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This critique might come from the idea that having a good analytic model, or at least some valuable analytic insights, involves much more than assigning some pr

This critique might come from the idea that having a good analytic model, or at least some valuable analytic insights, involves much more than assigning some priors. Of course, the two things don't exclude each other, but for some frequentists Bayesians have the wrong perspective - or at least that's the critique, whether it's true or not. Another issue that I personally have with Bayesianism is that I believe that assigning probabilities to singular events is only meaningful and admissible at all if there is a good analytic explanation for the respective propensity. For example, we may be able to deduce that a die is reasonably fair from the way it is constructed and our knowledge of physics, and later confirm this by frequentist analysis. Merely believing or claiming that the die is fair is not acceptable. Again, the difference is only one of attitude in the end, I suppose. Maybe philosophers have given Bayesian statistics a bad rap, too, because many of those who call themselves Bayesians are also "probabilists", i.e., they think that rational belief must conform to the probability calculus. There are many arguments against probabilism and the only arguments that speak for it are Dutch book arguments. The view does not have very strong foundations.

jbay808 7y ago
My understanding of physics is that no die toss can be considered "fair" because such a macroscopic system behaves deterministically according to Newton's laws, and isn't even too chaotic to model accurately. No matter the shape or balance of the die, the outcome is determined by the initial conditions and the toss. A skilled gambler can make a fair die land however they want. The only thing I know is that a well-made die is symmetrical, and so if I have no prior knowledge of its initial orientation then I have to use a uniform prior because nothing else has the requisite symmetry group. The same could be said for a die that is just sitting on the table without having been observed by me yet, no toss needed.
- tomnipotent 7y ago
  > A skilled gambler can make a fair die land however they want. No, they can't. Dice control is a myth, and there isn't a single study that backs it up.
loup-vaillant 7y ago
> assigning probabilities to singular events is only meaningful and admissible at all if there is a good analytic explanation for the respective propensity. Wait a minute, you are making a type error here: probabilities are not propensities. They're degrees of belief. (And even if you disagree in general, this is a Bayesian context you're talking about.) If I put a die on a table and hide it with a cup, you could still estimate your probability distribution about which face is up. My probability distribution would obviously be very different, since I put the die in there myself. (Replace "probability" by "betting ratio" or "degrees of belief" if it makes more sense to you.) > The [probabilism] view does not have very strong foundations. Read the first 2 chapters of Probability Theory: the Logic of Science, by E. T. Jaynes: "Plausible reasoning" and "The quantitative rules". It's very accessible, and you shall see how strong the foundations really are. http://www.med.mcgill.ca/epidemiology/hanley/bios601/GaussianModel/JaynesProbabilityTheory.pdf http://www.med.mcgill.ca/epidemiology/hanley/bios601/Gaussia...
- jonathanstrange 7y ago
  No, I was not speaking from a Bayesian perspective, I was laying out the propensity-theoretic explanation of probability. The propensity explanation is one of attempts of explaining why singular events might be said to give rise to probabilities, living besides frequentism and Bayesianism. Another perspective worth mentioning is the logical approach, which is in the end purely combinatorial. Some people think that you need to explain why a die can be fair, rather than just assuming it or only looking at it from a frequentist perspective. Of course, die-hard Bayesians don't think so, but that would be begging the question in the context of discussing criticisms of Bayesianism. > Read the first 2 chapters of Probability Theory: the Logic of Science, by E. T. Jaynes: "Plausible reasoning" and "The quantitative rules". It's very accessible, and you shall see how strong the foundations really are. I'm an expert on this topic. The only arguments for probabilism are Dutch book arguments, and there is a large number of arguments against these. See for example various articles by Hajek. Alternative representations of graded belief are, among others: - plausibility theory (Halpern at al.) - possibility theory (Dubois & Prade) - Haas-Spohn ranking theory and variants thereof - various notions of epistemic entrenchment - Dempster-Shafer belief theory - almost any quantitative or qualitative representation of belief in belief revision theory not covered by one of the above theories (e.g. belief update by Katsuno & Mendelsohn) - by a general logical connection, nonmonotonic logics and AAFs can generally represent notions of belief update, such that the underlying qualitative ordering of states is a representation of graded belief What you probably mean is that the above generalizations (or qualitative theories, in some cases) could be simulated with probabilities, e.g. by using convex sets of probabilities or what Josang is doing in his "subjective logic". That's true, but then we're no longer talking about probabilism in the sense I've used the word. Of course, you can also try arguing for probabilism like Savage did: Lay out a set of postulates for your subjective plausibility that happen to allow you to proof that this notion of subjective plausibility is in the end probability. Despite the merits of such work, it is in the end a form of cheating (or "reverse engineering"), because you could just as well come up with plausible postulates that yield the weaker axioms of possibility theory.

jbay808 7y ago

My understanding of physics is that no die toss can be considered "fair" because such a macroscopic system behaves deterministically according to Newton's laws, and isn't even too chaotic to model accurately. No matter the shape or balance of the die, the outcome is determined by the initial conditions and the toss. A skilled gambler can make a fair die land however they want. The only thing I know is that a well-made die is symmetrical, and so if I have no prior knowledge of its initial orientation then I have to use a uniform prior because nothing else has the requisite symmetry group. The same could be said for a die that is just sitting on the table without having been observed by me yet, no toss needed.

tomnipotent 7y ago
> A skilled gambler can make a fair die land however they want. No, they can't. Dice control is a myth, and there isn't a single study that backs it up.

loup-vaillant 7y ago

> assigning probabilities to singular events is only meaningful and admissible at all if there is a good analytic explanation for the respective propensity. Wait a minute, you are making a type error here: probabilities are not propensities. They're degrees of belief. (And even if you disagree in general, this is a Bayesian context you're talking about.) If I put a die on a table and hide it with a cup, you could still estimate your probability distribution about which face is up. My probability distribution would obviously be very different, since I put the die in there myself. (Replace "probability" by "betting ratio" or "degrees of belief" if it makes more sense to you.) > The [probabilism] view does not have very strong foundations. Read the first 2 chapters of Probability Theory: the Logic of Science, by E. T. Jaynes: "Plausible reasoning" and "The quantitative rules". It's very accessible, and you shall see how strong the foundations really are. http://www.med.mcgill.ca/epidemiology/hanley/bios601/GaussianModel/JaynesProbabilityTheory.pdf http://www.med.mcgill.ca/epidemiology/hanley/bios601/Gaussia...

jonathanstrange 7y ago
No, I was not speaking from a Bayesian perspective, I was laying out the propensity-theoretic explanation of probability. The propensity explanation is one of attempts of explaining why singular events might be said to give rise to probabilities, living besides frequentism and Bayesianism. Another perspective worth mentioning is the logical approach, which is in the end purely combinatorial. Some people think that you need to explain why a die can be fair, rather than just assuming it or only looking at it from a frequentist perspective. Of course, die-hard Bayesians don't think so, but that would be begging the question in the context of discussing criticisms of Bayesianism. > Read the first 2 chapters of Probability Theory: the Logic of Science, by E. T. Jaynes: "Plausible reasoning" and "The quantitative rules". It's very accessible, and you shall see how strong the foundations really are. I'm an expert on this topic. The only arguments for probabilism are Dutch book arguments, and there is a large number of arguments against these. See for example various articles by Hajek. Alternative representations of graded belief are, among others: - plausibility theory (Halpern at al.) - possibility theory (Dubois & Prade) - Haas-Spohn ranking theory and variants thereof - various notions of epistemic entrenchment - Dempster-Shafer belief theory - almost any quantitative or qualitative representation of belief in belief revision theory not covered by one of the above theories (e.g. belief update by Katsuno & Mendelsohn) - by a general logical connection, nonmonotonic logics and AAFs can generally represent notions of belief update, such that the underlying qualitative ordering of states is a representation of graded belief What you probably mean is that the above generalizations (or qualitative theories, in some cases) could be simulated with probabilities, e.g. by using convex sets of probabilities or what Josang is doing in his "subjective logic". That's true, but then we're no longer talking about probabilism in the sense I've used the word. Of course, you can also try arguing for probabilism like Savage did: Lay out a set of postulates for your subjective plausibility that happen to allow you to proof that this notion of subjective plausibility is in the end probability. Despite the merits of such work, it is in the end a form of cheating (or "reverse engineering"), because you could just as well come up with plausible postulates that yield the weaker axioms of possibility theory.