andrew_gelman_stats andrew_gelman_stats-2010 andrew_gelman_stats-2010-327 knowledge-graph by maker-knowledge-mining
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Introduction: Sam Seaver writes: I’m a graduate student in computational biology, and I’m relatively new to advanced statistics, and am trying to teach myself how best to approach a problem I have. My dataset is a small sparse matrix of 150 cases and 70 predictors, it is sparse as in many zeros, not many ‘NA’s. Each case is a nutrient that is fed into an in silico organism, and its response is whether or not it stimulates growth, and each predictor is one of 70 different pathways that the nutrient may or may not belong to. Because all of the nutrients do not belong to all of the pathways, there are thus many zeros in my matrix. My goal is to be able to use the pathways themselves to predict whether or not a nutrient could stimulate growth, thus I wanted to compute regression coefficients for each pathway, with which I could apply to other nutrients for other species. There are quite a few singularities in the dataset (summary(glm) reports that 14 coefficients are not defined because of sin
sentIndex sentText sentNum sentScore
1 Sam Seaver writes: I’m a graduate student in computational biology, and I’m relatively new to advanced statistics, and am trying to teach myself how best to approach a problem I have. [sent-1, score-0.23]
2 My dataset is a small sparse matrix of 150 cases and 70 predictors, it is sparse as in many zeros, not many ‘NA’s. [sent-2, score-0.578]
3 Each case is a nutrient that is fed into an in silico organism, and its response is whether or not it stimulates growth, and each predictor is one of 70 different pathways that the nutrient may or may not belong to. [sent-3, score-1.828]
4 Because all of the nutrients do not belong to all of the pathways, there are thus many zeros in my matrix. [sent-4, score-0.844]
5 My goal is to be able to use the pathways themselves to predict whether or not a nutrient could stimulate growth, thus I wanted to compute regression coefficients for each pathway, with which I could apply to other nutrients for other species. [sent-5, score-1.763]
6 So I was wondering if there are complementary and/or alternative methods to logistic regression that would give me a coefficient of a kind for each pathway? [sent-7, score-0.402]
7 My reply: If you have this kind of sparsity, I think you’ll need to add some prior information or structure to your model. [sent-8, score-0.255]
8 Our paper on bayesglm suggests a reasonable default prior, but it sounds to me that you’ll have to go further. [sent-9, score-0.142]
9 To put it another way: give up the idea that you’re estimating 70 distinct parameters. [sent-10, score-0.13]
10 Instead, think of these coefficients as linked to each other in a complex web. [sent-11, score-0.215]
11 More generally, I don’t think it ever makes sense to think of a problem with a lot of loose parameters. [sent-12, score-0.08]
12 One of our major research problems now is to set up general models for structured parameters, going beyond simple exchangeability. [sent-14, score-0.068]
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Introduction: Sam Seaver writes: I’m a graduate student in computational biology, and I’m relatively new to advanced statistics, and am trying to teach myself how best to approach a problem I have. My dataset is a small sparse matrix of 150 cases and 70 predictors, it is sparse as in many zeros, not many ‘NA’s. Each case is a nutrient that is fed into an in silico organism, and its response is whether or not it stimulates growth, and each predictor is one of 70 different pathways that the nutrient may or may not belong to. Because all of the nutrients do not belong to all of the pathways, there are thus many zeros in my matrix. My goal is to be able to use the pathways themselves to predict whether or not a nutrient could stimulate growth, thus I wanted to compute regression coefficients for each pathway, with which I could apply to other nutrients for other species. There are quite a few singularities in the dataset (summary(glm) reports that 14 coefficients are not defined because of sin
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Introduction: Rob Tibshirani writes : Hastie et al. (2001) coined the informal “Bet on Sparsity” principle. The l1 methods assume that the truth is sparse, in some basis. If the assumption holds true, then the parameters can be efficiently estimated using l1 penalties. If the assumption does not hold—so that the truth is dense—then no method will be able to recover the underlying model without a large amount of data per parameter. I’ve earlier expressed my full and sincere appreciation for Hastie and Tibshirani’s work in this area. Now I’d like to briefly comment on the above snippet. The question is, how do we think about the “bet on sparsity” principle in a world where the truth is dense? I’m thinking here of social science, where no effects are clean and no coefficient is zero (see page 960 of this article or various blog discussions in the past few years), where every contrast is meaningful—but some of these contrasts might be lost in the noise with any realistic size of data.
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Introduction: Eric Brown writes: I have come across a number of recommendations over the years about best practices for multilevel regression modeling. For example, the use of t-distributed priors for coefficients in logistic regression and standardizing input variables from one of your 2008 Annals of Applied Statistics papers; or recommendations for priors on variance parameters from your 2006 Bayesian Analysis paper. I understand that these are often of varied opinion of people in the field, but I was wondering if you have a reference that you point people to for a place to get started? I’ve tried looking through your blog posts but couldn’t find any summaries. For example, what are some examples of when I should use more than a two-level hierarchical model? Can I use a spike-slab coefficient model with a t-distributed prior for the slab rather than a normal? If I assume that my model is a priori wrong (but still useful), what are some recommended ways to choose how many interactions to u
Introduction: Since we’re talking about the scaled inverse Wishart . . . here’s a recent message from Chris Chatham: I have been reading your book on Bayesian Hierarchical/Multilevel Modeling but have been struggling a bit with deciding whether to model my multivariate normal distribution using the scaled inverse Wishart approach you advocate given the arguments at this blog post [entitled "Why an inverse-Wishart prior may not be such a good idea"]. My reply: We discuss this in our book. We know the inverse-Wishart has problems, that’s why we recommend the scaled inverse-Wishart, which is a more general class of models. Here ‘s an old blog post on the topic. And also of course there’s the description in our book. Chris pointed me to the following comment by Simon Barthelmé: Using the scaled inverse Wishart doesn’t change anything, the standard deviations of the invidual coefficients and their covariance are still dependent. My answer would be to use a prior that models the stan
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Introduction: “Ich glaube, dass die Wahrscheinlichkeitsrechnung das richtige Werkzeug zum Lösen solcher Probleme ist”, sagt Andrew Gelman , Statistikprofessor von der Columbia-Universität in New York. Wie oft aber derart knifflige Aufgaben im realen Leben auftauchen, könne er nicht sagen. Was fast schon beruhigend klingt. OK, fine.
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