andrew_gelman_stats andrew_gelman_stats-2013 andrew_gelman_stats-2013-1779 knowledge-graph by maker-knowledge-mining
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Introduction: Prasanta Bandyopadhyay and Gordon Brittan write : We introduce a distinction, unnoticed in the literature, between four varieties of objective Bayesianism. What we call ‘strong objective Bayesianism’ is characterized by two claims, that all scientific inference is ‘logical’ and that, given the same background information two agents will ascribe a unique probability to their priors. We think that neither of these claims can be sustained; in this sense, they are ‘dogmatic’. The first fails to recognize that some scientific inference, in particular that concerning evidential relations, is not (in the appropriate sense) logical, the second fails to provide a non-question-begging account of ‘same background information’. We urge that a suitably objective Bayesian account of scientific inference does not require either of the claims. Finally, we argue that Bayesianism needs to be fine-grained in the same way that Bayesians fine-grain their beliefs. I have not read their paper in detai
sentIndex sentText sentNum sentScore
1 Prasanta Bandyopadhyay and Gordon Brittan write : We introduce a distinction, unnoticed in the literature, between four varieties of objective Bayesianism. [sent-1, score-0.178]
2 What we call ‘strong objective Bayesianism’ is characterized by two claims, that all scientific inference is ‘logical’ and that, given the same background information two agents will ascribe a unique probability to their priors. [sent-2, score-0.768]
3 The first fails to recognize that some scientific inference, in particular that concerning evidential relations, is not (in the appropriate sense) logical, the second fails to provide a non-question-begging account of ‘same background information’. [sent-4, score-0.528]
4 We urge that a suitably objective Bayesian account of scientific inference does not require either of the claims. [sent-5, score-0.703]
5 I have not read their paper in detail but I think I pretty much agree with their criticism of classical or strong Bayesian philosophies of the objective or subjective variety. [sent-7, score-0.415]
6 In particular, I agree with them that (a) the traditional Bayesian philosophy (which culminates in the posterior probability of a model being true) is not a good model for the evaluation and replacement of scientific theories, but (b) a fuller, falsificationist Bayesian philosophy can do the job. [sent-8, score-1.122]
7 As always, I find it misleading to focus on the prior distribution as the locus of subjective uncertainty. [sent-10, score-0.315]
8 In some problems, there is more reasonable agreement on the population model; in others, there is more agreement on the data model. [sent-13, score-0.194]
9 It’s just that, for historical reason, “likelihood methods” have been grandfathered in as classical methods and thus don’t suffer the Bayesian taint. [sent-14, score-0.192]
10 All sorts of goofy stories that happened to have been placed in time before 100 BC become canonical; whereas everything that happened after is evaluated in the category of “history” rather than “religion. [sent-16, score-0.174]
11 ” This cuts both ways: in one direction, you have people who believe anything that happens to be in the official collection of biblical stories; on the other, historical stories get the benefit of being revisable by evidence. [sent-17, score-0.254]
12 Something similar happens in many statistical problems, when all sorts of critical thinking gets applied to the prior distribution, whereas conventional likelihoods just get accepted. [sent-18, score-0.243]
13 Before going on to the next issue, let me qualify the above by recognizing Deborah Mayo’s point that, in typical cases, the data model differs from the prior distribution by being more accessible to checking. [sent-19, score-0.35]
14 In practice, though, statisticians (including those of the classical or Bayesian variety who complain or rejoice about the subjectivity of prior distributions) often don’t take the opportunity to check the fit of their data models. [sent-20, score-0.215]
15 In the problems I’ve worked on, it’s never seemed to make any sense to talk about the posterior probability that a continuous parameter equals zero or that a particular model is true. [sent-23, score-0.369]
16 This sort of logic seems odd from a scientific perspective (it’s sort of like evaluating the weight of an object by assessing how heavy it looks), but, in the context of the sociology of science, the evaluation of evidence is clearly an important thing that we do. [sent-28, score-0.339]
17 ” I like this definition, and it gives a clue as to the scientific relevance of statements such as, “I don’t think this finding is actually statistically significant,” even in completely Bayesian settings. [sent-30, score-0.227]
18 In nontrivial settings, our inferences won’t be coherent—if they were, we could just skip Bayesian inference, posterior integration, Stan, etc. [sent-35, score-0.243]
19 , and simply look at data and write down our subjective posterior distributions. [sent-36, score-0.257]
20 Thus, I think coherence is a valuable concept, but not because Bayesian inferences are coherent (they’re not) but because Bayesian inference provides a mechanism for finding and resolving incoherences. [sent-38, score-0.664]
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