andrew_gelman_stats andrew_gelman_stats-2013 andrew_gelman_stats-2013-1926 knowledge-graph by maker-knowledge-mining
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Introduction: Following up on this story , Bob Goodman writes: A most recent issue of the New England Journal of Medicine published a study entitled “Biventricular Pacing for Atrioventricular Block and Systolic Dysfunction,” (N Engl J Med 2013; 368:1585-1593), whereby “A hierarchical Bayesian proportional-hazards model was used for analysis of the primary outcome.” It is the first study I can recall in this journal that has reported on Table 2 (primary outcomes) “The Posterior Probability of Hazard Ratio < 1" (which in this case was .9978). This is ok, but to be really picky I will say that there’s typically not so much reason to care about the posterior probability that the effect is greater than 1; I’d rather have an estimate of the effect. Also we should be using informative priors.
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Introduction: Following up on this story , Bob Goodman writes: A most recent issue of the New England Journal of Medicine published a study entitled “Biventricular Pacing for Atrioventricular Block and Systolic Dysfunction,” (N Engl J Med 2013; 368:1585-1593), whereby “A hierarchical Bayesian proportional-hazards model was used for analysis of the primary outcome.” It is the first study I can recall in this journal that has reported on Table 2 (primary outcomes) “The Posterior Probability of Hazard Ratio < 1" (which in this case was .9978). This is ok, but to be really picky I will say that there’s typically not so much reason to care about the posterior probability that the effect is greater than 1; I’d rather have an estimate of the effect. Also we should be using informative priors.
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Introduction: Philipp Doebler writes: I was quite happy that recently you shared some thoughts of yours and others on meta-analysis. I especially liked the slides by Chris Schmid that you linked from your blog. A large portion of my work deals with meta-analysis and I am also fond of using Bayesian methods (actually two of the projects I am working on are very Bayesian), though I can not say I have opinions with respect to the underlying philosophy. I would say though, that I do share your view that there are good reasons to use informative priors. The reason I am writing to you is that this leads to the following dilemma, which is puzzling me. Say a number of scientists conduct similar studies over the years and all of them did this in a Bayesian fashion. If each of the groups used informative priors based on the research of existing groups the priors could become more and more informative over the years, since more and more is known over the subject. At least in smallish studies these p
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Introduction: From my new article in the journal Epidemiology: Sander Greenland and Charles Poole accept that P values are here to stay but recognize that some of their most common interpretations have problems. The casual view of the P value as posterior probability of the truth of the null hypothesis is false and not even close to valid under any reasonable model, yet this misunderstanding persists even in high-stakes settings (as discussed, for example, by Greenland in 2011). The formal view of the P value as a probability conditional on the null is mathematically correct but typically irrelevant to research goals (hence, the popularity of alternative—if wrong—interpretations). A Bayesian interpretation based on a spike-and-slab model makes little sense in applied contexts in epidemiology, political science, and other fields in which true effects are typically nonzero and bounded (thus violating both the “spike” and the “slab” parts of the model). I find Greenland and Poole’s perspective t
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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
Introduction: Ratio estimates are common in statistics. In survey sampling, the ratio estimate is when you use y/x to estimate Y/X (using the notation in which x,y are totals of sample measurements and X,Y are population totals). In textbook sampling examples, the denominator X will be an all-positive variable, something that is easy to measure and is, ideally, close to proportional to Y. For example, X is last year’s sales and Y is this year’s sales, or X is the number of people in a cluster and Y is some count. Ratio estimation doesn’t work so well if X can be either positive or negative. More generally we can consider any estimate of a ratio, with no need for a survey sampling context. The problem with estimating Y/X is that the very interpretation of Y/X can change completely if the sign of X changes. Everything is ok for a point estimate: you get X.hat and Y.hat, you can take the ratio Y.hat/X.hat, no problem. But the inference falls apart if you have enough uncertainty in X.hat th
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Introduction: Following up on this story , Bob Goodman writes: A most recent issue of the New England Journal of Medicine published a study entitled “Biventricular Pacing for Atrioventricular Block and Systolic Dysfunction,” (N Engl J Med 2013; 368:1585-1593), whereby “A hierarchical Bayesian proportional-hazards model was used for analysis of the primary outcome.” It is the first study I can recall in this journal that has reported on Table 2 (primary outcomes) “The Posterior Probability of Hazard Ratio < 1" (which in this case was .9978). This is ok, but to be really picky I will say that there’s typically not so much reason to care about the posterior probability that the effect is greater than 1; I’d rather have an estimate of the effect. Also we should be using informative priors.
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Introduction: Philipp Doebler writes: I was quite happy that recently you shared some thoughts of yours and others on meta-analysis. I especially liked the slides by Chris Schmid that you linked from your blog. A large portion of my work deals with meta-analysis and I am also fond of using Bayesian methods (actually two of the projects I am working on are very Bayesian), though I can not say I have opinions with respect to the underlying philosophy. I would say though, that I do share your view that there are good reasons to use informative priors. The reason I am writing to you is that this leads to the following dilemma, which is puzzling me. Say a number of scientists conduct similar studies over the years and all of them did this in a Bayesian fashion. If each of the groups used informative priors based on the research of existing groups the priors could become more and more informative over the years, since more and more is known over the subject. At least in smallish studies these p
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Introduction: From my new article in the journal Epidemiology: Sander Greenland and Charles Poole accept that P values are here to stay but recognize that some of their most common interpretations have problems. The casual view of the P value as posterior probability of the truth of the null hypothesis is false and not even close to valid under any reasonable model, yet this misunderstanding persists even in high-stakes settings (as discussed, for example, by Greenland in 2011). The formal view of the P value as a probability conditional on the null is mathematically correct but typically irrelevant to research goals (hence, the popularity of alternative—if wrong—interpretations). A Bayesian interpretation based on a spike-and-slab model makes little sense in applied contexts in epidemiology, political science, and other fields in which true effects are typically nonzero and bounded (thus violating both the “spike” and the “slab” parts of the model). I find Greenland and Poole’s perspective t
Introduction: Phil Nelson writes in the context of a biostatistics textbook he is writing, “Physical models of living systems”: There are a number of classic statistical problems that arise every day in the lab, and which are discussed in any book: 1. In a control group, M untreated rats out of 20 got a form of cancer. In a test group, N treated rats out of 20 got that cancer. Is this a significant difference? 2. In a control group of 20 untreated rates, their body weights at 2 weeks were w_1,…, w_20. In a test group of 20 treated rats, their body weights at 2 weeks were w’_1,…, w’_20. Are the means significantly different? 3. In a group of 20 rats, each given dose d_i of a drug, their body weights at 2 weeks were w_i. Is there a significant correlation between d and w? I would like to ask: What are some situations in which the classical approach (or a naive implementation of it, based on cookbook recipes) gives worse results than a Bayesian approach, results that actually impeded the scien
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Introduction: Sciencedaily has posted an article titled Apes Unwilling to Gamble When Odds Are Uncertain : The apes readily distinguished between the different probabilities of winning: they gambled a lot when there was a 100 percent chance, less when there was a 50 percent chance, and only rarely when there was no chance In some trials, however, the experimenter didn’t remove a lid from the bowl, so the apes couldn’t assess the likelihood of winning a banana The odds from the covered bowl were identical to those from the risky option: a 50 percent chance of getting the much sought-after banana. But apes of both species were less likely to choose this ambiguous option. Like humans, they showed “ambiguity aversion” — preferring to gamble more when they knew the odds than when they didn’t. Given some of the other differences between chimps and bonobos, Hare and Rosati had expected to find the bonobos to be more averse to ambiguity, but that didn’t turn out to be the case. Thanks to Sta
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Introduction: Hear me interviewed on the topic here . P.S. The interview was fine but I don’t agree with everything on the linked website. For example, this bit: Global warming is not the first case of a widespread fear based on incomplete knowledge turned out to be false or at least greatly exaggerated. Global warming has many of the characteristics of a popular delusion, an irrational fear or cause that is embraced by millions of people because, well, it is believed by millions of people! All right, then.
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Introduction: People keep pointing me to this excellent news article by David Brown, about a scientist who was convicted of data manipulation: In all, 330 patients were randomly assigned to get either interferon gamma-1b or placebo injections. Disease progression or death occurred in 46 percent of those on the drug and 52 percent of those on placebo. That was not a significant difference, statistically speaking. When only survival was considered, however, the drug looked better: 10 percent of people getting the drug died, compared with 17 percent of those on placebo. However, that difference wasn’t “statistically significant,” either. Specifically, the so-called P value — a mathematical measure of the strength of the evidence that there’s a true difference between a treatment and placebo — was 0.08. . . . Technically, the study was a bust, although the results leaned toward a benefit from interferon gamma-1b. Was there a group of patients in which the results tipped? Harkonen asked the statis
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Introduction: Burak Bayramli writes: In this paper by Sunjin Ahn, Anoop Korattikara, and Max Welling and this paper by Welling and Yee Whye The, there are some arguments on big data and the use of MCMC. Both papers have suggested improvements to speed up MCMC computations. I was wondering what your thoughts were, especially on this paragraph: When a dataset has a billion data-cases (as is not uncommon these days) MCMC algorithms will not even have generated a single (burn-in) sample when a clever learning algorithm based on stochastic gradients may already be making fairly good predictions. In fact, the intriguing results of Bottou and Bousquet (2008) seem to indicate that in terms of “number of bits learned per unit of computation”, an algorithm as simple as stochastic gradient descent is almost optimally efficient. We therefore argue that for Bayesian methods to remain useful in an age when the datasets grow at an exponential rate, they need to embrace the ideas of the stochastic optimiz
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