Freq Out
Reader ECM points us to “The Great Statistical Schism“, by a fellow named Brendon Brewer who “is a senior lecturer in the Department of Statistics in Auckland.”
Brewer says, as I say, sort of, that it’s time to “teach Bayes first” and not frequentism. He also says, “Frequentist confidence intervals and p-values should still be taught to some extent”, with which I also agree, up to a point. His reasoning for that opinion is good, though “so much research is based on [p-values and confidence intervals], our students need to know what they are.”
P-values and confidence intervals should be taught in the same way phlogiston or communism are taught, as failed, unfortunate ideas which caused nothing but grief.
Brewer appears to be a subjective-objective Bayesian, which is the most common type. They agree probability is subjective, but go about assigning probabilities in an objectivish way.
Of course, probability is not subjective. Given there are two persons in the room, a male and a female, and one will walk out the door, the probability is 1/2 (deduced via something called a statistical syllogism) that it’s the male. But a subjectivist can say, “The probability it’s the male is 0.13424”, or any other number that strikes his fancy.
Yes. That’s what subjectivism implies: unfounded probabilities. But this tendency is but a minor foible next to hypothesis testing, which should be purged with extreme prejudice from science forthwith.
Not Altruism
Reader Tahir Nasser (who is a public personality) writes:
Great fun reading your blog. Always enjoy it and I learn something new each time. I wrote a piece too (published on Huffington Post blogs) re.: “are religiously educated up children less altruistic” study. I thought you might be interested to take a look/read:
“Why the Latest Study Showing ‘Religious’ Children are Less Moral is Just Bad Science”.
Do let me know your thoughts, particularly regarding the characterisation of probability modelling as a method to determine “correlation”. That’s how I understand r values in the context of probability models.
In his piece, Nasser shows some of the weaknesses of the “altruism” study. But he also writes:
Firstly, the conclusion is totally unsupported by the evidence. The study shows a correlation (not causation!) of -0.173 between religiosity and altruism. Correlation is measured on a scale of -1 to +1 with 0 meaning no correlation. To draw the authors’ conclusion from this meagre result is laughable. This small correlation indicates that other unaccounted factors are at work. What could they be?
I like the spirit and agree with the conclusion, but I don’t agree with the way it was reached for a technical reason. Probability models say nothing about cause. Even if the correlation was large, which it wasn’t, we could not say “altruism” caused stickers to be stuck in envelopes.
Of course altruistic kids would, ceteris paribus, share more stickers than non-altruistic kids. Why? Because they’re altruistic! We do not need a study to show this, because it’s something that everybody, except some scientists, already knows. But would “religious” kids share more? That’s a bigger mystery, because there are no such things as “religious” kids. There are only kids who have this-and-such beliefs. And the study did not, in any way, measure the beliefs of any kids.
Instead, the researchers developed some stupid pseudo-quantification of “religiosity.” What a farce.
People Who Need People
Reader Loras Holmberg writes (ellipses original):
Appearance on Joe Pags Radio Show…you made the comment that people concerned about population growth “don’t like people”. Disagree. I want a world for future generations that has room for ample wildlife and wild lands. I am 57…have seen changes with my own eyes that bring such a future into doubt. More people generally means less of each. Don’t consider myself extreme…on global warming or climate change, I say “maybe”. Don’t know. As you mentioned, once you scratch the surface, the physics are extremely complex.
Nah, more people do not mean less wildlife. You should see the deer problem my parents have. People don’t hunt as much as they used to, since meat appears like magic wrapped in see-through packaging.
Now you say you don’t not like people, but then you imply you’d rather have less of them in preference for more poisonous snakes, leeches, and cockroaches (well, I filled in the blanks on the kinds of animals). That sounds like not liking people overly much to me.
Yes, the physics on global warming are extremely complex. This is probably why they still can’t make good forecasts, and that they can’t make good forecasts is why we should not believe threats of doom.
may be the first thing to do is to abolish the gaussian distribution…
“Yes, the physics on global warming are extremely complex. This is probably why they still can’t make good forecasts…
David Evans says it’s not the complex physics; it’s incorrectly representing the physics in the models. http://joannenova.com.au/2015/11/new-science-19b-a-synopsis/ Have you been following this? Any thoughts beyond “He’ll have to make and prove a prediction”?
Would you say the subjective Bayesians with their unfounded probabilities are akin to the political progressives?
Bullwinkle makes more sense than a lot of real persons. Just sayin’.
Gary,
There are levels of physics. Yes, in theory, we know most or even all of the physics. But that doesn’t mean we’re applying the physics right in the models. The equations of motion on the large scale are surely right, but not so much on the smaller scales. I mean, there’s lots of averaging going on, most of small consequence. The physics of clouds are parameterized, and they stink. And that means precip forecasts stink. There’s the physics/chemistry of land- or ocean-atmosphere and the closer you get to local the poorer these are. Radiative transfer? Forget about it.
Of course, you can write down the equations for a photon coursing through air and so forth. No problem. At that point you can say “We know the physics.” But how do you model countless photons over an entire rotating globe? Answer: nobody knows for sure. No, the “physics” is far from “settled.”
Marco,
I’m right there with you.
Briggs,
Evans is saying that photons radiate to space through four different channels and that the channels do not transmit a fixed flux, but adjust and compensate for each other depending on conditions. The flaw he identifies in the models is not accounting for the compensation. Certainly the parameterizations and scaling issues are problems. This is a criticism that may be right or wrong. At least it’s novel.
The way I learned Bayes’s Rule was that it is a conversion from a normalization along one axis to that of another. IOW: converting Pr(E|H) to Pr(H|E). That the prior can’t be anything is most easily seen when viewing a table of relative frequencies. The Subjectivist approach seems to arise from a total misunderstanding of the purpose of the rule.
The Subjective Bayes side of things isn’t a very big deal to me, because at least it recognizes the need to state assumptions and condition on them. If they say “the probability is assigned because I want it to be that” then we all know and can see it.
Your headline says “autism,” not “altruism.”
Gail,
My enemies’ reach has extended to my headlines!
“on global warming or climate change, I say “maybe”.
None of their predictions has come true, but she still says maybe. That’s really keeping an open mind.
Briggs, usually I sit at the feet of the master and digest pearls of wisdom. (wait–that mixed metaphor won’t work.) But I do have a small bone to pick with you. You said
“Yes. That’s what subjectivism implies: unfounded probabilities.”
I read some time ago Richard Jeffries “Subjective Probability” and from what he says, the beliefs on which priors are based are founded on evidence–Dutch bet type arguments and so forth. However, I would be happy to be enlightened why this isn’t correct.
PS–I am waiting for your book to get the true scoop.
http://www.wbur.org/npr/447202433/-great-pause-among-forensic-scientists-as-dna-proves-fallible
I’d expect there’s some real statistics — and statistics having very real significance — addressed in that link…is anyone up to tackling that head-on?
Loras’s statement that fewer people would leave room for wildlife and wild lands is not necessarily true. One of the major reasons the open spaces in Wyoming are disappearing is not oil and gas, but internet sales of ranches cut up into 40 acre lots. One only need run a blade over the prairie and call it a road, then sell the lots without services. As you can imagine, this is highly lucrative. Not everyone buying builds on the lots, but some do. South of my house, which used to be open prairie is now a small town of 20 acre lots (these do have services). Horses are “welcome” and owners often graze the prairie down to sand. The only way this can be stopped is to change the rules and forbid dividing ranches. Then the rancher can only sell to someone who wants to pay the millions of dollars a ranch costs in one piece. If the government buys them, then the government decides who gets to go there and who does not. It would be easy to shut everyone out but scientists (already suggested by at least one scholar) and elitists. This already the case in Europe—due to private land ownership. The realtors would be furious and fight this tooth and nail. I really wish there was a way to preserve the land as I love the open spaces and wildlife, but I have not found any method that seems feasible. (Briggs–definite deer problem in cities and towns nationwide, along with coyotes, etc. Wildlife is very adaptable.)
Bob,
Jeffrey was wrong. Those Dutch-book procedures rely on introspection, making “bets” with oneself, on how one “feels”. The example I gave above fits perfectly in these schemes.
They have something called “empirical Bayes” which uses the same data to assign priors to parameters and to quantify the uncertainty in the observable. Not a coherent procedure, but it’s good for introducing frequentists to Bayesian ideas.
The real problem is parameters, which don’t exist. About that, I have much in the book.
Sheri,
” I really wish there was a way to preserve the land as I love the open spaces and wildlife, but I have not found any method that seems feasible.”
Form a non-profit funded by like minded individuals and buy land at market rates for preservation. There are several non-profits in the US that have built private wildlife refuges this way. Some will donate the land to the state for management once the refuge is large enough. This avoids the issue of coercion involved in using eminent domain to build refuges/state forests.
There are several in my home state of Wisconsin where the land was acquired with private money then turned over to the state for long term management.
Presumably that’s David Evans of Notch Solar Model fame, whose theory was shredded by fellow skeptics. The thing about contrarians is that most of the time they are wrong about most things, but they are also essential. Without them, there would be no scientific progress.
I’m still waiting for Dr Briggs who regularly complains that causation doesn’t prove cause, to list what things do prove cause. Crickets…
Oops, that was meant to be correlation. ;-P
Looks like I get another chance to try for an answer to this question:
“Given there are two persons in the room, a male and a female, and one will walk out the door, the probability is 1/2 (deduced via something called a statistical syllogism) that it’s the male.”
How do you get the 1/2 without some additional assumptions? Why 1/2 rather than any other probability? What is the syllogism? Feel free to be as explicit as you want (but you need not be gentle: I’ve studied probability theory pretty deeply (but not so much statistics)). Possible shortcut: do you claim this is the same problem as an urn with an equal number of white and black balls? If so, is that the unstated assumption?
I’ve been in a lot of rooms with a lot of women. The woman leaves first. Especially if there is any number of beer, snacks, couch and tv in the room.
Excellent point… Who in general needs to use the bathroom more frequently, a man or a woman? Besides anatomical differences, it may be the case that women are more health conscious and tend to drink more water, and so on. The 50/50 distribution is merely an assumption, not a fact.
How do you get the 1/2 without some additional assumptions?
Probability describes your level of knowledge. With only two choices of events and without any additional information, the probability of each event must be equal or else you are unjustifiably biasing yourself toward one outcome over the other. Hence, with two outcomes, the probability of either is 1/2.
It is 1/2 because there is no other information than the number and labels of the outcomes. It takes additional assumptions to arrive at anything else.
I’d also add that even if Dr Brigg’s reverts to an urn of black and white balls, there multiple problems. For example –
1. The black paint may be thicker than the white paint. This means that the smaller objects (the white balls) will tend very slightly to be found more at the bottom of the urn. So the distribution is not random, although it would be close.
2. Any problem of any scientific interest, has such confounding factors as mentioned in (1). If you add the disclaimer, “all else being equal, my argument is correct” — the problem is that this is never the case. That’s merely an abstraction, which implies that Dr Brigg’s argument applies only to abstractions.
Will Nitschke,
You are missing the point made many times here over the years that probability is a measure of knowledge or certainty in the outcome.
The lack of information other than there are two outcomes means that certainty in either outcome must be equal. The resulting 1/2 is the numerical equivalent of don’t know.
All,
Given only the information that A and B are in a bag, and one must be pulled out, via the statistical syllogism (Lee, this is in my book, and at the Classic Posts page), the probability B is pulled if 0.5.
If A and B are woman and man, it’s the same.
Of course, if you add information that was not specified as part of the problem, then the probability is still 0.5. Because adding information is verboten. But if you do add, then of course the probability changes. Because why? Because the premises change.
For some reason, people have a difficult time taking probability problems as stated. They’re inveterate information adders. This never happens in algebra. If I say, “y is less than 5 and x plus y = 17, then solve for x” no precise value can be found. Everybody accepts that. Nobody says, “Well, I knew of a situation once like this where the sum was also 17 and where x was close to 8, therefore it’s likely x is close to 8 this time.”
Moral: do not add information.
It’s a fuzzy world where is’s become if’s.
For example,
probability B is pulled if 0.5.
Because a adding information if verboten.
DAV,
My enemies grow stronger every day.
“The resulting 1/2 is the numerical equivalent of don’t know.”
You don’t know if pulling the ball out of the bag will result in a white or black ball 50% of the time. That’s a subjective assumption. Of course you can say, whatever the actual probability is, once you’ve worked it out, declare that the result is objective. Or create an unreal situation by adding the premise “all else being equal.” Great, that’s true. But useless. Unless you consider probability to be about telling you things you already know. Which sort of defeats the purpose of the exercise.
That’s a subjective assumption.
Subjective only because your information may be different. In that sense probability is always subjective. it’s not an assumption. I’t derived from the available information. There is no “all else being equal”..
Unless you consider probability to be about telling you things you already know.
Maybe you’re catching on. Or maybe not. You expect probability to tell you what you don’t know? How would it do that?
Again, If you have no other information that there are black and white balls in the urn then your certainty in selecting black must be the same as selecting white. The 1/2 is saying you have insufficient information to predict the outcome.
All,
Before us is a Metalunan Interocitor. It can and must take one of n states. The probability, given this information, that it is in state j (where j is between 1 and n inclusive) is 1/n.
This probability says nothing about how often the Interocitor is in state j, or in any other state. And indeed, the Interocitor will never be in any state, because there are no such things as interocitors.
Funny that we make mistakes in probability that we never make in logic. That’s because there is an enormous empirical bias to probability problems that you don’t find in logic.
Suppose: All Interocitors favor state j. “Bob” is an Interocitor. We conclude “Bob” favors state j. If anybody got that on a logic quiz, they’d have no difficulties answering or understanding it. But through probability into the mix and the veil descends.
“because there are no such things as interocitors. ”
Prove it. 🙂
Ah, the interocitor. I think that was the occasion of my objection before. I said that P was not known to be 1/n, just as I say now that the P of man leaving the room is not known to be 1/2. I think I found the classic post that you wanted me to see. So why do I persist? I am not adding information. I am just refusing to assume unstated assumptions. This has nothing to do with probability theory, which is a branch of mathematics that deals with how to combine and calculate with probabilities to arrive at other probabilities. It has nothing to say about how to assign probabilities to things a priori. But we still have to have opinions about that.
Here is an urn. It has some white balls in it and some black ones. If you reach in and remove a ball, what is the probability that you will get a white one? You seem committed to the idea that this must = 1/2. But I happen to know that this is wrong, because I put in 75 white balls and 25 black ones. Your 1/2 comes from an assumption that the number of white balls = the number of black balls. You say that this expresses the degree of your knowledge; I say that you should simply refuse to assign a probability without further information. Does this make me a frequentist?
Well, if I am doomed to life as a frequentist, I should make the most of it, and explain why I think your way is problematic, without rehashing that vast debate out there. Why assign probabilities to anything at all? Presumably, so we can use them in calculations to try to understand things, and make predictions (estimates) and decisions. What if I had put in million black balls and one white one. You would be calculating based on P = 1/2, and all these calculations would be worthless. Far better to refuse to proceed until we have a basis to assign a meaningful probability.
Last count there were three of us either living in Wyoming or claiming to be from Wyoming that regularly visit this site.
What are the odds on that?
P[Bill S commenting | Briggs insulting use of Gaussian distributions] = 1.0
“Again, If you have no other information that there are black and white balls in the urn then your certainty in selecting black must be the same as selecting white. ”
As yes, the Argumentum ad Ignorantiam. X must be true because I lack information to suggest otherwise. Also a popular fallacy among global warming academics.
Argumentum ad Ignorantiam. X must be true because I lack information to suggest otherwise.
However, in this case it is true because it conforms to the definition of probability.
You obviously don’t agree. What do you think probability is?
Bill S,
Three is very odd.
Lee Phillips,
What if I had put in million black balls and one white one. You would be calculating based on P = 1/2, and all these calculations would be worthless.
What if some of them are green? At any given time you don’t know how many of each color is present unless you have prior knowledge Your what-if is adding information — actually, supposing it.
The 1/2 is not an assumption. It’s a deduction from the information. The only calculation is to distribute the uncertainty among all events because that’s all the information has provided. As more information is obtained the probability (level of knowledge;certainty in outcome) will change.
Debates are never over technical descriptions but over application. Any global warming alarmist can declare that the science is settled because it’s all just “basic physics”. That isn’t the issue, because the devil is in the application of the physics. Or in this thread, in the application of statistical techniques. 1 divided by 2 is objectively 0.5. That doesn’t tell you that you will always draw a black ball from the urn 50% of the time just because you know there are black and white balls in the urn. The world is full of facts. When you misapply them, you go astray.
Or in this thread, in the application of statistical techniques. 1 divided by 2 is objectively 0.5. That doesn’t tell you that you will always draw a black ball from the urn 50% of the time just because you know there are black and white balls in the urn.
You are right. It isn’t supposed to and doesn’t. It’s just saying in the next draw the confidence that black will be drawn is equal to the confidence that white will be drawn. Says nothing about how often each will be drawn. It might in some applications but not in general. Probability is not a frequency. It’s a level of certainty.
The probability of black/white in the next draw is not much different than saying teams A and B are equally likely to win the next competition which, of course, is not the same as saying how often each will prevail in subsequent competitions.
Well if the urn has 99 black balls and one white ball and you wish to believe that there is a 50/50 chance that the white ball will be drawn next, then you are wrong. The fact that you are wrong doesn’t change the fact that 1/2 = 0.5. Appealing to the fact that 1/2 always equals 0.5 and this is “objective” doesn’t help you either. You’re still wrong. In that situation you will always be wrong. The original point I made which I’m now belabouring, is that declaring that objective facts about the world exist, doesn’t help you. If probability doesn’t help you make better future predictions, it serves no useful purpose. It’s not probability that is wrong. It is your application (misunderstanding) that is the problem and why you keep failing to predict the future accurately.
Well if the urn has 99 black balls a
This is adding information not in the original premise which has no information leading to favoring one outcome over the other. Doing that would be wrong. Probability is obtained from current information and updated as more information is obtained. There is no objective probability in the sense of One True Value. It depends only on available information. If your information is different than mine the you likely would (and should) have a different assessment.
Seems you want o introduce facts into evidence and run with them and you seem to have a deep sense that probability is an expression of frequencies of occurrence. Some people do as well but find themselves stymied when asked about the chances of outcome of a one time even such as the next Lakers game.
If x and y are non-negative real numbers such that x+y=1, what is x? Based on our Mr.Briggs’ comment of November 17, 2015 at 6:23 PM, it seems the answer that everyone accepts is “no precise value can be found.” Yet if x is the probability that the man leaves the room, and y the probability that the woman leaves the room as in Briggs’ original post, then we deduce that x=1/2. Is that correct?
Yet if x is the probability that the man leaves the room, and y the probability that the woman leaves the room as in Briggs’ original post, then we deduce that x=1/2. Is that correct?
Not really. The information used to get to the 1/2 only logically allows for x=y. Anything else requires assumptions not present in the given information.
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