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1 andrew gelman stats-2013-12-31-No on Yes-No decisions

Introduction: Just to elaborate on our post from last month (“I’m negative on the expression ‘false positives’”), here’s a recent exchange exchange we had regarding the relevance of yes/no decisions in summarizing statistical inferences about scientific questions. Shravan wrote : Isn’t it true that I am already done if P(theta>0) is much larger than P(theta<0)? I don't need to compute any loss function if the former is 0.99 and the latter 0.01. In most studies of the type that people like me do [Shravan is a linguist], we set up experiments where we have a decisive test like this for theory A and against theory B. To which I replied : In some way the problem is with the focus on “theta.” Effects (and, more generally, comparisons) vary, they can be positive for some people in some settings and negative for other people in other settings. If you’re talking about a single “theta,” you have to define what population and what scenario you are thinking about. And it’s probably not the popul

2 andrew gelman stats-2013-12-30-Bill Gates’s favorite graph of the year

Introduction: Under the subject line “Blog bait!”, Brendan Nyhan points me to this post at the Washington Post blog: For 2013, we asked some of the year’s most interesting, important and influential thinkers to name their favorite graph of the year — and why they chose it. Here’s Bill Gates’s. Infographic by Thomas Porostocky for WIRED. “I love this graph because it shows that while the number of people dying from communicable diseases is still far too high, those numbers continue to come down. . . .” As Brendan is aware, this is not my favorite sort of graph, it’s a bit of a puzzle to read and figure out where all the pieces fit in, also weird stuff going on like 3-D effects and the big space taken up by those yellow and green borders, as well as tricky things like understanding what some of those little blocks are, and perhaps the biggest question, what is the definition of an “untimely death.” But, as often is the case, the defects of the graph form a statistical perspective can

3 andrew gelman stats-2013-12-29-“Statistics Done Wrong”

Introduction: Govind Manian points me to this online textbook by Alex Reinhart. It’s hard for me to evaluate because I am so close to the material. But on first glance it looks pretty reasonable to me.

4 andrew gelman stats-2013-12-28-Using randomized incentives as an instrument for survey nonresponse?

Introduction: I received the following question: Is there a classic paper on instrumenting for survey non-response? some colleagues in public health are going to carry out a survey and I wonder about suggesting that they build in a randomization of response-encouragement (e.g. offering additional $ to a subset of those who don’t respond initially). Can you recommend a basic treatment of this, and why it might or might not make sense compared to IPW using covariates (without an instrument)? My reply: Here’s the best analysis I know of on the effects of incentives for survey response. There have been several survey-experiments on the subject. The short answer is that the effect on nonresponse is small and the outcome is highly variable, hence you can’t very well use it as an instrument in any particular survey. My recommended approach to dealing with nonresponse is to use multilevel regression and poststratification; an example is here . Inverse-probability weighting doesn’t really w

5 andrew gelman stats-2013-12-27-Should statistics have a Nobel prize?

Introduction: Xiao-Li says yes: The most compelling reason for having highly visible awards in any field is to enhance its ability to attract future talent. Virtually all the media and public attention our profession received in recent years has been on the utility of statistics in all walks of life. We are extremely happy for and proud of this recognition—it is long overdue. However, the media and public have given much more attention to the Fields Medal than to the COPSS Award, even though the former has hardly been about direct or even indirect impact on everyday life. Why this difference? . . . these awards arouse media and public interest by featuring how ingenious the awardees are and how difficult the problems they solved, much like how conquering Everest bestows admiration not because the admirers care or even know much about Everest itself but because it represents the ultimate physical feat. In this sense, the biggest winner of the Fields Medal is mathematics itself: enticing the brig

6 andrew gelman stats-2013-12-27-(R-Py-Cmd)Stan 2.1.0

Introduction: We’re happy to announce the release of Stan C++, CmdStan, RStan, and PyStan 2.1.0. This is a minor feature release, but it is also an important bug fix release. As always, the place to start is the (all new) Stan web pages: http://mc-stan.org Major Bug in 2.0.0, 2.0.1 Stan 2.0.0 and Stan 2.0.1 introduced a bug in the implementation of the NUTS criterion that led to poor tail exploration and thus biased the posterior uncertainty downward. There was no bug in NUTS in Stan 1.3 or earlier, and 2.1 has been extensively tested and tests put in place so this problem will not recur. If you are using Stan 2.0.0 or 2.0.1, you should switch to 2.1.0 as soon as possible and rerun any models you care about. New Target Acceptance Rate Default for Stan 2.1.0 Another big change aimed at reducing posterior estimation bias was an increase in the target acceptance rate during adaptation from 0.65 to 0.80. The bad news is that iterations will take around 50% longer

7 andrew gelman stats-2013-12-26-Statistical evidence for revised standards

Introduction: In response to the discussion of X and me of his recent paper , Val Johnson writes: I would like to thank Andrew for forwarding his comments on uniformly most powerful Bayesian tests (UMPBTs) to me and his invitation to respond to them. I think he (and also Christian Robert) raise a number of interesting points concerning this new class of Bayesian tests, but I think that they may have confounded several issues that might more usefully be examined separately. The first issue involves the choice of the Bayesian evidence threshold, gamma, used in rejecting a null hypothesis in favor of an alternative hypothesis. Andrew objects to the higher values of gamma proposed in my recent PNAS article on grounds that too many important scientific effects would be missed if thresholds of 25-50 were routinely used. These evidence thresholds correspond roughly to p-values of 0.005; Andrew suggests that evidence thresholds around 5 should continue to be used (gamma=5 corresponds approximate

8 andrew gelman stats-2013-12-25-Spam!

Introduction: This one totally faked me out at first. It was an email from “Nick Bagnall” that began: Dear Dr. Gelman, I made contact last year regarding your work in the CMG: Reconstructing Climate from Tree Ring Data project. We are about to start producing the 2014 edition and I wanted to discuss this with you as we still remain keen to feature your work. Research Media are producing a special publication in February of 2014, within this report we will be working with a small selected number of PI’s with a focus on geosciences, atmospheric and geospace sciences and earth Sciences.. At this point, I’m thinking: Hmmm, I don’t remember this guy, is this some sort of collaborative project that I’d forgotten about? The message then continues: The publication is called International Innovation . . . Huh? This doesn’t sound so good. The email then goes on with some very long lists, and then finally the kicker: The total cost for each article produced in this report is fixed a

9 andrew gelman stats-2013-12-25-Measuring Beauty

Introduction: Anaface analysis of Michelangelo’s David I’ve come across a paper that was using “beauty” as one of the predictors. To measure beauty, the authors used Anaface.com I don’t trust metrics without trying them on a gold standard first. So, I tried how well Anaface does on something that the arts world considers as one of gold standards of beauty – Michelangelo’s David. My annotation might be imperfect, but David only gets to be only a good 7: his nose is too narrow and his eyes are too close. Of course, I applaud the use of interesting predictors in studies, and Anaface is a better tool than anything I’ve seen before, but maybe we need better metrics! What do you think?

10 andrew gelman stats-2013-12-24-NYT version of birthday graph

Introduction: They didn’t have room for all four graphs of the time-series decomposition so they just displayed the date-of-year graph: They rotated so the graph fit better on the page. The rotation worked for me, but I was a bit bummed that that they put the title and heading of the graph (“The birthrate tends to drop on holidays . . .”) on the left in the Mar-Apr slot, leaving no room to label Leap Day and April Fool’s. I suggested to the graphics people that they put the label at the very top and just shrink the rest of the graph by 5 or 10% so as to not take up any more total space. Then there’d be plenty of space to label Leap Day and April Fool’s. But they didn’t do it, maybe they felt that it wouldn’t look good to have the label right at the top, I dunno.

11 andrew gelman stats-2013-12-24-Estimating and summarizing inference for hierarchical variance parameters when the number of groups is small

Introduction: Chris Che-Castaldo writes: I am trying to compute variance components for a hierarchical model where the group level has two binary predictors and their interaction. When I model each of these three predictors as N(0, tau) the model will not converge, perhaps because the number of coefficients in each batch is so small (2 for the main effects and 4 for the interaction). Although I could simply leave all these as predictors as unmodeled fixed effects, the last sentence of section 21.2 on page 462 of Gelman and Hill (2007) suggests this would not be a wise course of action: For example, it is not clear how to define the (finite) standard deviation of variables that are included in interactions. I am curious – is there still no clear cut way to directly compute the finite standard deviation for binary unmodeled variables that are also part of an interaction as well as the interaction itself? My reply: I’d recommend including these in your model (it’s probably easiest to do so

12 andrew gelman stats-2013-12-23-I hate this stuff

Introduction: Aki pointed me to this article . I’m too exhausted to argue all this in detail yet one more time, but let me just say that I hate this stuff for the reasons given in Section 5 of this paper from 1998 (based on classroom activities from 1994). I’ve hated this stuff for a long time. And I don’t think Yitzhak likes it either; see this discussion from 2005 and this from 2009.

13 andrew gelman stats-2013-12-22-The kluges of today are the textbook solutions of tomorrow.

Introduction: From a response on the Stan help list: Yes, indeed, I think it would be a good idea to reduce the scale on priors of the form U(0,100) or N(0,100^2). This won’t solve all problems but it can’t hurt. If the issue is that the variance parameter can be very small in the estimation, yes, one approach would be to put in a prior that keeps the variance away from 0 (lognormal, gamma, whatever), another approach would be to use the Matt trick. Some mixture of these ideas might help. And, by the way: when you do these things it might feel like an awkward bit of kluging to play around with the model to get it to convert properly. But the kluges of today are the textbook solutions of tomorrow. When it comes to statistical modeling, we’re living in beta-test world; we should appreciate the opportunities this gives us!

14 andrew gelman stats-2013-12-21-Chasing the noise

Introduction: Fabio Rojas writes : After reading the Fowler/Christakis paper on networks and obesity , a student asked why it was that friends had a stronger influence on spouses. In other words, if we believe the F&C; paper, they report that your friends (57%) are more likely to transmit obesity than your spouse (37%) (see page 370). This might be interpreted in two ways. First, it might be seen as a counter argument. This might really indicate that homophily is at work. We probably select spouses for some traits that are not self-similar. While we choose friends mainly on self-similarity of leisure and consumption (e.g, diet and exercise). Second, there might be an explanation based on transmission. We choose friends because we want them to influence us, while spouses are (supposed?) to accept us. Your thoughts? My thought: No. No no no no no. No no no. No. From the linked paper: A person’s chances of becoming obese increased by 57% (95% confidence interval [CI], 6 to 123) if h

15 andrew gelman stats-2013-12-20-Don’t douthat, man! Please give this fallacy a name.

Introduction: Regular readers of this blog will know that I’m always on the lookout for new items for the lexicon . It’s been a good month on that front. In addition to the Garden of Forking Paths, I’ve encountered two entirely new (to me) fallacies. The first of the two new fallacies has a name that’s quite a mouthful; I’ll hold off on telling you about it right now, as Eric Loken and I are currently finishing a paper on it. Once the paper’s done, I’ll post it in the usual place (or here , once it is scheduled to be published) and I’ll add it to the lexicon as well. What I want to talk about today is a fallacy I noticed a couple days ago. I can’t think of a good name for it. And that’s where you, the readers, come in. Please give this fallacy a name! Here’s the story. The other day on the sister blog I reported on a pair of studies involving children and political orientation: Andrew Oswald and Nattavudh Powdthavee found that, in Great Britain, parents of girls were more likely

16 andrew gelman stats-2013-12-19-Revised evidence for statistical standards

Introduction: X and I heard about this much-publicized recent paper by Val Johnson, who suggests changing the default level of statistical significance from z=2 to z=3 (or, as he puts it, going from p=.05 to p=.005 or .001). Val argues that you need to go out to 3 standard errors to get a Bayes factor of 25 or 50 in favor of the alternative hypothesis. I don’t really buy this, first because Val’s model is a weird (to me) mixture of two point masses, which he creates in order to make a minimax argument, and second because I don’t see why you need a Bayes factor of 25 to 50 in order to make a claim. I’d think that a factor of 5:1, say, provides strong information already—if you really believe those odds. The real issue, as I see it, is that we’re getting Bayes factors and posterior probabilities we don’t believe, because we’re assuming flat priors that don’t really make sense. This is a topic that’s come up over and over in recent months on this blog, for example in this discussion of why I d

17 andrew gelman stats-2013-12-19-Happy birthday

Introduction: (Click for bigger image.) The above is Akiâ€™s decomposition of the birthdays data (the number of babies born each day in the United States, from 1968 through 1988) using a Gaussian process model, as described in more detail in our book .

18 andrew gelman stats-2013-12-18-In Memoriam Dennis Lindley

Introduction: So. Farewell then Dennis Lindley. You held the Hard line on Bayesianism When others Had doubts. And you share The name of a famous Paradox. What is your subjective Prior now? We can only Infer. R. A. Thribb (17 1/2) P.S.

19 andrew gelman stats-2013-12-17-Replication backlash

Introduction: Raghuveer Parthasarathy pointed me to an article in Nature by Mina Bissell, who writes , “The push to replicate findings could shelve promising research and unfairly damage the reputations of careful, meticulous scientists.” I can see where she’s coming from: if you work hard day after day in the lab, it’s gotta be a bit frustrating to find all your work questioned, for the frauds of the Dr. Anil Pottis and Diederik Stapels to be treated as a reason for everyone else’s work to be considered guilty until proven innocent. That said, I pretty much disagree with Bissell’s article, and really the best thing I can say about it is that I think it’s a good sign that the push for replication is so strong that now there’s a backlash against it. Traditionally, leading scientists have been able to simply ignore the push for replication. If they are feeling that the replication movement is strong enough that they need to fight it, that to me is good news. I’ll explain a bit in the conte

20 andrew gelman stats-2013-12-16-Whither the “bet on sparsity principle” in a nonsparse world?

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.