ch. xxvii.
[13] Timaeus xli.
[14] D. 7, iv. 6.
[15] Ch. iii. 4; xii. 3.
[16] See above: But the Commentator…p. 46.
[17] 3, iv. 11; 6, ii. 8.
[18] Averroës, 12 Metaph. t. c. 41.
[19] See above: To this we reply…p. 46.
[20] Ch. vii. seqq.
[21] Cf. ch. xiii.: Since, however,…p. 31.
[22] Bk. IV., ch. xcvii.
[23] Cf. 1 Phys. ii.

On Being Certain There’s No Certainty

I’m certain I’m pretty sure that that’s Voltaire.

Neurologist Robert Burton describes this “delusion of certainty” in his book On Being Certain: Believing You Are Right Even When You’re Not: “Despite how certainty feels, it is neither a conscious choice nor even a thought process. Certainty and similar states of ‘knowing what we know’ arise out of involuntary brain mechanisms that, like love or anger, function independently of reason.”

This was quoted in “Christianity is wildly Improbable” by John W. Loftus in the book The End of Christianity edited by the same gentleman (this is the book in which Richard Carrier’s deeply flawed essay appears). Loftus was concerned of his friend’s disquieting certainty that God exists.

Loftus, who was certain he was right that his friend’s certainty in God’s existence was flawed because one cannot be truly certain, was quoting Burton in support of his (Loftus’s) certain belief that one cannot be certain, because Burton is authoritatively certain that his theory, that no one can really be certain, is certainly true.

Got it?

Now what I’m hoping is that Loftus’s passion that he be certain that there is no certainty has misled him about Burton’s theory, and that Burton didn’t really mean what his words seem to mean. Where would academia be if people actually thought things like that?

On the other hand, don’t we already know?

Wasn’t it Voltaire, another reliable voice, perhaps following Pliny the Elder who said “The only certainty is that nothing is certain”, who said, “Doubt is not a pleasant condition, but certainty is absurd”? Yes; yes, it was Voltaire. I’m certain of that. Voltaire was certain that certainty was absurd. And I’m pretty sure that it was John Stuart Mill who said, “There is no such thing as absolute certainty, but there is assurance sufficient for the purposes of human life.” I am sure that Mill—if, indeed, it was Mill, and it surely was—was certain there was no such thing as absolute certainty.

And didn’t the greatest brain of them all (forget he rejected the confirmed portions of quantum mechanics as being certainly wrong), Albert Einstein, say, “I believe in intuitions and inspirations. I sometimes feel that I am right. I do not know that I am” (and now recall that he rejected the confirmed portions of quantum mechanics of being certainly wrong).

This is how we can be certain that many modern philosophers are skeptics when it comes to certainty. I have witnessed the uncertainty in certainty. These fellows—fellowettes, too!—agree that one cannot be truly certain of anything. And that’s a certainty.

Why, take Mr Falsifiability himself, Karl Popper, who unmistakably said, “Our aim as scientists is objective truth; more truth, more interesting truth, more intelligible truth. We cannot reasonably aim at certainty. Once we realize that human knowledge is fallible, we realize also that we can never be completely certain that we have not made a mistake.” Make no mistake: he also said, “Since we can never know anything for sure, it is simply not worth searching for certainty”. I certainly won’t.

I don’t know if the skeptical philosophers, who are legion in the academy, in being certain there is no certainty, know of Burton’s work that all certainty is really just various arrangements of neurochemicals (or whatever), that it’s our brains telling us to feel certain, even when there is no certainty. But if these philosophers aren’t aware, upon hearing of it, it’s certain they would be certain Burton is right, because Burton’s theory would be pleasing to them, as certain confirmation their philosophy holds.

How nice to think we are nothing but irresponsible unaccountable unpunishable, and of course in a few cases superior, bundle of chemicals!

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