William M. Briggs

Statistician to the Stars!

The Crisis Of Evidence: Why Probability And Statistics Cannot Discover Cause. New Paper

A PM2.5 Storm

A PM2.5 Storm

Cancer of the albondigas is horrifyingly under-diagnosed. See your doctor today and ask him if Profitizol is right for you.

Today’s post, in a way, is at Arxiv: The Crisis Of Evidence: Why Probability And Statistics Cannot Discover Cause. Here’s the abstract (the official one has two typos, meaning my enemies are gaining in power and scope!):

Probability models are only useful at explaining the uncertainty of what we do not know, and should never be used to say what we already know. Probability and statistical models are useless at discerning cause. Classical statistical procedures, in both their frequentist and Bayesian implementations, falsely imply they can speak about cause. No hypothesis test, or Bayes factor, should ever be used again. Even assuming we know the cause or partial cause for some set of observations, reporting via relative risk exaggerates the certainty we have in the future, often by a lot. This over-certainty is made much worse when parametric and not predictive methods are used. Unfortunately, predictive methods are rarely used; and even when they are, cause must still be an assumption, meaning (again) certainty in our scientific pronouncements is too high.

I use PM2.5 (particulate matter 2.5 microns or smaller, i.e. dust) as a running example, since it is one of the EPA’s favorite thing to regulate. I’ll be giving a version of this paper at this weekend’s Doctors for Disaster Preparedness conference in LA. I’ll concentrate more on the PM2.5 angle there, naturally, but I will and must hit the primary focus, which is that probability cannot discover cause.

“But, Briggs, isn’t all of statistics designed around discovering what causes what? Isn’t that what hypothesis tests and Bayes factors do?”

This is true: this is what people think statistics can do. And they are wrong. We bring knowledge of cause to data, we don’t get cause from data. Not directly. Understanding cause is something that is above or beyond any set of data. To understand that, you’ll have to read the paper, a mere 21 pages. If you expect that you have understood my argument by only considering what is in this post, you will be wrong.

An out-of-context-ish quotation (in a low or no group of 1,000 5 people got cancer of the albondigas, and in the “some” or high PM2.5 group of 1,000 15 did):

There is no indication in the data that high levels of PM2.5 cause cancer of the albondigas. If high levels did cause cancer, then why didn’t every of the 1,000 folks in the high group develop it? Think about that question. If high PM2.5 really is a cause—and recall we’re supposing every individual in the high group had the same exposure—then it should have made each person sick. Unless it was prevented from doing so by some other thing or things. And that is the most we can believe. High PM2.5 cannot be a complete cause: it may be necessary, but it cannot be sufficient. And it needn’t be a cause at all. The data we have is perfectly consistent with some other thing or things, unmeasured by us, causing every case of cancer. And this is so even if all 1,000 individuals in the high group had cancer.

This is true for every hypothesis test; that is, every set of data. The proposed mechanism is either always an efficient cause, though it sometimes may be blocked or missing some “key” (other secondary causes or catalysts), or it is never a cause. There is no in-between. Always-or-never a cause is tautological, meaning there is no information added to the problem by saying the proposed mechanism might be a cause. From that we deduce a proposed cause, absent knowledge of essence (to be described in a moment), said or believed to be a cause based on some function of the data, is always a prejudice, conceit, or guess. Because our knowledge that the proposed cause only might be always (albeit possibly sometimes blocked) or never an efficient cause, and this is tautological, we cannot find a probability the proposed cause is a cause.

Consider also that the cause of the cancer could not have been high PM2.5 in the low group, because, of course, the 5 people there who developed cancer were not exposed to high PM2.5 as a possible cause. Therefore, their cause or causes must have been different if high PM2.5 is a cause. But since we don’t know if high PM2.5 is a cause, we cannot know whether whatever caused the cancers in the low group didn’t also cause the cancers in the high group. Recall that there may have been as many as 20 different causes. Once again we have concluded that nothing in the plain observations is of any help in deciding what is or isn’t a cause.

There are some papers by Jerrett mentioned in the body. See this article, and links therein, for more details.


Stream: Vatican Environmental Conference: A Marriage of Bad Governors and Bad Science


Today’s post is at the Stream: Vatican Environmental Conference: A Marriage of Bad Governors and Bad Science.

The excerpt here keeps my caveman joke which was lost somewhere downstream.

Jerry Brown, the majestic governor of California, a state with a list of stultifying regulations longer than the available “genders” on Facebook, while he was at the Vatican, called me, a climate scientist, a “Troglodyte“.

I immediately thought of the Jimmy Castor Bunch and their song of the same name.

He’d go down to the lake, where all the woman would be swimming, or washing clothes or something. He’d look around and just reach in and grab one.

“Come here. Come here.”…

This one woman just lay there, wet and frightened. He said: “Move. Move.”

She got up. She was a big woman. BIG woman. Her name was Bertha. Bertha Butt. She was one of the Butt sisters.

Since I am a troglodyte, it follows that my wife is one of the Butt sisters. I told her so. It was then I learned, in certain and colorful terms, that Governor Brown was wrong.

Go there to read the rest.


Is God is a Mathematician? Guest Post by Bob Kurland


Coincidentally, Bob Kurland sent this guest post on the day of miracles, a good follow up to yesterday’s post.

Feynman: “Do you know calculus?” Wouk: I admitted that I didn’t. Feynman: “You had better learn it…It’s the language God talks.” Herman Wouk, conversation with Richard Feynman in The Language God Talks, p.5.

In his very fine book, Is God a Mathematician?, Mario Livio gives a good history of mathematics and its foundational applications to science. He also discusses whether mathematics is a Platonic ideal or is a construction of the human mind—i.e. is mathematics “discovered” or “invented”? But he does not address the question posed in his title.

Now it goes without saying (although I will say it), that if God is omniscient, he knows everything and therefore, perforce, must know all mathematics. These propositions do not, however, require that reality is altogether mathematical, as suggested by Max Tegmark in his book, Our Mathematical Universe. If reality is altogether mathematical, then everything can be quantified, represented by numbers or properties that can put into correspondence with numbers. Is this so?

I invite the reader to suggest things that cannot be quantified by numbers. Here’s my list of a few such: self-awareness, consciousness (“Cogito, ergo sum”), moments of communion with God, The Holy Spirit, Jesus, love of another, shame, anger, pain, happiness, joy, feelings aroused by nature, feelings aroused by music, feelings aroused by intellectual discovery, the literary excellence of a poem, a short story, a novel, boredom on reading blog posts dealing with the reality of mathematics, etc.

Now psychologists might say that most, if not all of the above can be quantified: just use the simple 1-5 scale as, in satisfaction response surveys. I claim that, unlike measuring the mass of a steel ball or its radius, such a procedure would not yield a universal measurement—one person’s “2” might well be another person’s “4”. The qualia referred to in the above items are non-quantifiable, in the sense that a universally applicable measurement cannot be applied.

Let’s explore just one of the above in more detail—feelings aroused by music. In another post, God’s Gift to Man—the Transforming Power of Music, I’ve discussed the emotional and spiritual impact music has had on me, an effect which cannot be explained by mathematical relationships. The Pythagorean harmonies have no place in the dissonances of Bartok, Berlioz or even Mozart (Symphony #40, the Great G-Minor).

The inability of computation–mathematics—to emulate musical creativity is illustrated in a science-fiction story by James Blish, “A Work of Art“. In this tale “mind sculptors” of the future install a recreation of Richard Strauss in a non-musical volunteer. The volunteer thinks of himself as a resurrected Strauss, composes an opera, and then realizes it uses old musical devices and is not creative. At the concert in which the work is premiered, the volunteer knows that the resounding applause is for the mind sculptors, not for his musical work.

The eminent mathematical physicist, Roger Penrose, has said the mind is not a computer. Penrose demonstrates, using Godel’s Incompleteness Theorem and Turing’s Halting Theorem, that the human can know the truth of a mathematical theorem even when a computer can not.

In Shadows of the Mind he gives four types of belief or non-belief in the possibility of Artificial Intelligence (AI), that self-aware intelligence can be programmed by some set of algorithms:

  1. Consciousness is reducible to computation (the view of strong-AI proponents);
  2. Consciousness can be simulated by a computer, but the simulation couldn’t produce “real understanding” (John Searle’s view);
  3. Consciousness can’t even be simulated by computer, but nevertheless has a scientific explanation (Penrose’s own view)
  4. Consciousness doesn’t have a scientific explanation at all (the view of Thomas Nagel—see Mind and Cosmos)

The philosopher John Searle posits, as does Penrose, that consciousness has a scientific explanation , but that it will be an explanation in which consciousness is an “emergent” property of the brain’s biochemistry and biophysics, much as wetness can be explained by theories of surface tension for water.

A quantum computer (i.e. a scientist engaged in quantum computation), Scott Aaronson, has given an amusing and almost-convincing critique of Penrose’s thesis in one of his Physics Lectures. Some of his criticisms can be answered, particularly the one dealing with the Libet experiment, but I don’t propose to engage that discussion here. The critique relies primarily on two features: the activities of the mind are finite, not infinite; a computer which would be allowed to make mistakes would not be bound by Goedel’s Theorem.

Finally, note that Max Tegmark does not show in Our Mathematical Universe how consciousness can be explained as a mathematical phenomenon. He claims that this will be done in the future, but that seems to me very much like a scientism of the gaps.

If mathematics is to be the end-all and be-all of what is, then it seems reasonable to suppose that mathematics is complete in itself—there are no loose ends. A primitive view of Goedel’s and Turing’s theorems suggest that this is not so.

Faith, religion, beauty, love are non-mathematical and above the bounds of logic. As Pope St. John Paul II, said in Fides et Ratio:

Faith and reason are like two wings on which the human spirit rises to the contemplation of truth; and God has placed in the human heart a desire to know the truth—in a word, to know himself—so that, by knowing and loving God, men and women may also come to the fullness of truth about themselves.

So my answer to the question in the title is, God is much more than a mathematician.


Bread From Something Or Nothing? Or, What’s A Miracle?


We interrupt our tour of Summa Contra Gentiles for this brief message.

You’ve heard of the miracle of loaves and fishes? What’s a miracle? How do miracles happen? Read these for a refresher:

A man came from Baal-shalishah bringing the man of God twenty barley loaves made from the first fruits, and fresh grain in the ear. Elisha said, “Give it to the people to eat.”

But his servant objected, “How can I set this before a hundred?” Elisha again said, “Give it to the people to eat, for thus says the LORD: You will eat and have some left over.”

He set it before them, and when they had eaten, they had some left over, according to the word of the LORD.

After this, Jesus went across the Sea of Galilee. A large crowd followed him, because they saw the signs he was performing on the sick. Jesus went up on the mountain, and there he sat down with his disciples. The Jewish feast of Passover was near. When Jesus raised his eyes and saw that a large crowd was coming to him, he said to Philip, “Where can we buy enough food for them to eat?”

He said this to test him, because he himself knew what he was going to do.

Philip answered him, “Two hundred days’ wages worth of food would not be enough for each of them to have a little.”

One of his disciples, Andrew, the brother of Simon Peter, said to him, “There is a boy here who has five barley loaves and two fish; but what good are these for so many?”

Jesus said, “Have the people recline.” Now there was a great deal of grass in that place. So the men reclined, about five thousand in number. Then Jesus took the loaves, gave thanks, and distributed them to those who were reclining, and also as much of the fish as they wanted. When they had had their fill, he said to his disciples, “Gather the fragments left over, so that nothing will be wasted.”

So they collected them, and filled twelve wicker baskets with fragments from the five barley loaves that had been more than they could eat.

When the people saw the sign he had done, they said, “This is truly the Prophet, the one who is to come into the world.” Since Jesus knew that they were going to come and carry him off to make him king, he withdrew again to the mountain alone.

So I’m visiting a church and the deacon (I think) mounted the high ambo to give the homily. “Today’s reading is all about food,” he said. He mentioned “foodies” and food television and celebrity chefs. “Imagine you were one of the characters in the story,” he offered. “Imagine you were one of the loaves and fishes waiting to be handed out.”

It was at that point that I stopped listening and started thinking about what the passages—for these are the readings today—really meant.

Let’s accept the reported events occurred. How could they? God cannot do the impossible. He can’t, for instance, make himself not exist. That means if miracles like this are going to happen, there are only one of two ways that I see.

Now we know that matter and energy are related; E = mc2 and all that. So the first way would be to take existing equivalent masses or energies and convert them to the desired form—and in the require short time. So, rocks or grassy fields or whatever (mass or energy from elsewhere in the universe would have to be transported, and that requires even more work) are rearranged, via some mechanism, into sufficient bread or bread and fish to feed a multitude. Given what we know about nuclear physics, that would require a magnificent amount of energy. Think of the apparatus required to manipulate just one atom. Here were talking many.

How many? A good spherical cow problem. Should be able to get within an order of magnitude or two the mass involved, and thus a rough count of subatomic particles, and thus some idea of how to rearrange what’s on hand and what that would cost in terms on energy. Since I’m writing this right now this morning and in a hurry, I’ll leave this as a homework problem. The answer will be incomprehensibly beyond any human capacity.

The second way would be to create the masses (of bread or fish) ex nihilo. That requires infinite energy. Nothing is no thing, not some thing. Energy is something, and so is existing mass. So creating from nothing obviously requires Omnipotence. Nothing else could do it.

Point is, given that these events happened, if they happened by manipulating existing mass and energy, it would require something very like magic (but not). Like God. And if the masses were created from nothing, only God could do it.

Now there are other instances of creation ex nihilo and no reports of missing mass or flashing lights or anything like that. And there is nothing we know that would allow nuclear reactions to occur this quickly. This is circumstantial evidence, of course, but it does hint toward ex nihilo. And God. Of course, even rearranging mass points toward God.

And that’s what these passages are really about.

Since I wrote this as a replacement post and, as I said, in a hurry, I may update it as the day goes along.

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