andrew_gelman_stats andrew_gelman_stats-2012 andrew_gelman_stats-2012-1155 knowledge-graph by maker-knowledge-mining
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Introduction: Some recent blog discussion revealed some confusion that I’ll try to resolve here. I wrote that I’m not a big fan of subjective priors. Various commenters had difficulty with this point, and I think the issue was most clearly stated by Bill Jeff re erys, who wrote : It seems to me that your prior has to reflect your subjective information before you look at the data. How can it not? But this does not mean that the (subjective) prior that you choose is irrefutable; Surely a prior that reflects prior information just does not have to be inconsistent with that information. But that still leaves a range of priors that are consistent with it, the sort of priors that one would use in a sensitivity analysis, for example. I think I see what Bill is getting at. A prior represents your subjective belief, or some approximation to your subjective belief, even if it’s not perfect. That sounds reasonable but I don’t think it works. Or, at least, it often doesn’t work. Let’s start
sentIndex sentText sentNum sentScore
1 Some recent blog discussion revealed some confusion that I’ll try to resolve here. [sent-1, score-0.19]
2 I wrote that I’m not a big fan of subjective priors. [sent-2, score-0.441]
3 Various commenters had difficulty with this point, and I think the issue was most clearly stated by Bill Jeff re erys, who wrote : It seems to me that your prior has to reflect your subjective information before you look at the data. [sent-3, score-1.347]
4 But this does not mean that the (subjective) prior that you choose is irrefutable; Surely a prior that reflects prior information just does not have to be inconsistent with that information. [sent-5, score-1.884]
5 But that still leaves a range of priors that are consistent with it, the sort of priors that one would use in a sensitivity analysis, for example. [sent-6, score-0.42]
6 A prior represents your subjective belief, or some approximation to your subjective belief, even if it’s not perfect. [sent-8, score-1.463]
7 That sounds reasonable but I don’t think it works. [sent-9, score-0.077]
8 You hop on a scale that gives unbiased measurements with errors that have a standard deviation of 0. [sent-12, score-0.275]
9 To do Bayesian analysis, you assign a N(0,10000^2) prior on your true weight. [sent-14, score-0.58]
10 Instead of thinking of these as subjective beliefs, I prefer to think of the joint probability distribution as a model, reflecting a set of assumptions. [sent-19, score-0.823]
11 In some settings these assumptions represent subjective beliefs, in other settings they don’t. [sent-20, score-0.74]
12 If I could go back and alter it, I’d add something on weakly informative priors, but I still agree with the general approach discussed there. [sent-22, score-0.228]
13 Just to give an example of what I mean by prior information: The analyses in Red State Blue State all use noninformative prior distributions. [sent-25, score-1.247]
14 But a lot of prior information comes in, in the selection of what questions to study, what models to consider, and what variables to include in the model. [sent-26, score-0.721]
15 For example, as state-level predictors we include region of the country, Republican vote in the previous presidential election, and average state income. [sent-27, score-0.309]
16 Prior information goes into the choice and construction of all these predictors. [sent-28, score-0.201]
17 But the prior distribution is a particular probability distribution that in this case is flat and does not reflect prior knowledge. [sent-29, score-1.587]
18 One way to think about informative prior distributions is as a form of smoothing: when setting the parameters of a probability distribution based on prior knowledge, we are imposing some time smoothness on the parameters. [sent-30, score-1.612]
19 I think that’s probably a good idea and that the Red State Blue State analyses (among others) would be better for it. [sent-31, score-0.165]
20 I didn’t set up this prior structure because I wasn’t easily equipped to do so and it seemed like too much effort, but perhaps at some future time this sort of structuring will be as commonplace as hierarchical modeling is today. [sent-32, score-0.77]
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Introduction: Some recent blog discussion revealed some confusion that I’ll try to resolve here. I wrote that I’m not a big fan of subjective priors. Various commenters had difficulty with this point, and I think the issue was most clearly stated by Bill Jeff re erys, who wrote : It seems to me that your prior has to reflect your subjective information before you look at the data. How can it not? But this does not mean that the (subjective) prior that you choose is irrefutable; Surely a prior that reflects prior information just does not have to be inconsistent with that information. But that still leaves a range of priors that are consistent with it, the sort of priors that one would use in a sensitivity analysis, for example. I think I see what Bill is getting at. A prior represents your subjective belief, or some approximation to your subjective belief, even if it’s not perfect. That sounds reasonable but I don’t think it works. Or, at least, it often doesn’t work. Let’s start
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Introduction: Nick Firoozye writes: While I am absolutely sympathetic to the Bayesian agenda I am often troubled by the requirement of having priors. We must have priors on the parameter of an infinite number of model we have never seen before and I find this troubling. There is a similarly troubling problem in economics of utility theory. Utility is on consumables. To be complete a consumer must assign utility to all sorts of things they never would have encountered. More recent versions of utility theory instead make consumption goods a portfolio of attributes. Cadillacs are x many units of luxury y of transport etc etc. And we can automatically have personal utilities to all these attributes. I don’t ever see parameters. Some model have few and some have hundreds. Instead, I see data. So I don’t know how to have an opinion on parameters themselves. Rather I think it far more natural to have opinions on the behavior of models. The prior predictive density is a good and sensible notion. Also
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Introduction: I received the following email: I have an interesting thought on a prior for a logistic regression, and would love your input on how to make it “work.” Some of my research, two published papers, are on mathematical models of **. Along those lines, I’m interested in developing more models for **. . . . Empirical studies show that the public is rather smart and that the wisdom-of-the-crowd is fairly accurate. So, my thought would be to tread the public’s probability of the event as a prior, and then see how adding data, through a model, would change or perturb our inferred probability of **. (Similarly, I could envision using previously published epidemiological research as a prior probability of a disease, and then seeing how the addition of new testing protocols would update that belief.) However, everything I learned about hierarchical Bayesian models has a prior as a distribution on the coefficients. I don’t know how to start with a prior point estimate for the probabili
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Introduction: Some recent blog discussion revealed some confusion that I’ll try to resolve here. I wrote that I’m not a big fan of subjective priors. Various commenters had difficulty with this point, and I think the issue was most clearly stated by Bill Jeff re erys, who wrote : It seems to me that your prior has to reflect your subjective information before you look at the data. How can it not? But this does not mean that the (subjective) prior that you choose is irrefutable; Surely a prior that reflects prior information just does not have to be inconsistent with that information. But that still leaves a range of priors that are consistent with it, the sort of priors that one would use in a sensitivity analysis, for example. I think I see what Bill is getting at. A prior represents your subjective belief, or some approximation to your subjective belief, even if it’s not perfect. That sounds reasonable but I don’t think it works. Or, at least, it often doesn’t work. Let’s start
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