William M. Briggs

Statistician to the Stars!

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C.S. Lewis On The Validity of Reasoning

The S was for Staples!

From Miracles (Touchstone edition, 1996, pp 23-24; original 1947):

All possible knowledge, then, depends on the validity of reasoning. If the feeling of certainty which we express by words like must be and therefore and since is a real perception of how things outside our minds really “must” be, well and good. But if this certainty is merely a feeling in our own minds and not a genuine insight into realities beyond them—if it merely represents the way our minds happen to work—then we can have no knowledge. Unless human reasoning is valid no science can be true.

It follows that no account of the universe can be true unless that account leaves it possible for our thinking to be a real insight. A theory which explained everything else in the whole universe but which made it impossible to believe that our thinking was valid, would be utterly out of court. For that theory would itself have to be reaching by thinking, and if thinking is not valid that theory would, of course, be itself demolished…It would be an argument which proved that no arguments was sound—a proof that there are no such things as proofs—which is nonsense.

Thus a strict materialism refutes itself for the reason given long ago by Professor Haldane: “If my mental processes are determined wholly by the motions of atoms in my brain, I have no reason to suppose that my beliefs are true…and hence I have no reason for supposing my brain to be composed of atoms.” (Possible Worlds, p. 209.)

We are more than we seem to be; we are more than meat machines.


Update


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Another Revolution In College Learning

Quantitative support!

Did you hear? Our top universities gathered their number-one administrators and professors at a secret conclave and, acting as one, created a new device which will “revolutionize” college learning.

You’ve seen the stories. Even the Washington Post is writing about it: An online college revolution is coming.

Seems the device is made to store the knowledge of any professor and transmit it to any student. Free. There are minor costs in producing the device, but they will be absorbed by the universities themselves. Students themselves pay nothing.

And who’s a student? Anybody. Unlike MOOCS—massive open on-line courses—and other distance-learning schemes, these new devices will be available both on-line and off-line. To anybody who says, “Me, please.” That is what makes them so revolutionary.

Anybody, anywhere, and almost any time may walk into one of thousands of distribution centers and pick up, at zero cost, one of these devices. Or they may download them on line instantly (though sometimes there is a small fee for recently produced on-line devices). Either way, the students take the devices home with them and then access the material.

You do not have to be registered at a university, there is almost no paperwork required (except for signing your name on the registration form at the distribution center; every city has at least one location), and there is no schedule. You do all this at your own pace with nobody ever breathing over your neck. Talk about stress relief!

Imagine! All the world’s knowledge available at your fingertips! There is nothing you cannot learn! Just grab and go. I mean it. Any subject from astronomy to zoology yours for the asking. Just ask! Did I mention it was free?

Yes, sir. It really is just that easy. I’m so breathless because the implications of this new program are huge; incalculable, really. It is impossible to over superlativeize (yes, superlativeize). One professor maps to a potentially infinite number of students. Everything worth knowing will be input into these devices and no student is barred from learning. Even prisons—yes, prisons—will have these devices. These devices are entirely judgement free, making them the first things mankind has ever created that was.

The on-line material you already know about (since you are reading this on an on-line blog), but a few words must be sad about the off-line devices. Universities being what they are, the folks who created these devices has the poor and downtrodden at the top of their minds from the get go. That is why the devices can be accessed at no cost.

But it’s better than that. The devices are supported in every known language. They are made of renewable material and are nigh on indestructible. Unlike Kindles, Nooks and the like, they require no machine to run on: they are entirely self-contained. And, get this, the off-line devices are designed to work without active energy input. They work on the African veldt miles away from any outlet. They use the ambient electromagentic field to operate.

While marvelous, the details can get technical. But the good news is that the devices require no operating instructions: they are that easy to use.

All we have to do to make this revolution happen—imagine how the world will be a better place!—is to get the word out to students. That’s where we need your help: to pass on the word. We don’t want these things to remain a secret and all that learning going to waste.

Hey, student! Look at what you can do! You say you want to learn? Well here is the tool to make that happen. All we need is you to do what you say you wanted to do: learn. Walk into a distribution center today, pick up one of hundreds of thousands of devices, and access the material.

What are you waiting for! Get going!



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Bishop Tutu: “I’d Rather Go To Hell Than…”

Remember me?

Desmond Tutu, the once-famous Anglican bishop, made the news when he said yesterday, “I would not worship a God who is homophobic and that is how deeply I feel about this…I would refuse to go to a homophobic heaven. No, I would say sorry, I mean I would much rather go to the other place.”

Now I was curious about this; I mean, about his level of earnestness. Everybody in the heat of political passion says stupid things (regular readers will agree), and the bombast required to get your name in the newspaper is increasingly noticeable, so it remains a healthy possibility that Tutu was either blowing off steam or exaggerating for effect. He hasn’t been talked about of late and perhaps he missed those heady days where his every word was weighed and marvelled at.

But while there may be elements of Look-At-Me! in his quote, I think there is another explanation.

The man is a bishop and therefore trained in the idea of Hell. Many modern Anglican theologians don’t believe in it. Not as an actual place where one is parked in the afterlife, but instead as a description of the aches and pains which must be endured here on earth. But if non-existence of Hell is also Tutu’s opinion, then there’s no literal point in saying he’d like to pay it an extended visit.

And then it’s not clear what Tutu’s belief in God is. Wearing of the dog collar is only positively correlated with belief and not certainly predictive of it. If Tutu is on the wrong side of belief, again there is no literal point in his statements.

But he’s on the right side, he must surely know that you cannot dictate to God about what’s right and what wrong. If God has decided, for example, that homosexual acts are a sin, why then they are a sin, even if Tutu (or anybody) doesn’t want them to be. It does not good whatsoever to rail against God. Thus again his statements cannot be taken at their face value.

What we’re left with is circumlocution. I believe what Tutu meant to say, in his literary and not literal manner, is not that he’d like to go to Hell but that he doesn’t believe homosexual (and other sexual) acts are sinful. And he doesn’t think you should think so, either. This is evident from the close of his statement: “I am as passionate about this campaign as I ever was about apartheid. For me, it is at the same level.”

You cannot have a “campaign” to change what is sinful into what is not. You can have a campaign to change minds or to educate.

Along the same line, it is also possible that his statement not only means he’s “for” non-biological sexuality, but that since he well knows that, according to most interpretations, homosexual acts are indeed sinful, that he doesn’t believe in a God who would make this so. In other words, Tutu may be telling us that he doesn’t believe in the Western/Abrahamic God, either.

Of course, we cannot express an opinion on whether Tutu’s desire will be granted if he’s guessed wrong about the theology, other than to say let’s pray not.



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More On True Models And Predictive Inference

Not all models are false. So much we have discussed before.

To say a model is false is to show that one of the premises which comprise the model is false. There are thus certainly many false models. But then there are many true ones. Casinos positively rely on them—and make, as my sister would say, beaucoup bucks doing so. It would be too tedious to rehearse the premises of dice throws and the like. Regular readers will know them off their hearts. But for the freshly minted, this series is pretty good showing some true models.

In order to say a thing is false we must have proof in the form of a logically valid argument. It is no good whatsoever to say, “Ah, the model can’t be true.” This isn’t a valid argument, even though, stripped down, it is the most popular one.

One such proof would be in the form, “The third premise in the model is false because of this true condition.” If such proof isn’t forthcoming, we don’t know the model is false. And some models we can even prove are true, as just said. These start with accepted premises and move to a conclusion the probability of which can be deduced. This probability can even be 1, as in mathematical theorems.

Mathematicians, even of the statistical variety, are comfortable with proof and use it often. But not when it comes to saying this or that model is false.

A true model is not falsified when it says, “The probability of C is X” where C is some proposition and X is some number between 0 and 1, because no observation of C or not-C can ever falsify that model. If a model says “The probability of C is 0″ or 1, or these numbers are in its boundaries, then that model can be falsified if it says C is impossible but C obtains. But it cannot always be falsified if it says C is certain and we don’t see C—unless contained in C are other indicators, such as timeliness.

A model cannot be falsified if it says “The probability of C is exceedingly small” and then C is later found to be be true, because the model did not say C was impossible. It is here where many mistakes are made.

Now many, many models statisticians use are false. Every “normal” model is, which includes all regressions and so forth, and these comprise the bulk of workaday models. Every normal model eventually says, “The probability of C is 0″ where C is almost any proposition, and where C’s “pop up” with regularity. For example, in modeling temperature a normal is often used, and this model must say, “The probability the temperature will be T is 0″ for any T. Yet we will certainly see some T, and when we do we have immediately falsified the model.

Since normal and other “continuous” models, which are models incorporating mathematical infinities and used on finite realities, are used, they are always false. This may be where the perception that “all” models are false originated.

The second portions of Box’s quip is that false models can be useful. Here is where it gets interesting. Take any normal model which is used in practice. If any thought about its validity is made it will be realized the model is false. But it will still be used. Mostly because of inertia or custom, but also because of the sense that the model is “close enough.”

It is that unquantified “close enough” which is fascinating. The average user of statistical models never considers it, at least not seriously. And the statistician is usually satisfied if his math works out or that his simulations are pretty (not worrying that many of these run dangerously close to, or actually are, instances of circular logic).

It is true that sometimes “close enough” is indeed close enough. But since many models don’t get real checking on truly independent evidence, many times “close” isn’t even in the general vicinity.

This is why predictive inference is such a good idea. I often give examples using regression which show both classical frequentist and Bayesian results are “good” in the sense indicated in those theories. But when the model is used in its real-life sense—i.e. its predictive mode, making probability statements about the same observables that were modeled, which after all is the reason for the model in the first place—then it becomes glaringly obvious the models stink worse than a skunk on the side of the road in August.

Examples to come!



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