William M. Briggs

Statistician to the Stars!

Page 148 of 708

St Paddy’s Day Parade Report

Not the parade, but it is St Patrick.

I sauntered early up 64th to 5th avenue next to the grandstand and the first event o’ the day was a woman weaving eastwards with enormous bare thighs thrusting out from under a tiny tutu. Green, naturally. She was giggling with her mate, a lovely, healthy young thing who wore shorts and a t-shirt that came just above her pertinents.

My thoughts at the time: Boy, must they be cold, I wonder what St Patrick thinks about this and Confirmation of earlier reports that the pubs opened with the sunrise.

From there, a tremendous lull in the action.

Anyway, since the parade has been made into yet another political event—from which there are precious few, and dwindling, respites—it’s as well to get that nonsense out of the way.

Mayor de Blasio didn’t show in yet another year of protest. He claimed there were not enough marchers who announced with whom or with what they would like to have sexual relations with. (About one such group, more below.) This being the question is today’s society, perhaps he felt everybody should wear some kind of sticker or emblem so that passersby could know whom to hit on and whom to ignore.

Some of us weren’t buying his excuse, though. De Blasio’s relations with police—they and their supporters are a major parade presence—are sour at best, and I think he didn’t want to risk boos from the crowd. He’s a sensitive creature.

A shillelagh-wielding Cardinal Dolan and retinue trotted past shortly after the Fighting 69th, who opened festivities. The prelate received a few polite applause and a wave from two sisters standing nearby.

The first pipe band was announced by a wee Irish lass who shouted to her mother, “Look! A man wearing a skirt!” Poor thing isn’t up on her politics. But she was right. Indeed, it was many men. And boy did they rouse the blood!

I stood next to an Irish gentleman and his wife. A giant, frat-boy leprechaun who was working the crowd, encouraging young ladies to have pictures taken with him. I asked if the gentleman got that sort of thing back home. “Started by the yanks,” he said.

It was yanks who invented the selfie stick, too. An annoying wispy-haired tourist elbowed to the barricade and proceeded to photograph himself in every conceivable pose, but always with the same unhappy smile and the parade at his back, after which he left. As I’ve said before, when one day I read the headline, “Obnoxious Tourist Beaten To Death With Selfie Stick” I won’t weep any tears.

Lots of cops, firemen (the Danish have helmets that look like those from the movie Fahrenheit 459), soldiers, sailors, airmen, marines, veterans, sanitation crews, teachers, Irish appreciated societies, high school marching bands from the world over, drill teams, pipe bands galore, Ancient Order of Hibernians suborders with patron saint banners and chaplains, bands of religious with various Our Ladies, and, near the end, one set of political folks.

They were dull. By the time the “I want to have sex with people of the same sex” contingent (and their allies) marched by the grandstand (about 4:20), the television cameras had been off for over an hour and most of the spectators had departed. The south stands had one person, the main bleachers about twenty, and the north exactly ten folks (I counted), mostly playing on their devices. North half of 64th to 65th on the east side was empty.

Still, the small green-sashed group eeked out some thumbs up and applause from the people remaining. The marchers were loosely surrounded by as many bored cops, some wearing light blue “Community Affairs” jackets (but still armed). The only thing approaching excitement was when the sex group got stopped at 65th to let a firetruck (with sirens blazing) pass (65th is one of Central Park’s exit, cross-town streets).

Doubtless there will be complaints that the “I’m a man/woman and like to see other men/women naked” people should have been more prominently placed (“They didn’t even let us on TV!”). Everybody wants to not only to be a victim, but to be so publicly.

But maybe organizers will realize that, for just one day a year, and for only four hours out of that day, in a parade devoted to one saint and featuring several others, we can do without the politics and just enjoy ourselves.

Answering A Critic On Sampling Variability


Alfred ‘Dominant Strategy’ (ADS) is confused that “William Briggs is confused on sampling variability”.

I wrote an article highlighting misconceptions and mistakes people make when thinking about sampling variability, and ADS kindly answered (I couldn’t discover the gentleman’s full name). In the spirit of peer review done rightly—openly, and not as a blunt instrument to suppress unpopular or misunderstood views—this answer to his rebuttal.

ADS says I think sample variability “is due to the assumption that the population follows some underlying probability distribution. That is not the case.” Well, I agree, and I don’t see how ADS missed my agreement.

It isn’t the case, i.e. it is false, that anything “follows” a probability distribution. As I say in the article and in another article which I linked to (repeated here), to say “variables” “follow probability distributions” or are “distributed as” this or that probability distribution is a common mistake and an error in ascribing cause.

It is our knowledge of the value of certain propositions that is quantified by probability distributions. Epistemology not ontology.

ADS and I agree we’re discussing a “population” of a fixed size about which we want to characterize the uncertainty of some measurement on each member of the population. As is typical, ADS gives a blizzard of math in place of simple words and speaks of “random samples” with “non-zero probability” for collecting samples from the population.

ADS agrees with me that if we knew the values of the thing for each member of the population, we’d be done. I state simply we’d know the values and therefore don’t need probability models. ADS says the average of the thing (across the population) “is not a random variable!” Although I didn’t say it in the sampling piece, I often say that “random” only means unknown, and variable means can take more than one value. So to say a thing is not a random variable is to say we know its value, which is much simpler, no?

ADS is only concerned with taking the average of the measurement across the population, whereas I talked about ascertaining the values of the measure for each individual, so my view was broader. But except for the unnecessary (mystical) language about randomness, there is no real divergence thus far.

I said we start with probative evidence about the thing of interest and use it to deduce a probability (model) to characterize the uncertainty in the unmeasured values of each member of the population, which if you like (cartoon) math is written:

     [A] Pr( Measure takes these values in the 300+ million citizens | Probative Evidence),

which can be converted to the following if we’re only interested in the mean across the population of the measure:

     [A’] Pr( Mean value of the measure of the 300+ million citizens | Probative Evidence).

This puts ADS and me on the same ground. Now suppose we have take a sample of measurements, which we can and should use to give us:

     [B’] Pr( Mean value of the measure of all citizens | Observations & Probative Evidence).

And we’re done, because [B’] can be expanded to accommodate all the measurements we have (on the right hand side). Of course, [B’] doesn’t tell us the exact value of the mean (of the thing), but gives us the probability it takes whatever values we supply (e.g. Pr( Mean = 17.32 | Observations & Probative Evidence) = 0.02, etc., etc.).

ADS goes the classical route and speaks of the sample mean being an estimate of the population mean, and that we can calculate the “variance” of the sample mean, variability which he calls sampling error. Of course, the classical interpretation of the “confidence interval” which uses this variance is itself a problem (see this or the Classic Posts page).

The problem is we don’t care about the sample mean and some interval. We want [B’]. If we had to guess what the population mean was based on [B’], we could, but that’s a decision (a prediction!); the best guess would depend on what penalties we’d pay for being wrong and so forth. If we don’t need to decide, we fall back on [B’], which contains everything we know about the uncertain quantity given the totality of our evidence.

ADS says “William Briggs is confused because he mixes sampling error with statistical inference.” Rather, ADS is confused about the goal of measuring a sample. But his is a common mistake; indeed, his view is taught as the correct way to do things.

I Made “Climate Denial MVP”!

Mine didn't have the white stripe, and was one model year earlier.

Mine didn’t have the white stripe, and was one model year earlier.

Gollum (who’s he? see this post on the political witch hunt of scientists) wrote yesterday to announce that a group of us made the “Climate Denial MVP” List.

I admit to being just a little proud of the distinction. I replied to Gollum saying, “When the hysteria ends and Science returns to the Real World, we’ll all be able to look upon this list and be satisfied that while everybody else had lost their way, we stayed on the path of Truth.”

The List (which is published under another name) appears at a site called “Inside Climate News” by one Katherine Bagley. Who’s she? A writer whose “print and multimedia work has appeared in…YouBeauty.com…” Here is what she wrote for my mini-biography:

Briggs is a statistician at Cornell University in Ithaca, N.Y., and a consultant at New York Methodist Hospital. More than two decades ago, he spent a year as a meteorologist for the National Weather Service. He is listed as an expert on the Heartland Institute’s website, where he wrote, “Climate change is of no real interest to anyone except climatologists.” Earlier this year, he co-wrote an article in the peer-reviewed Chinese Science Bulletin with fellow climate denialists Christopher Monckton and Willie Soon arguing that the IPCC’s models are inaccurate and the world won’t warm dangerously this century.

I also for one year drove a 1964 Plymouth Barracuda with a 273 cu. in. V8 automatic, red with curved rear window, chrome gas pipe, and AM radio, which I rebuilt and repaired and which I loved. Had to sell it when I got orders to PCS to Okinawa. Ah well.

How is my owning this gorgeous muscle car relevant to the work I’ve done in climatology? It isn’t. Neither is it relevant that Bagley wrote for YouBeauty.com to her announcing my coveted status on this MVP list. Whatever I or Bagley says on any subject must be judged by the merits of our arguments, not on who we are.

Our professional qualifications are interesting only to the extent that they tweak your interest into considering what we might say, or as possible reasons why what we have said was true or false.

That’s why I’m sure Bagley won’t mind that I pulled the same trick she pulled on me and left off a few of her more pertinent accomplishments. Those include also writing for “Popular Science, OnEarth, YouBeauty.com, Audubon, The Scientist and Science Illustrated, among others” and that she “holds master’s degrees in journalism and earth and environmental sciences from Columbia University.”

Since I’m guessing Bagley won’t be available to make corrections, here’s more about me.

My ties to Cornell are looser than Bagely lets on—I’m a Adjunct there—but I am a part-time consultant at Methodist, among other places (and why haven’t you hired me yet, dear reader?). I did spend a year launching enormous hydrogen filled balloons for the Weather Service. It is also true that climate change is of no real interest to anyone except climatologists, and I do say the world won’t warm dangerously this century (Bagely’s implication is that, of course it will).

Here’s what was left out (and which was available for a click). Both my Bachelor’s and Master’s are in the atmospheric sciences; my PhD is in mathematical statistics (with dissertation angled towards the atmospheric sciences). I served for several years on the American Meteorological Society’s Probability and Statistics Committee. I was also for several years an Associate Editor at Monthly Weather Review (if you don’t know what that is, you shouldn’t be reading Inside Climate News).

I have published in the Journal of Climate, and in several other like sources. On what subject? How to measure forecast goodness. And how to quantify how useful and valuable predictions are. Mixtures of physics, phrobability, and philosophy (yes, phrobability).

This is how I know that long-term climate models aren’t of much value. Models which predict out a handful of months ahead, however, have modest usefulness, diminishing as lead time increases. But those IPCC-like models which predict years ahead aren’t any good. You’d do better with persistence, which is the forecast that next year will look like this year. If a model can’t beat persistence, it shouldn’t be used. Simple as that.

Gollum didn’t mention if there’d be a trophy or honorarium. I’m guessing not. Climate science does not pay well to those unwilling to toe the Government Consensus line.


Note I’m growing concerned about Gollum. He predicted the DOJ would enter the witch hunt, but so far it hasn’t. But he made that prediction before Senator Inhofe’s blowback; plus the DOJ is spending a lot of time trying to get their new rights-rights-rights boss installed. So stay tuned.

Summary Against Modern Thought: God Is Infinite

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.

There are different kinds of infinity, a non-simple concept. But infinity is nothing in St Thomas’s hands. Those who know something of the history of mathematics will enjoy his arguments. See [10] & [17] in particular.

Chapter 43 That God is Infinite

[1] Since, as the philosophers teach, “the infinite accompanies quantity,” infinity cannot be attributed to God on the ground of multitude. For we have shown that there is only one God and that no composition of parts or accidents is found in Him. Nor, again, according to continuous quantity can God be called infinite, since we have shown that He is incorporeal. It remains, then, to investigate whether according to spiritual magnitude it befits God to be infinite.

Notes God is not a body, is not material; these things were proved. God is no infinite in a countable way, as, say, the integers are.

[2] We speak of spiritual magnitude with reference to two points: namely, power and the goodness or completeness of one’s own nature. For something is said to be more or less white according to the mode in which its whiteness is completed. The magnitude of its power likewise is measured from the magnitude of its action or its works. Of these magnitudes one follows the other. For, from the fact that something is in act it is active, and hence the mode of the magnitude of its power is according to the mode in which it is completed in its act. Thus, it remains that spiritual beings are called great according to the mode of their completion. Augustine himself says that “in beings that are great but not in bulk, to be greater is the same as to be better.”

Notes St Thomas is prepping us to recall God is pure act, i.e. He has no potentiality. Recall that having potentiality, which is in a way the ability to change, accounts or the lack of perfection. Only that which has no potentiality is perfect.

[3] We must therefore show that God is infinite according to the mode of this sort of magnitude. The infinite here will not be taken in the sense of privation, as in the case of dimensive or numerical quantity. For this quantity is of a nature to have a limit, so that such things are called infinites according as there is removed from them the limits they have by nature; which means that in their case the infinite designates an imperfection. But in God the infinite is understood only in a negative way, because there is no terminus or limit to His perfection: He is supremely perfect. It is thus that the infinite ought to be attributed to God.

[4] For everything that according to its nature is finite is determined to the nature of some genus. God, however, is not in any genus; His perfection, as was shown above, rather contains the perfections of all the genera. God is, therefore, infinite.

Notes God Is Not In A Genus: “Whatever is in a genus differs as to being from the other things contained in the same genus: otherwise a genus would not be predicated of several things.” Etc.

[6] …Furthermore, in reality we find something that is potency alone, namely, prime matter, something that is act alone, namely, God, as was shown above, and something that is act and potency, namely, the rest of things. But, since potency is said relatively to act, it cannot exceed act either in a particular case or absolutely. Hence, since prime matter is infinite in its potentiality, it remains that God, Who is pure act, is infinite in His actuality.

Notes Prime matter is a sort of goo from which all form has been removed. Formless building (shapeless, as it were) blocks of the universe; prime matter can become, i.e. be formed, into anything—though there is much more to it (see here for example).

[7] Moreover, an act is all the more perfect by as much as it has less of potency mixed with it. Hence, every act with which potency is mixed is terminated in its perfection. But, as was shown above, God is pure act without any potency. He is, therefore, infinite.

Notes An analogy. Perhaps it helps to think of perfection as a ratio of act to potential, and as potential progresses to the limit of 0, the ratio jumps to infinity. Again, an analogy.

[9] …Then, too, what has a certain perfection is the more perfect as it participates in that perfection more fully. But there cannot be a mode of perfection, nor is one thinkable, by which a given perfection is possessed more fully than it is possessed by the being that is perfect through its essence and whose being is its goodness. In no way, therefore, is it possible to think of anything better or more perfect than God. Hence, God is infinite in goodness.

Notes Recall that God’s essence and existence are one. The limit analogy is useful here, too.

[10] Our intellect, furthermore, extends to the infinite in understanding; and a sign of this is that, given any finite quantity, our intellect can think of a greater one. But this ordination of the intellect would be in vain unless an infinite intelligible reality existed. There must, therefore, be some infinite intelligible reality, which must be the greatest of beings. This we call God. God is, therefore, infinite.

Notes All will accept the first premise, but the second? This states a moderate realist and not a nominalist or Platonic view, a view which is being taken up (again) in mathematics, notably by Jim Franklin and others. And by you, dear reader, if you’ve ever used mathematics to understand the real world. Best short introduction here (pdf): “The neglect of epistemology accounts for two strange absences in the philosophy of mathematics: understanding (and mathematics is where one first goes to experience pure understanding) and measurement (the primary way in which mathematics joins to the world).”

[11] Again, an effect cannot transcend its cause. But our intellect can be only from God, Who is the first cause of all things. Our intellect, therefore, cannot think of anything greater than God. If, then, it can think of something greater than every finite thing, it remains that God is not finite.

Notes Don’t forget our intellect is not material. We are not our brains. And if not material, it has to come from something. St Thomas tackles this argument in the next chapter (next week for us, so belay questions for now).

[12] There is also the argument that an infinite power cannot reside in a finite essence. For each thing acts through its form, which is either its essence or a part of the essence, whereas power is the name of a principle of action. But God does not have a finite active power. For He moves in an infinite time, which can be done only by an infinite power, as we have proved above. It remains, then, that God’s essence is infinite…

[15] Each thing, moreover, is more enduring according as its cause is more efficacious. Hence, that being whose duration is infinite must have been from a cause of infinite efficaciousness. But the duration of God is infinite, for we have shown above that He is eternal. Since, then, He has no other cause of His being than Himself, He must be infinite…

Note A sweet little argument. Don’t forget eternal means, essentially, outside time.

[17] The sayings of the most ancient philosophers are likewise a witness to this truth. They all posited an infinite first principle of things, as though compelled by truth itself. Yet they did not recognize their own voice. They judged the infinity of the first principle in terms of discrete quantity, following Democritus, who posited infinite atoms as the principles of things, and also Anaxagoras, who posited infinite similar parts as the principles of things. Or they judged infinity in terms of continuous quantity, following those who posited that the first principle of all things was some element or a confused infinite body. But, since it was shown by the effort of later philosophers that there is no infinite body, given that there must be a first principle that is in some way infinite, we conclude that the infinite which is the first principle is neither a body nor a power in a body.

Notes St Thomas means to quote Aristotle (here, Section IV):

Belief in the existence of the infinite comes mainly from five considerations:

(1) From the nature of time-for it is infinite.

(2) From the division of magnitudes-for the mathematicians also use the notion of the infinite.

(3) If coming to be and passing away do not give out, it is only because that from which things come to be is infinite.

(4) Because the limited always finds its limit in something, so that there must be no limit, if everything is always limited by something different from itself.

(5) Most of all, a reason which is peculiarly appropriate and presents the difficulty that is felt by everybody-not only number but also mathematical magnitudes and what is outside the heaven are supposed to be infinite because they never give out in our thought.

Aristotle also says, “Also, if void and place are infinite, there must be infinite body too, for in the case of eternal things what may be must be.” If the universe was already infinitely old, we wouldn’t be here.

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