andrew_gelman_stats andrew_gelman_stats-2011 andrew_gelman_stats-2011-846 knowledge-graph by maker-knowledge-mining
Source: html
Introduction: Ryan King writes: I was wondering if you have a brief comment on the state of the art for objective priors for hierarchical generalized linear models (generalized linear mixed models). I have been working off the papers in Bayesian Analysis (2006) 1, Number 3 (Browne and Draper, Kass and Natarajan, Gelman). There seems to have been continuous work for matching priors in linear mixed models, but GLMMs less so because of the lack of an analytic marginal likelihood for the variance components. There are a number of additional suggestions in the literature since 2006, but little robust practical guidance. I’m interested in both mean parameters and the variance components. I’m almost always concerned with logistic random effect models. I’m fascinated by the matching-priors idea of higher-order asymptotic improvements to maximum likelihood, and need to make some kind of defensible default recommendation. Given the massive scale of the datasets (genetics …), extensive sensitivity a
sentIndex sentText sentNum sentScore
1 Ryan King writes: I was wondering if you have a brief comment on the state of the art for objective priors for hierarchical generalized linear models (generalized linear mixed models). [sent-1, score-1.536]
2 There seems to have been continuous work for matching priors in linear mixed models, but GLMMs less so because of the lack of an analytic marginal likelihood for the variance components. [sent-3, score-1.095]
3 There are a number of additional suggestions in the literature since 2006, but little robust practical guidance. [sent-4, score-0.073]
4 I’m interested in both mean parameters and the variance components. [sent-5, score-0.423]
5 I’m fascinated by the matching-priors idea of higher-order asymptotic improvements to maximum likelihood, and need to make some kind of defensible default recommendation. [sent-7, score-0.58]
6 Given the massive scale of the datasets (genetics …), extensive sensitivity analysis won’t really be an option. [sent-8, score-0.491]
7 ” As a scientist, I try to be objective as much as possible, but I think the objectivity comes in the principle, not the prior itself. [sent-10, score-0.601]
8 A prior distribution–any statistical model–reflects information, and the appropriate objective procedure will depend on what information you have. [sent-11, score-0.481]
9 That said, I do like the idea of weakly informative priors and I also respect the need for default procedures. [sent-12, score-0.883]
10 When it comes to non-varying parameters, I’m currently happy with my weakly informative t priors (after appropriately rescaling the predictors), as discussed in my 2008 paper with Jakulin et al. [sent-13, score-1.144]
11 For variance parameters estimated using full Bayes, I like the half-t family from my 2006 paper you noted above, or else something hierarchical-hierarchical if you have multiple variance parameters. [sent-14, score-0.724]
12 This is discussed in detail in my paper with Yeojin, Sophia, Jingchen, and Vince, and it’s implemented in blmer/bglmer. [sent-16, score-0.247]
wordName wordTfidf (topN-words)
[('priors', 0.289), ('objective', 0.282), ('weakly', 0.231), ('variance', 0.224), ('parameters', 0.199), ('default', 0.193), ('informative', 0.17), ('linear', 0.165), ('scale', 0.159), ('generalized', 0.152), ('mixed', 0.14), ('prior', 0.126), ('browne', 0.124), ('yeojin', 0.117), ('defensible', 0.112), ('kass', 0.112), ('objectivity', 0.112), ('likelihood', 0.109), ('vince', 0.108), ('hierarchical', 0.106), ('jingchen', 0.105), ('sophia', 0.102), ('fascinated', 0.102), ('appropriately', 0.102), ('jakulin', 0.102), ('rescaling', 0.102), ('asymptotic', 0.094), ('extensive', 0.094), ('models', 0.093), ('gamma', 0.092), ('discussed', 0.092), ('analytic', 0.09), ('sensitivity', 0.085), ('ryan', 0.085), ('reflects', 0.084), ('genetics', 0.083), ('comes', 0.081), ('massive', 0.08), ('improvements', 0.079), ('matching', 0.078), ('implemented', 0.078), ('paper', 0.077), ('king', 0.075), ('keeps', 0.075), ('depend', 0.073), ('number', 0.073), ('datasets', 0.073), ('brief', 0.073), ('reasonably', 0.071), ('art', 0.071)]
simIndex simValue blogId blogTitle
same-blog 1 1.0000002 846 andrew gelman stats-2011-08-09-Default priors update?
Introduction: Ryan King writes: I was wondering if you have a brief comment on the state of the art for objective priors for hierarchical generalized linear models (generalized linear mixed models). I have been working off the papers in Bayesian Analysis (2006) 1, Number 3 (Browne and Draper, Kass and Natarajan, Gelman). There seems to have been continuous work for matching priors in linear mixed models, but GLMMs less so because of the lack of an analytic marginal likelihood for the variance components. There are a number of additional suggestions in the literature since 2006, but little robust practical guidance. I’m interested in both mean parameters and the variance components. I’m almost always concerned with logistic random effect models. I’m fascinated by the matching-priors idea of higher-order asymptotic improvements to maximum likelihood, and need to make some kind of defensible default recommendation. Given the massive scale of the datasets (genetics …), extensive sensitivity a
2 0.42599812 779 andrew gelman stats-2011-06-25-Avoiding boundary estimates using a prior distribution as regularization
Introduction: For awhile I’ve been fitting most of my multilevel models using lmer/glmer, which gives point estimates of the group-level variance parameters (maximum marginal likelihood estimate for lmer and an approximation for glmer). I’m usually satisfied with this–sure, point estimation understates the uncertainty in model fitting, but that’s typically the least of our worries. Sometimes, though, lmer/glmer estimates group-level variances at 0 or estimates group-level correlation parameters at +/- 1. Typically, when this happens, it’s not that we’re so sure the variance is close to zero or that the correlation is close to 1 or -1; rather, the marginal likelihood does not provide a lot of information about these parameters of the group-level error distribution. I don’t want point estimates on the boundary. I don’t want to say that the unexplained variance in some dimension is exactly zero. One way to handle this problem is full Bayes: slap a prior on sigma, do your Gibbs and Metropolis
Introduction: Deborah Mayo sent me this quote from Jim Berger: Too often I see people pretending to be subjectivists, and then using “weakly informative” priors that the objective Bayesian community knows are terrible and will give ridiculous answers; subjectivism is then being used as a shield to hide ignorance. . . . In my own more provocative moments, I claim that the only true subjectivists are the objective Bayesians, because they refuse to use subjectivism as a shield against criticism of sloppy pseudo-Bayesian practice. This caught my attention because I’ve become more and more convinced that weakly informative priors are the right way to go in many different situations. I don’t think Berger was talking about me , though, as the above quote came from a publication in 2006, at which time I’d only started writing about weakly informative priors. Going back to Berger’s article , I see that his “weakly informative priors” remark was aimed at this article by Anthony O’Hagan, who w
4 0.34855571 1092 andrew gelman stats-2011-12-29-More by Berger and me on weakly informative priors
Introduction: A couple days ago we discussed some remarks by Tony O’Hagan and Jim Berger on weakly informative priors. Jim followed up on Deborah Mayo’s blog with this: Objective Bayesian priors are often improper (i.e., have infinite total mass), but this is not a problem when they are developed correctly. But not every improper prior is satisfactory. For instance, the constant prior is known to be unsatisfactory in many situations. The ‘solution’ pseudo-Bayesians often use is to choose a constant prior over a large but bounded set (a ‘weakly informative’ prior), saying it is now proper and so all is well. This is not true; if the constant prior on the whole parameter space is bad, so will be the constant prior over the bounded set. The problem is, in part, that some people confuse proper priors with subjective priors and, having learned that true subjective priors are fine, incorrectly presume that weakly informative proper priors are fine. I have a few reactions to this: 1. I agree
5 0.29973304 801 andrew gelman stats-2011-07-13-On the half-Cauchy prior for a global scale parameter
Introduction: Nick Polson and James Scott write : We generalize the half-Cauchy prior for a global scale parameter to the wider class of hypergeometric inverted-beta priors. We derive expressions for posterior moments and marginal densities when these priors are used for a top-level normal variance in a Bayesian hierarchical model. Finally, we prove a result that characterizes the frequentist risk of the Bayes estimators under all priors in the class. These arguments provide an alternative, classical justification for the use of the half-Cauchy prior in Bayesian hierarchical models, complementing the arguments in Gelman (2006). This makes me happy, of course. It’s great to be validated. The only think I didn’t catch is how they set the scale parameter for the half-Cauchy prior. In my 2006 paper I frame it as a weakly informative prior and recommend that the scale be set based on actual prior knowledge. But Polson and Scott are talking about a default choice. I used to think that such a
6 0.24494658 1465 andrew gelman stats-2012-08-21-D. Buggin
7 0.23633686 2129 andrew gelman stats-2013-12-10-Cross-validation and Bayesian estimation of tuning parameters
8 0.23475248 1946 andrew gelman stats-2013-07-19-Prior distributions on derived quantities rather than on parameters themselves
9 0.22975841 1155 andrew gelman stats-2012-02-05-What is a prior distribution?
10 0.21909876 1474 andrew gelman stats-2012-08-29-More on scaled-inverse Wishart and prior independence
11 0.20788555 2143 andrew gelman stats-2013-12-22-The kluges of today are the textbook solutions of tomorrow.
12 0.20186748 1486 andrew gelman stats-2012-09-07-Prior distributions for regression coefficients
13 0.2011044 1454 andrew gelman stats-2012-08-11-Weakly informative priors for Bayesian nonparametric models?
14 0.19185624 1046 andrew gelman stats-2011-12-07-Neutral noninformative and informative conjugate beta and gamma prior distributions
15 0.19128108 2109 andrew gelman stats-2013-11-21-Hidden dangers of noninformative priors
16 0.19034803 247 andrew gelman stats-2010-09-01-How does Bayes do it?
17 0.18229492 1941 andrew gelman stats-2013-07-16-Priors
18 0.18182972 1247 andrew gelman stats-2012-04-05-More philosophy of Bayes
19 0.18169565 669 andrew gelman stats-2011-04-19-The mysterious Gamma (1.4, 0.4)
20 0.18160331 1858 andrew gelman stats-2013-05-15-Reputations changeable, situations tolerable
topicId topicWeight
[(0, 0.213), (1, 0.279), (2, 0.037), (3, 0.063), (4, -0.026), (5, -0.074), (6, 0.179), (7, -0.027), (8, -0.227), (9, 0.139), (10, 0.06), (11, -0.0), (12, 0.092), (13, 0.061), (14, 0.041), (15, -0.02), (16, -0.044), (17, 0.03), (18, 0.013), (19, 0.017), (20, -0.059), (21, -0.036), (22, 0.035), (23, 0.062), (24, -0.015), (25, 0.01), (26, -0.008), (27, 0.05), (28, -0.017), (29, 0.002), (30, 0.003), (31, -0.015), (32, 0.038), (33, -0.024), (34, 0.005), (35, 0.006), (36, -0.013), (37, -0.011), (38, 0.021), (39, 0.02), (40, -0.027), (41, -0.013), (42, 0.047), (43, 0.06), (44, -0.009), (45, -0.002), (46, -0.052), (47, -0.03), (48, 0.018), (49, -0.023)]
simIndex simValue blogId blogTitle
same-blog 1 0.98617262 846 andrew gelman stats-2011-08-09-Default priors update?
Introduction: Ryan King writes: I was wondering if you have a brief comment on the state of the art for objective priors for hierarchical generalized linear models (generalized linear mixed models). I have been working off the papers in Bayesian Analysis (2006) 1, Number 3 (Browne and Draper, Kass and Natarajan, Gelman). There seems to have been continuous work for matching priors in linear mixed models, but GLMMs less so because of the lack of an analytic marginal likelihood for the variance components. There are a number of additional suggestions in the literature since 2006, but little robust practical guidance. I’m interested in both mean parameters and the variance components. I’m almost always concerned with logistic random effect models. I’m fascinated by the matching-priors idea of higher-order asymptotic improvements to maximum likelihood, and need to make some kind of defensible default recommendation. Given the massive scale of the datasets (genetics …), extensive sensitivity a
2 0.92345488 779 andrew gelman stats-2011-06-25-Avoiding boundary estimates using a prior distribution as regularization
Introduction: For awhile I’ve been fitting most of my multilevel models using lmer/glmer, which gives point estimates of the group-level variance parameters (maximum marginal likelihood estimate for lmer and an approximation for glmer). I’m usually satisfied with this–sure, point estimation understates the uncertainty in model fitting, but that’s typically the least of our worries. Sometimes, though, lmer/glmer estimates group-level variances at 0 or estimates group-level correlation parameters at +/- 1. Typically, when this happens, it’s not that we’re so sure the variance is close to zero or that the correlation is close to 1 or -1; rather, the marginal likelihood does not provide a lot of information about these parameters of the group-level error distribution. I don’t want point estimates on the boundary. I don’t want to say that the unexplained variance in some dimension is exactly zero. One way to handle this problem is full Bayes: slap a prior on sigma, do your Gibbs and Metropolis
3 0.92004359 801 andrew gelman stats-2011-07-13-On the half-Cauchy prior for a global scale parameter
Introduction: Nick Polson and James Scott write : We generalize the half-Cauchy prior for a global scale parameter to the wider class of hypergeometric inverted-beta priors. We derive expressions for posterior moments and marginal densities when these priors are used for a top-level normal variance in a Bayesian hierarchical model. Finally, we prove a result that characterizes the frequentist risk of the Bayes estimators under all priors in the class. These arguments provide an alternative, classical justification for the use of the half-Cauchy prior in Bayesian hierarchical models, complementing the arguments in Gelman (2006). This makes me happy, of course. It’s great to be validated. The only think I didn’t catch is how they set the scale parameter for the half-Cauchy prior. In my 2006 paper I frame it as a weakly informative prior and recommend that the scale be set based on actual prior knowledge. But Polson and Scott are talking about a default choice. I used to think that such a
4 0.91964716 1858 andrew gelman stats-2013-05-15-Reputations changeable, situations tolerable
Introduction: David Kessler, Peter Hoff, and David Dunson write : Marginally specified priors for nonparametric Bayesian estimation Prior specification for nonparametric Bayesian inference involves the difficult task of quantifying prior knowledge about a parameter of high, often infinite, dimension. Realistically, a statistician is unlikely to have informed opinions about all aspects of such a parameter, but may have real information about functionals of the parameter, such the population mean or variance. This article proposes a new framework for nonparametric Bayes inference in which the prior distribution for a possibly infinite-dimensional parameter is decomposed into two parts: an informative prior on a finite set of functionals, and a nonparametric conditional prior for the parameter given the functionals. Such priors can be easily constructed from standard nonparametric prior distributions in common use, and inherit the large support of the standard priors upon which they are based. Ad
5 0.8919543 1474 andrew gelman stats-2012-08-29-More on scaled-inverse Wishart and prior independence
Introduction: I’ve had a couple of email conversations in the past couple days on dependence in multivariate prior distributions. Modeling the degrees of freedom and scale parameters in the t distribution First, in our Stan group we’ve been discussing the choice of priors for the degrees-of-freedom parameter in the t distribution. I wrote that also there’s the question of parameterization. It does not necessarily make sense to have independent priors on the df and scale parameters. In some sense, the meaning of the scale parameter changes with the df. Prior dependence between correlation and scale parameters in the scaled inverse-Wishart model The second case of parameterization in prior distribution arose from an email I received from Chris Chatham pointing me to this exploration by Matt Simpson of the scaled inverse-Wishart prior distribution for hierarchical covariance matrices. Simpson writes: A popular prior for Σ is the inverse-Wishart distribution [ not the same as the
7 0.87146556 63 andrew gelman stats-2010-06-02-The problem of overestimation of group-level variance parameters
8 0.87019575 1465 andrew gelman stats-2012-08-21-D. Buggin
9 0.86982459 1092 andrew gelman stats-2011-12-29-More by Berger and me on weakly informative priors
10 0.83388245 1087 andrew gelman stats-2011-12-27-“Keeping things unridiculous”: Berger, O’Hagan, and me on weakly informative priors
11 0.83368027 468 andrew gelman stats-2010-12-15-Weakly informative priors and imprecise probabilities
12 0.82916313 1946 andrew gelman stats-2013-07-19-Prior distributions on derived quantities rather than on parameters themselves
13 0.8271777 669 andrew gelman stats-2011-04-19-The mysterious Gamma (1.4, 0.4)
15 0.82258654 2017 andrew gelman stats-2013-09-11-“Informative g-Priors for Logistic Regression”
16 0.82247883 1454 andrew gelman stats-2012-08-11-Weakly informative priors for Bayesian nonparametric models?
17 0.81921351 184 andrew gelman stats-2010-08-04-That half-Cauchy prior
18 0.81538892 2129 andrew gelman stats-2013-12-10-Cross-validation and Bayesian estimation of tuning parameters
19 0.81268609 1155 andrew gelman stats-2012-02-05-What is a prior distribution?
20 0.79798889 1486 andrew gelman stats-2012-09-07-Prior distributions for regression coefficients
topicId topicWeight
[(0, 0.038), (8, 0.012), (15, 0.02), (16, 0.069), (24, 0.281), (30, 0.019), (79, 0.01), (81, 0.031), (84, 0.014), (86, 0.072), (88, 0.011), (89, 0.064), (99, 0.241)]
simIndex simValue blogId blogTitle
same-blog 1 0.98561406 846 andrew gelman stats-2011-08-09-Default priors update?
Introduction: Ryan King writes: I was wondering if you have a brief comment on the state of the art for objective priors for hierarchical generalized linear models (generalized linear mixed models). I have been working off the papers in Bayesian Analysis (2006) 1, Number 3 (Browne and Draper, Kass and Natarajan, Gelman). There seems to have been continuous work for matching priors in linear mixed models, but GLMMs less so because of the lack of an analytic marginal likelihood for the variance components. There are a number of additional suggestions in the literature since 2006, but little robust practical guidance. I’m interested in both mean parameters and the variance components. I’m almost always concerned with logistic random effect models. I’m fascinated by the matching-priors idea of higher-order asymptotic improvements to maximum likelihood, and need to make some kind of defensible default recommendation. Given the massive scale of the datasets (genetics …), extensive sensitivity a
2 0.97335649 779 andrew gelman stats-2011-06-25-Avoiding boundary estimates using a prior distribution as regularization
Introduction: For awhile I’ve been fitting most of my multilevel models using lmer/glmer, which gives point estimates of the group-level variance parameters (maximum marginal likelihood estimate for lmer and an approximation for glmer). I’m usually satisfied with this–sure, point estimation understates the uncertainty in model fitting, but that’s typically the least of our worries. Sometimes, though, lmer/glmer estimates group-level variances at 0 or estimates group-level correlation parameters at +/- 1. Typically, when this happens, it’s not that we’re so sure the variance is close to zero or that the correlation is close to 1 or -1; rather, the marginal likelihood does not provide a lot of information about these parameters of the group-level error distribution. I don’t want point estimates on the boundary. I don’t want to say that the unexplained variance in some dimension is exactly zero. One way to handle this problem is full Bayes: slap a prior on sigma, do your Gibbs and Metropolis
3 0.96452975 953 andrew gelman stats-2011-10-11-Steve Jobs’s cancer and science-based medicine
Introduction: Interesting discussion from David Gorski (which I found via this link from Joseph Delaney). I don’t have anything really to add to this discussion except to note the value of this sort of anecdote in a statistics discussion. It’s only n=1 and adds almost nothing to the literature on the effectiveness of various treatments, but a story like this can help focus one’s thoughts on the decision problems.
4 0.96295917 1368 andrew gelman stats-2012-06-06-Question 27 of my final exam for Design and Analysis of Sample Surveys
Introduction: 27. Which of the following problems were identified with the Burnham et al. survey of Iraq mortality? (Indicate all that apply.) (a) The survey used cluster sampling, which is inappropriate for estimating individual out- comes such as death. (b) In their report, Burnham et al. did not identify their primary sampling units. (c) The second-stage sampling was not a probability sample. (d) Survey materials supplied by the authors are incomplete and inconsistent with published descriptions of the survey. Solution to question 26 From yesterday : 26. You have just graded an an exam with 28 questions and 15 students. You fit a logistic item- response model estimating ability, difficulty, and discrimination parameters. Which of the following statements are basically true? (Indicate all that apply.) (a) If a question is answered correctly by students with very low and very high ability, but is missed by students in the middle, it will have a high value for its discrimination
5 0.96136475 1367 andrew gelman stats-2012-06-05-Question 26 of my final exam for Design and Analysis of Sample Surveys
Introduction: 26. You have just graded an an exam with 28 questions and 15 students. You fit a logistic item- response model estimating ability, difficulty, and discrimination parameters. Which of the following statements are basically true? (Indicate all that apply.) (a) If a question is answered correctly by students with very low and very high ability, but is missed by students in the middle, it will have a high value for its discrimination parameter. (b) It is not possible to fit an item-response model when you have more questions than students. In order to fit the model, you either need to reduce the number of questions (for example, by discarding some questions or by putting together some questions into a combined score) or increase the number of students in the dataset. (c) To keep the model identified, you can set one of the difficulty parameters or one of the ability parameters to zero and set one of the discrimination parameters to 1. (d) If two students answer the same number of q
6 0.9597193 197 andrew gelman stats-2010-08-10-The last great essayist?
7 0.95873892 1455 andrew gelman stats-2012-08-12-Probabilistic screening to get an approximate self-weighted sample
8 0.95719564 2231 andrew gelman stats-2014-03-03-Running into a Stan Reference by Accident
10 0.95580024 1999 andrew gelman stats-2013-08-27-Bayesian model averaging or fitting a larger model
11 0.95557785 1474 andrew gelman stats-2012-08-29-More on scaled-inverse Wishart and prior independence
12 0.95537031 1062 andrew gelman stats-2011-12-16-Mr. Pearson, meet Mr. Mandelbrot: Detecting Novel Associations in Large Data Sets
14 0.95494282 1376 andrew gelman stats-2012-06-12-Simple graph WIN: the example of birthday frequencies
15 0.95491326 1221 andrew gelman stats-2012-03-19-Whassup with deviance having a high posterior correlation with a parameter in the model?
16 0.95440602 2017 andrew gelman stats-2013-09-11-“Informative g-Priors for Logistic Regression”
17 0.95390135 1087 andrew gelman stats-2011-12-27-“Keeping things unridiculous”: Berger, O’Hagan, and me on weakly informative priors
18 0.95233321 278 andrew gelman stats-2010-09-15-Advice that might make sense for individuals but is negative-sum overall
19 0.95139974 482 andrew gelman stats-2010-12-23-Capitalism as a form of voluntarism
20 0.95047659 743 andrew gelman stats-2011-06-03-An argument that can’t possibly make sense