Байесовская вероятность и попперианский подход: дискуссия

Байесовская вероятность и попперианский подход: дискуссия

by Евгений Волков -
Number of replies: 0

Очень интересные комментарии в группе к этой публикации:

«Байесианцы признают, что ваша оценка вероятности данного утверждения может отличаться от моей. Но, поскольку вероятность, как красота, заключается в глазах смотрящего, нет способа узнать, кто из нас прав. Действительно, как сказал статистик, который положил начало современной фазе этого течения, байесианцы «утверждают, что вероятность, являющаяся лишь мерой чьего-то верования, не подвержена доказыванию или опровержению фактами» (De Finetti 1962: 360) Ни в чём себе не отказывайте!»


Andrei Mirovan загрузил файл в группе «critical rationalism».
21 ч · 

~ Peter Milne, "A Bayesian defence of Popperian science?" (1995) ~

I, for one, am no supporter of Bayesian statistics, but this short article might be of some (even if polemical) interest.

Matt Dioguardi
Matt Dioguardi The paper looks a bit intimidating. But the issue should be straightforward shouldn't it?

If as part of an empirical theory Bayes' theorem would apply deductively, then there's no problem. It's perfectly fine. I think Popper would be the first to ackn
owledge this.

The problem arises when the theory is used in some manner or other as signifying some type of epistemic justification. In that case, certain assumptions have to be made. It's those assumptions that are problematic.

Even if we're just measuring confidence, then what is that? A psychological theory? A justification for believing something? A theory about rationality? Why should we be concerned about even attempting to measure confidence?

There's no clear connection that I can see between a person's confidence, presuming it could be measured, and the truth.

I guess I can see the inductive appeal of that Bayes theorem might have to people. Like a last ditch attempt to save the inductive approach. But it might be better just to ditch the inductive approach.
· 20h
Fredrick George Welfare
Fredrick George Welfare 'Surprise' looks subjective; your degree of surprise as the relation between an hypothesis and the evidence may differ from someone else's degree of surprise. It is also doubtful that surprise or any subjective impression can be quantified precisely, perhaps roughly.

Popper disagrees with Bayes but there does not seem to be any reason why anyone should not update their beliefs once their beliefs have been falsified, or proven wrong. The problem is that many people, experts (Tetlock, 2005) do not update their beliefs and persist in making the same error (Bueno De Mesquita, 2009)

When Popper developed his 3 Worlds theory, 2 problems emerged: World 2 as subjectivity mediated the relation between Worlds 1 and 3, and World 3 could contain any old notion whatsoever, including quantified subjective impressions, or subjective probabilities. The process of subjectivity or mental processes is a lacuna in Popper's work.
Phil Wood
Phil Wood This is a topic of interest to me as I have interests in both Popper and Bayesian statistics. Popper was no friend of Bayesian inductivism, it is true, but to me that is a different topic entirely than the worth of Bayesian statistics, which is the mathematical application of Bayes' Theorem to data. To that end, I think Bayesian statistics is very useful. Frequentist statistics allows us to test a hypothesis conditional on the data and a host of side assumptions (e.g., normality of error of dependent variance for some models). Modern Bayesian statistics using the MCMC sampler, for example, allows the researcher to assess not only the conditional probability of a theory but also the plausibility of these side assumptions. Second, modern Bayesian techniques are also interested in quantifying the "amount" of disconfirmation. Old approaches such as the Bayes factor are one approach to this, but new approaches to model comparison use the LOO or WAIC. Quantifying the degree of refutation of candidate models seems useful to me. for what it's worth.
 · 17h
Luc Castelein
Luc Castelein I just wish I could understand that, Phil Wood.. But I guess it's not the most important thing for me...
Phil Wood
Phil Wood Luc Castelein Let me make the case briefly, then. We're talking here about using statistics to falsify a theory, not the clear "Hit it out of the ballpark with photos of an eclipse" scenario. Suppose a researcher wants to falsify a theory using some data. A statistician will say "Suppose that the to-be-refuted theory is true. If so, and if errors of prediction follow some known distribution such as the normal, then the probability of these data happening under the theory is very small and if small enough, we will count that as a refutation." The problem is that a skeptic of this skeptical approach will counterargue that the assumption of conditional normality was not appropriate. Bayesians have a different mathematical approach entirely and want to look at the likelihood of unknown parameters using distributions but, prior to the MCMC sampler, the same counterarguments could be made.
 · 16h
Luc Castelein
Luc Castelein Thanks for trying, Phil, but I just don't have the basic knowledge...
Clovis Roussy
Clovis Roussy Most people mistake probability for what Popper would call the degree of corroboration, which characterizes our best explanations and produces a psychological impression of "plausibility". Mentally we treat plausibility just like probability, as something like "credence" or "degree of belief". Applying Bayesian reasoning to epistemology is nothing more than an analogy.
Matt Dioguardi
Matt Dioguardi Clovis Roussy:

>>Mentally we treat plausibility just like probability, as something like "credence" or "degree of belief". 

But we don't need to treat probability this way, right? That's a philosophical supposition.

It could be the world is probabilistic, and probabilities are real in some sense.

In this manner the probabilities are a facet of our empirical theory.

Thus, just as "inductive" reasoning can be criticized, applying probability as a degree of belief can be criticized.

This would, of course, restrict the use of probability to theories about the world and avoid claims about mounting evidence.

I've often seen Bayesians make a claim about the world, and then insist the evidence was so wrong it would be incorrect in some manner not to share their belief. It's that specific move that isn't credible.
 · 7h
Clovis Roussy
Clovis Roussy I fully agree with that. Bayesian reasoning is an essential tool to deal with probabilities. The problem is that you need a prior theory to assign prior and conditional probabilities to events. The probability of that theory being true has nothing to do with those prior probabilities.

I think about probabilities as objective in the same sense as our theories are objective. They still express the limits of our knowledge. Bayesian reasoning allows us to fully use the content of our theories to refine the probabilities we assign to events according to our conjectures about their relationships. If the probabilities are off, it's as clear a refutation as we can get.
 · 6h ·
Clovis Roussy
Clovis Roussy The difference between probability and "plausibility" in the sense outlined above: if my theory tells me there's a 95% chance some event will occur, it doesn't mean that "I feel sure at 95% of absolute certainty" that this event will occur. It just means 95% chance.

The theory I use to arrive at 95% might be the most well corroborated ever, I could feel just as confident in my call that I'm confident the sun will rise tomorrow - it still says nothing about the probability my theory is true, because I have no idea what other theories could explain everything that went into the corroboration process.
· 5h ·
Peter Földiák
Peter Földiák For an opposing view, read E. T. Jaynes, specifically page 310 of his book PROBABILITY THEORY: THE LOGIC OF SCIENCE (Cambridge University Press)
Fredrick George Welfare
Fredrick George Welfare Since raising the issue of Bayesianism confuses most people because it is couched in math and statistics and other "verbiage," a useful characterization and criticism of this domain is provided by Mario Bunge.

from Bunge, M 2012 "Evaluating Philosophi
es," ch11,

"Bayesianism is the opinion that probabilities are a matter of opinion. This is because they would only measure the strength of our beliefs (De Finetti 1972; Jeffreys 1975; Keynes 1957; Savage 1954). That view is generally known as Bayesianism because of its heavy reliance on a certain interpretation of Bayes’ theorem, a piece of pure mathematics that actually refers neither to the knowing subject nor to the real world.
More precisely, according to Bayesians, all and only propositions (or statements) qualify as more or less probable—although they do not bother to explain what is meant by “this proposition is probable”, or by “this proposition is more probable than that one.”

Bayesians admit that your assessment of the probability of a given proposition is likely to differ from mine. But, because probability, like beauty, would be in the eye of the beholder, there is no way to tell which of us is right. Indeed, as the statistician who started the contemporary phase of this current put it, Bayesians “maintain that a probability, being but a measure of someone’s belief, is not susceptible of being proved or disproved by the facts” (De Finetti 1962 : 360). Anything goes!

My goal in this chapter is to examine Bayesianism to find out whether it is scientific, and thus deserves the attention of scientists, engineers, legal experts, medical doctors, and other specialists. To perform this task I will draw heavily on some earlier work of mine (Bunge 1951, 1955, 1976, 1981, 1988, 2006, 2008, 2010)."

Bunge uses clear language and does not obfuscate the issues like Bayesians do!
 · Ответить · 6h

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