andrew_gelman_stats andrew_gelman_stats-2012 andrew_gelman_stats-2012-1205 knowledge-graph by maker-knowledge-mining
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Introduction: Deborah Mayo collected some reactions to my recent article , Induction and Deduction in Bayesian Data Analysis. I’m pleased that that everybody (philosopher Mayo, applied statistician Stephen Senn, and theoretical statistician Larry Wasserman) is so positive about my article and that nobody’s defending the sort of hard-core inductivism that’s featured on the Bayesian inference wikipedia page. Here’s the Wikipedia definition, which I disagree with: Bayesian inference uses aspects of the scientific method, which involves collecting evidence that is meant to be consistent or inconsistent with a given hypothesis. As evidence accumulates, the degree of belief in a hypothesis ought to change. With enough evidence, it should become very high or very low. . . . Bayesian inference uses a numerical estimate of the degree of belief in a hypothesis before evidence has been observed and calculates a numerical estimate of the degree of belief in the hypothesis after evidence has been obse
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1 Deborah Mayo collected some reactions to my recent article , Induction and Deduction in Bayesian Data Analysis. [sent-1, score-0.254]
2 I’m pleased that that everybody (philosopher Mayo, applied statistician Stephen Senn, and theoretical statistician Larry Wasserman) is so positive about my article and that nobody’s defending the sort of hard-core inductivism that’s featured on the Bayesian inference wikipedia page. [sent-2, score-0.805]
3 Here’s the Wikipedia definition, which I disagree with: Bayesian inference uses aspects of the scientific method, which involves collecting evidence that is meant to be consistent or inconsistent with a given hypothesis. [sent-3, score-0.4]
4 As evidence accumulates, the degree of belief in a hypothesis ought to change. [sent-4, score-0.548]
5 Bayesian inference uses a numerical estimate of the degree of belief in a hypothesis before evidence has been observed and calculates a numerical estimate of the degree of belief in the hypothesis after evidence has been observed. [sent-9, score-1.595]
6 Bayesian inference usually relies on degrees of belief, or subjective probabilities, in the induction process and does not necessarily claim to provide an objective method of induction. [sent-13, score-0.349]
7 As I write in my article, the above does not describe what I do in my applied work. [sent-15, score-0.113]
8 I do go through models, sometimes starting with something simple and building up from there, other times starting with my first guess at a full model and then trimming it down until I can understand it in the context of data. [sent-16, score-0.386]
9 And in any reasonably large problem I will at some point discard a model and replace it with something new. [sent-17, score-0.149]
10 I’m unhappy when people identify “Bayesian statistics” with a set of procedures that I don’t actually do. [sent-18, score-0.092]
11 Now here are my reactions to the reactions to my article: Mayo, the philosopher , asks about the connections between Bayesian model checking and the severe testing described by her neo-Popperian philosophy. [sent-19, score-0.713]
12 ) I don’t know the answer to this one, but on some conceptual level I think her approach and mine are similar to each other—and very different from what is described in that Wikipedia excerpt. [sent-21, score-0.078]
13 ” This echoes a line from page 77 of my article: “My point here is not to say that my preferred methods are better than others but rather to couple my admission of philosophical incoherence with a reminder that there is no available coherent alternative. [sent-25, score-0.146]
14 ” Wasserman, the theoretical statistician , writes that “a pragmatic Bayesian will temporarily embrace the Bayesian viewpoint as a way to frame their analysis. [sent-26, score-0.427]
15 ” I agree, with the slight modification that a goodness-of-fit test can itself be Bayesian (as I discuss briefly in sections 4 and 5 of the article under discussion, and in more detail in chapter 6 of Bayesian Data Analysis). [sent-28, score-0.114]
16 Bayes means different things to different people, but to me it’s all about conditional probabilities of unknowns given model and data, and goodness-of-fit tests definitely fit into this framework. [sent-29, score-0.312]
17 ” I’m sure he’s right about that; see footnotes 1 and 4 of my article. [sent-31, score-0.084]
18 As I wrote in my article, any given Bayesian method can be interpreted as a classical estimator or testing procedure and its frequency properties evaluated; conversely, non-Bayesian procedures can typically be reformulated as approximate Bayesian inferences under suitable choices of model. [sent-33, score-0.666]
19 These processes of translation are valuable for their own sake and not just for communication purposes. [sent-34, score-0.194]
20 These acts of translation represent just one of the ways in which statistical theory can be relevant for applied statistics. [sent-36, score-0.305]
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