andrew_gelman_stats andrew_gelman_stats-2012 andrew_gelman_stats-2012-1165 knowledge-graph by maker-knowledge-mining
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Introduction: Continuing with my discussion of the articles in the special issue of the journal Rationality, Markets and Morals on the philosophy of Bayesian statistics: Larry Wasserman, “Low Assumptions, High Dimensions”: This article was refreshing to me because it was so different from anything I’ve seen before. Larry works in a statistics department and I work in a statistics department but there’s so little overlap in what we do. Larry and I both work in high dimesions (maybe his dimensions are higher than mine, but a few thousand dimensions seems like a lot to me!), but there the similarity ends. His article is all about using few to no assumptions, while I use assumptions all the time. Here’s an example. Larry writes: P. Laurie Davies (and his co-workers) have written several interesting papers where probability models, at least in the sense that we usually use them, are eliminated. Data are treated as deterministic. One then looks for adequate models rather than true mode
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1 Larry works in a statistics department and I work in a statistics department but there’s so little overlap in what we do. [sent-2, score-0.568]
2 Larry and I both work in high dimesions (maybe his dimensions are higher than mine, but a few thousand dimensions seems like a lot to me! [sent-3, score-0.641]
3 His article is all about using few to no assumptions, while I use assumptions all the time. [sent-5, score-0.224]
4 Laurie Davies (and his co-workers) have written several interesting papers where probability models, at least in the sense that we usually use them, are eliminated. [sent-8, score-0.147]
5 One then looks for adequate models rather than true models. [sent-10, score-0.26]
6 His basic idea is that a distribution P is an ad- equate approximation for x1,…,xn, if typical data sets of size n, generated under P look like x1,…,xn. [sent-11, score-0.46]
7 In other words, he asks whether we can approximate the deterministic data with a stochastic model. [sent-12, score-0.24]
8 I do a lot of work with survey data, where the sample is intended to mimic the population, and a key step comes in the design, which is all about probability sampling. [sent-15, score-0.51]
9 In short, typical statisticians such as myself see probability modeling as a valuable tool that is central to applied statistics, while Wasserman appears to see probability as an example of an assumption to be avoided. [sent-17, score-0.577]
10 Just to be clear: I’m not at all saying Wasserman is wrong in any way here; rather, I’m just marveling on how different his perspective is from mine. [sent-18, score-0.16]
11 I can’t immediately see how his assumption-free approach could possibly be used to estimate public opinion or votes cross-classified by demogtaphics, income, and state. [sent-19, score-0.111]
12 But, then again, maybe my models wouldn’t work so well on the applications on which Wasserman works. [sent-20, score-0.242]
13 Bridges from both directions would probably be good. [sent-21, score-0.078]
14 With different methods and different problems come different philosophies. [sent-22, score-0.48]
15 My use of generative modeling motivates, and allows, me to check fit to data using predictive simulation. [sent-23, score-0.319]
16 Wasserman’s quite different approach motivates him to understand his methods using other tools. [sent-24, score-0.519]
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Introduction: Continuing with my discussion of the articles in the special issue of the journal Rationality, Markets and Morals on the philosophy of Bayesian statistics: Larry Wasserman, “Low Assumptions, High Dimensions”: This article was refreshing to me because it was so different from anything I’ve seen before. Larry works in a statistics department and I work in a statistics department but there’s so little overlap in what we do. Larry and I both work in high dimesions (maybe his dimensions are higher than mine, but a few thousand dimensions seems like a lot to me!), but there the similarity ends. His article is all about using few to no assumptions, while I use assumptions all the time. Here’s an example. Larry writes: P. Laurie Davies (and his co-workers) have written several interesting papers where probability models, at least in the sense that we usually use them, are eliminated. Data are treated as deterministic. One then looks for adequate models rather than true mode
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Introduction: Leading theoretical statistician Larry Wassserman in 2008 : Some of the greatest contributions of statistics to science involve adding additional randomness and leveraging that randomness. Examples are randomized experiments, permutation tests, cross-validation and data-splitting. These are unabashedly frequentist ideas and, while one can strain to fit them into a Bayesian framework, they don’t really have a place in Bayesian inference. The fact that Bayesian methods do not naturally accommodate such a powerful set of statistical ideas seems like a serious deficiency. To which I responded on the second-to-last paragraph of page 8 here . Larry Wasserman in 2013 : Some people say that there is no role for randomization in Bayesian inference. In other words, the randomization mechanism plays no role in Bayes’ theorem. But this is not really true. Without randomization, we can indeed derive a posterior for theta but it is highly sensitive to the prior. This is just a restat
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