5 ms·

As someone who didn't study statistics in college, a paper like this is right in that uncomfortable no-man's land between what I understand and what I'm interes

As someone who didn't study statistics in college, a paper like this is right in that uncomfortable no-man's land between what I understand and what I'm interested in - it seems to tie into several subjects I have layman's interest in. For instance, there is the controversy over how useful models are - are they worthwhile goals we can actually draw conclusions from, or are they simply shortcuts on our way to a more reductionist understanding of a phenomena? Is "emergence" a meaningful concept or an empty concept? Is "systems thinking" a valid concept or just a lack of discipline in the effort to understanding things in a reductionist manner? People here seem to hate Stephen Wolfram but his writing has made some concepts approachable to me that I might not have grasped otherwise - for instance, that computational irreducibility means that even if the world is entirely reductionist, it still doesn't mean that we can deduce the reductionist reality/inputs from an output. And so therefore, models are useful even though they are wrong. This is also a point that Paul Krugman often makes about economic models - people who disregard models on the grounds that they are wrong just don't grasp the value of them, he argues. Most of what I've learned about Bayesianism is what I've read from the first few articles over at lesswrong.com - but I noticed pretty early on that I had a discomfort in using probability as a description of what I believed to be true. It seems the general point of this paper is that Bayesianism is useful for deductive techniques - as a tool in a toolset to support a frequentist view? - but not so much as an expression of a subjectivist philosophy. I appreciated this point: "Beyond the philosophical difficulties, there are technical problems with methods that purport to determine the posterior probability of models, most notably that in models with continuous parameters, aspects of the model that have essentially no effect on posterior inferences within a model can have huge effects on the comparison of posterior probability among models." More generally the paper seems to be making the point that using the Bayesian philosophy to address models is improper in general since the premise of Bayesianism is to update beliefs based off of evidence/data, while we know that belief-in-a-model is pointless since models are wrong. But past that point I got pretty lost.

loup-vaillant 14y ago
> I noticed pretty early on that I had a discomfort in using probability as a description of what I believed to be true. If it can ease your discomfort: what else? In colloquial language, we already do have pretty good descriptors of subjective beliefs, such as "I don't think so", "I'm damned sure", "maybe"… It is only natural to call the quantitative version of those "probabilities" —at least to me. As for frequency properties of seemingly "random" phenomenons, they're a property of the real world, ready for the study. I'd have much more discomfort calling that "probabilities".
- tunesmith 14y ago
  I agree that colloquially speaking, it aligns most with what we believe. What I have trouble with is that you and I could assign different probabilities (via beliefs) to an external event that has only one probability of happening. Just in that sentence I used the word "probability" correctly both times, yet it has two different conflicting meanings.
  - loup-vaillant 14y ago
    Then just use different words. Break it down to "degree of subjective belief" and "frequency property" if you have to. Still, I prefer to use the short hand "probability" to mean the former, for two reasons: first, "degree of subjective belief" is what most lay-people will understand when we say "probability". Second, even scientists have this meaning messing up with their intuitions, even if when they write papers, they really do mean "frequency property". That can be a major obstacle for science. Let me quote Edwin T. Jaynes (long, but worth it): Those who cling to a belief in the existence of "physical probabilities" may react to the above arguments by pointing to quantum theory, in which physical probabilities appear to express the most fundamental laws of physics. Therefore let us explain why this is another case of circular reasoning. We need to understand that present quantum theory uses entirely different standards of logic than does the rest of science. In biology or medicine, if we note that an effect E (for example, muscle contraction, phototropism, digestion of protein) does not occur unless a condition C (nerve impulse, light, pepsin) is present, it seems natural to infer that C is a necessary causative agent for E. Most of what is known in all elds of science has resulted from following up this kind of reasoning. But suppose that condition C does not always lead to eect E; what further inferences should a scientist draw? At this point the reasoning formats of biology and quantum theory diverge sharply. In the biological sciences one takes it for granted that in addition to C there must be some other causative factor F, not yet identied. One searches for it, tracking down the assumed cause by a process of elimination of possibilities that is sometimes extremely tedious. But persistence pays off; over and over again medically important and intellectually impressive success has been achieved, the conjectured unknown causative factor being finally identified as a definite chemical compound. Most enzymes, vitamins, viruses, and other biologically active substances owe their discovery to this reasoning process. In quantum theory, one does not reason in this way. Consider, for example, the photoelectric effect (we shine light on a metal surface and find that electrons are ejected from it). The experimental fact is that the electrons do not appear unless light is present. So light must be a causative factor. But light does not always produce ejected electrons; even though the light from a unimode laser is present with absolutely steady amplitude, the electrons appear only at particular times that are not determined by any known parameters of the light. Why then do we not draw the obvious inference, that in addition to the light there must be a second causative factor, still unidentified, and the physicist's job is to search for it? What is done in quantum theory today is just the opposite; when no cause is apparent one simply postulates that no cause exists —ergo, the laws of physics are indeterministic and can be expressed only in probability form. The central dogma is that the light determines, not whether a photoelectron will appear, but only the probability that it will appear. The mathematical formalism of present quantum theory —incomplete in the same way that our present knowledge is incomplete— does not even provide the vocabulary in which one could ask a question about the real cause of an event. Biologists have a mechanistic picture of the world because, being trained to believe in causes, they continue to use the full power of their brains to search for them —and so they find them. Quantum physicists have only probability laws because for two generations we have been indoctrinated not to believe in causes —and so we have stopped looking for them. Indeed, any attempt to search for the causes of microphenomena is met with scorn and a charge of professional incompetence and `obsolete mechanistic materialism'. Therefore, to explain the indeterminacy in current quantum theory we need not suppose there is any indeterminacy in Nature; the mental attitude of quantum physicists is already sufficient to guarantee it. This one has been quite an eye opener, making me doubt even Many Worlds, which for one still doesn't explain the Born statistics. Still, thanks to Eliezer's Quantum Physics sequence, I'm now convinced that to the best of Science's knowledge (and despite what many physicists say) the laws of physics are most probably deterministic. Which would instantly solve the conflict by rendering "probability" nonsensical when applied to physical phenomena.

loup-vaillant 14y ago

> I noticed pretty early on that I had a discomfort in using probability as a description of what I believed to be true. If it can ease your discomfort: what else? In colloquial language, we already do have pretty good descriptors of subjective beliefs, such as "I don't think so", "I'm damned sure", "maybe"… It is only natural to call the quantitative version of those "probabilities" —at least to me. As for frequency properties of seemingly "random" phenomenons, they're a property of the real world, ready for the study. I'd have much more discomfort calling that "probabilities".

tunesmith 14y ago
I agree that colloquially speaking, it aligns most with what we believe. What I have trouble with is that you and I could assign different probabilities (via beliefs) to an external event that has only one probability of happening. Just in that sentence I used the word "probability" correctly both times, yet it has two different conflicting meanings.
- loup-vaillant 14y ago
  Then just use different words. Break it down to "degree of subjective belief" and "frequency property" if you have to. Still, I prefer to use the short hand "probability" to mean the former, for two reasons: first, "degree of subjective belief" is what most lay-people will understand when we say "probability". Second, even scientists have this meaning messing up with their intuitions, even if when they write papers, they really do mean "frequency property". That can be a major obstacle for science. Let me quote Edwin T. Jaynes (long, but worth it): Those who cling to a belief in the existence of "physical probabilities" may react to the above arguments by pointing to quantum theory, in which physical probabilities appear to express the most fundamental laws of physics. Therefore let us explain why this is another case of circular reasoning. We need to understand that present quantum theory uses entirely different standards of logic than does the rest of science. In biology or medicine, if we note that an effect E (for example, muscle contraction, phototropism, digestion of protein) does not occur unless a condition C (nerve impulse, light, pepsin) is present, it seems natural to infer that C is a necessary causative agent for E. Most of what is known in all elds of science has resulted from following up this kind of reasoning. But suppose that condition C does not always lead to eect E; what further inferences should a scientist draw? At this point the reasoning formats of biology and quantum theory diverge sharply. In the biological sciences one takes it for granted that in addition to C there must be some other causative factor F, not yet identied. One searches for it, tracking down the assumed cause by a process of elimination of possibilities that is sometimes extremely tedious. But persistence pays off; over and over again medically important and intellectually impressive success has been achieved, the conjectured unknown causative factor being finally identified as a definite chemical compound. Most enzymes, vitamins, viruses, and other biologically active substances owe their discovery to this reasoning process. In quantum theory, one does not reason in this way. Consider, for example, the photoelectric effect (we shine light on a metal surface and find that electrons are ejected from it). The experimental fact is that the electrons do not appear unless light is present. So light must be a causative factor. But light does not always produce ejected electrons; even though the light from a unimode laser is present with absolutely steady amplitude, the electrons appear only at particular times that are not determined by any known parameters of the light. Why then do we not draw the obvious inference, that in addition to the light there must be a second causative factor, still unidentified, and the physicist's job is to search for it? What is done in quantum theory today is just the opposite; when no cause is apparent one simply postulates that no cause exists —ergo, the laws of physics are indeterministic and can be expressed only in probability form. The central dogma is that the light determines, not whether a photoelectron will appear, but only the probability that it will appear. The mathematical formalism of present quantum theory —incomplete in the same way that our present knowledge is incomplete— does not even provide the vocabulary in which one could ask a question about the real cause of an event. Biologists have a mechanistic picture of the world because, being trained to believe in causes, they continue to use the full power of their brains to search for them —and so they find them. Quantum physicists have only probability laws because for two generations we have been indoctrinated not to believe in causes —and so we have stopped looking for them. Indeed, any attempt to search for the causes of microphenomena is met with scorn and a charge of professional incompetence and `obsolete mechanistic materialism'. Therefore, to explain the indeterminacy in current quantum theory we need not suppose there is any indeterminacy in Nature; the mental attitude of quantum physicists is already sufficient to guarantee it. This one has been quite an eye opener, making me doubt even Many Worlds, which for one still doesn't explain the Born statistics. Still, thanks to Eliezer's Quantum Physics sequence, I'm now convinced that to the best of Science's knowledge (and despite what many physicists say) the laws of physics are most probably deterministic. Which would instantly solve the conflict by rendering "probability" nonsensical when applied to physical phenomena.