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> like I've suddenly gone soft and introduced a bunch of nebulous, touchy-feely context into the objective truth This drives me nuts. If you haven't, check out

> like I've suddenly gone soft and introduced a bunch of nebulous, touchy-feely context into the objective truth This drives me nuts. If you haven't, check out the paper "Beyond subjective and objective in statistics" by Gelman and Hennig (2017). Right at the beginning they make the point that any analysis includes external information in many ways, such as adjusting variables for imbalance, how we deal with outliers, regularization, etc. Especially if you're doing any sort of causal inference, you're usually making strong assumptions before estimating your model, even just in terms of which variables are included and how they're connected. The idea that priors are somehow ruining an "objective" model is just absurd to me. You're already making so many other decisions about your model that will affect estimates and your interpretation of them. Priors seem like another perfectly reasonable decision to have to make as well, with the benefit of getting results that I think in general are must more easily understood by a lay audience. (E.g., I don't think I've ever encountered someone not on my data science team that actually understands what a p-value is. But people are much better at understanding when I say, there's an X percent chance that there is a positive effect here.)

dhfromkorea 7y ago
> The idea that priors are somehow ruining an "objective" model is just absurd to me. I think some caution can be justified to a certain extent (not the blind "emotional" objections). When establishing priors in a low data regime, one must necessarily be careful. It's a knob whose mass can change a lot in the inference conclusion. That said, if we trust our belief about the region the available data do not inform us well of, why not utilize our domain knowledge/belief?
jonathanstrange 7y ago
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

dhfromkorea 7y ago

> The idea that priors are somehow ruining an "objective" model is just absurd to me. I think some caution can be justified to a certain extent (not the blind "emotional" objections). When establishing priors in a low data regime, one must necessarily be careful. It's a knob whose mass can change a lot in the inference conclusion. That said, if we trust our belief about the region the available data do not inform us well of, why not utilize our domain knowledge/belief?

jonathanstrange 7y ago

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