Statistical Modeling, Causal Inference, and Social Science

Poststratification uses population data on X to estimate E(Y) via E(E(Y | X, R = 1)), where R = 1 are survey respondents who provide Y and X. When the inner expectation “E” is estimated via Multilevel Regression, this is called MRP. The outer “E” needs p(X), population data on X. Sometimes we have to estimate the population distributions. We’ve seen a few examples: “2 flavors of calibration”: Say we have p(X), but we also need p(Z | X), the population distribution of another variable Z. We can…

Joshua Brooks writes: I know you’ve posted on the topic more generally but don’t recall if you’ve discussed this in particular. Given the timing in relation to cuts in food assistance, It seems a particularly egregious example of the politicization of data. The news article, published in late 2025 by an organization called Food Tank (“The Think Tank for Food”) is titled, USDA Ends Key Food Security Report, Leaving Advocates in the Dark, and it begins: The U.S. Department of Agriculture (USDA)…

In a post entitled, “You’re Writing a Book. So Stop Writing a Movie,” Rebecca Makkai writes: You want to set your movie in a futuristic New York where every building has a flying car port on top and there are highways through the air and half the people are genetically modified to be 7 feet tall and the sky is red and everyone’s left hand is a phone and all the police are robots? Cool—that will take you all of about ten seconds to get across onscreen. You want to do all that stuff on the page?…

This is quite possibly the stupidest thing in the Epstein files. Lord knows there’s lots of competition from the likes of Soon-Yi “Woody” Allen, Larry “Lawrence” Summers, Nathan “Clippy” Myhrvold, and Columbia’s own Richard “Axel” Foley, but I think this one takes the cake. In honor of another Epstein associate (see here), I’ll frame it as a “Linda problem”: Vilayanur is 74 years old, outspoken, and very bright. She majored in neuroscience. As an adult, he was deeply concerned with issues of…

Tom Ferguson came across this news article, Who Really Has the 2026 Midterms Cash Edge?, and was disappointed to see this completely wrong graph: The problem here is not the inclusion of no-longer-candidate Platner, as that’s noted in a footnote. Rather, as Ferguson says, The Times shows Platner outraising Collins; whereas she is millions and millions of dollars ahead, as our charts show. Here’s the chart that Ferguson shared with us the other day: If Collins raised $39 million, why did the…

I came across this webpage by Sheeva Azma entitled, “Here’s every scientist I have found in the Epstein Files so far.” She’s missing a few big fish: Dan Ariely (professor at MIT and Duke, Ted talk star, and teller of a story about a possibly nonexistent paper shredder) Donald Rubin (professor at Harvard and one of the most influential statisticians of the twentieth century) Stephen Hawking (late physicist and culture hero) Henry Rosovsky (professor and dean at Harvard; ok, he’s just an…

I recently learned from a blog comment that Herman Chernoff passed away last week at the age of 103. He was born the same year as my dad. I first met Chernoff–it’s not like he was a particularly formal guy, but I can’t imagine calling him “Herman”–when I was a student at MIT. I’d taken a statistics course and really liked it, and I wanted to know what class to take next. The instructor, Stephan Morgenthaler, recommended I ask Chernoff, who in turn told me that MIT didn’t have much to offer in…

Roughly speaking, Bayesian Workflow is to Bayesian Data Analysis in 2026 what Bayesian Data Analysis was to earlier Bayesian books in 1995: it builds upon everything that came before. With Bayesian Data Analysis, the big steps forward were: Going beyond Bayesian inference to also consider Bayesian model building (as a researcher, you construct the model, it isn’t just given to you as in a textbook), model checking (breaking through the absolutely horrible attitude, common to Bayesians in the…

Evan Rosenman writes: The implosion of Graham Platner’s Senate campaign in Maine has upended a marquee Senate race, leaving the state Democratic party just a few weeks to choose a substitute nominee. A planned nominating convention on July 25th has drawn considerable candidate interest. But the mathematical properties of ranked choice voting add a strange wrinkle to these deliberations. The Maine Democratic Gubernatorial Primary Three of the top contenders to replace Platner are former…

We’ve talked about uncertainty in polls (see Margin of Error, Total Margin of Error, Total Margin of Error II) and we’ve talked about ranked data (see exploded logit !). A new paper, Rosenman & Liang 2026, looks at uncertainty in ranked choice voting (RCV) polls. Recall the multinomial logit model that Train (2009) Chapter 7 calls the exploded logit: P[ranking Other then Left then Right] = exp(f_Other) / sum_c’ exp(f_c’) * exp(f_Left) / (exp(f_Left) + exp(f_Right)) Without covariates, it has…

I took a look at the above-titled book by economists Duncan Foley and Ellis Scharfenaker. It’s an interesting read, in many ways a throwback to the 1950s when a group of mathematicians brewed a heady mix of operations research, game theory, probability theory, and economics in an attempt to create a unified theory of social science, or to map the limitations of this effort. Important figures in this effort include John Maynard Keynes, John Von Neumann, Jimmie Savage, Milton Friedman, Duncan…

The following came in the email the other day: I’m reaching out to introduce the Voter Impact Index, a new data tool from PowerMoves that assigns every U.S. zip code a voter impact score based on the recent competitiveness of six federal and state elections tied to that location. The Index may be useful in your teaching or research in a few concrete ways: — Classroom discussions on political geography, voter mobilization, and the relationship between where people live and how much their votes…

Apropos of our recent discussion on the estimation of historical population sizes, Sean Manning writes: Some archaeologists have measured house sizes for Gini-coefficient-style studies aside from studying human remains to measure nutrition and rates of illness. I think that was what Michael E. Smith meant when he talked about hypothetical data: “archaeology can’t give social scientists population or GDP, but here are some things we can measure that might be useful for social science.” I asked…

In an abstract entitled, “Statistical dust and sweeping claims about maternal warmth,” John Richters and Everett Waters write: Alley and colleagues draw on mediation analyses of longitudinal data from Millennium Cohort Study to argue that their findings “highlight the critically important role that childhood maternal warmth plays in shaping mental and physical health into late adolescence” (p. 716), and “suggest public health interventions aimed at increasing maternal warmth “may be…

I was cc-ed on a message sent by 18 members of the board of the journal Statistics and Computing, quitting their posts because the publisher (Springer) has announced a new policy whereby all authors will have to pay publication charges. The soon-to-be-former associate editors write, “Statistics and Computing will no longer publish the best science, both due to financial exclusion of those researchers who cannot afford to pay, and those community-minded researchers who refuse to pay on…

Retraction Watch reports: A Canadian journal has issued corrections on 138 case reports it published over the last 25 years to add a disclaimer: The cases described are fictional. Paediatrics & Child Health, the journal of the Canadian Paediatric Society, has published the cases since 2000 in articles for a series for its Canadian Paediatric Surveillance Program. The articles usually start with a case description followed by “learning points” that include statistics, clinical observations and…

Andy King writes: I have a question for you–and, if you think it worthwhile, for your readers. A few weeks ago, I was deposed by Harvard’s lawyers in the lawsuit between Francesca Gino and Harvard. Much of the questioning focused on my replications of research by Harvard Business School professor George Serafeim and my allegations of research misconduct against him and his coauthors. That experience has led to a lively online debate about two questions: 1. Is fabricating data worse than…

Last week we talked about The Big Changes Coming to the Times/Siena Poll: New weighting variable: support score = E(2024 vote | other X variables). New weighting method: energy balancing (Huling & Mak, 2024) Ben Schneider helpfully blogged about energy balancing as well: Raking and similar calibration methods are based on balancing means or totals for specific variables…The energy balancing method does something different: it calibrates based on an entire multivariate distribution, as measured…

This post is from Bob The sausage So as not to bury the lead (or “lede” if you want a mid-20th-century newspaper vibe), check out the this 3D HMC animation generator. It can render regular animations or produce anaglyph 3D encoding (red/blue). Unless you have 3D glasses, unclick the “Anaglyph 3D” checkbox at the bottom of the upper left corner control box. The app let you zoom in and rotate the visualization with obvious controls (explanation in the footer of the visualization). The app also…

Dear Dr. Tavris: I saw in a recent issue of the Times Literary Supplement that you have been critical of the “chambermaid” study which purported to show that people were losing weight without changing their diet or exercise. I agree that this study did not show what it claimed. Along these lines, you might be interested in two articles I recently published with Nicholas Brown: – How statistical challenges and misreadings of the literature combineto produce unreplicable science: An example from…

Qin Huang, Moyan Liu, and Upmanu Lall write: Extreme weather events, e.g., droughts, floods, heatwaves, and freezes, are increasing in frequency and intensity, posing severe socio-economic impacts as growing populations heighten exposure to risks that conventional infrastructure cannot fully address. We propose supplementing disaster management with Weather Jiu-Jitsu: a strategy that exploits the chaotic sensitivity of mid-latitude atmospheric dynamics to redirect destructive weather…

This came in the email from the U.S. National Institutes of Health: How Would You Measure and Reward Scientific Impact and Replicable Research Practices? As NIH continues efforts to strengthen rigor, reproducibility, and public trust in science, we are seeking input from the research community on an important question: Are we measuring and rewarding the activities that matter most for advancing biomedical discovery? NIH wants to hear your perspectives on how scientific impact and rigorous…

So, I came across this news article titled, “Riley Thinks Suits Make the Coach. Research Says He Might Be Right.”: The suit had a classic name: the Clark Gable. Navy blue and cut just right, it was the creation of Giorgio Armani, the legendary Italian designer. It was the piece that made Pat Riley, the legendary NBA coach and executive, believe in the power of style. . . . “I think an audience wants to see somebody on the sidelines who looks like a leader, dresses like a leader, acts like a…

Andy King writes: 𝗪𝗵𝘆 𝗛𝗮𝗿𝘃𝗮𝗿𝗱’𝘀 𝗹𝗮𝘄𝘆𝗲𝗿𝘀 𝘀𝘂𝗯𝗽𝗼𝗲𝗻𝗮𝗲𝗱 𝗺𝗲 𝗶𝗻 𝘁𝗵𝗲 𝗙𝗿𝗮𝗻𝗰𝗲𝘀𝗰𝗮 𝗚𝗶𝗻𝗼 𝗰𝗮𝘀𝗲 My wife called to me. A constable was at the door. He handed me a subpoena to appear for a deposition in the case of Francesca Gino v. President and Fellows of Harvard College and Srikant Datar. The subpoena puzzled us. I don’t believe I’ve ever met Francesca Gino, and I am certainly not an expert on her case. Why not call me or email me with any questions? As directed, I arrived at the offices of Ropes & Gray,…

This post is by Bob. I’ve been thinking a lot lately about R-hat given that I’m using it for online converging monitoring in our new Walnuts implementation. In that setting, where I use Welford accumulators to update R-hat estimates every iteration, I can’t use split R-hat without way too much buffering. So I’ve been thinking about the effect of splitting, too, and whether we need it. I asked Andrew and he said Kenny Shirley once produced an example where split R-hat diagnosed non-convergence…

Just in time for July 4th, Tom Ferguson, Paul Jorgensen, Matthias Lalisse, and Jie Chen share the above graph and write: What can one Senate race reveal about the hidden machinery of American politics? In Maine, donor patterns expose how campaign finance can shape party competition, political narratives, and the choices voters are asked to make long before ballots are counted. . . . Platner is strongly supported by Senator Bernie Sanders and other progressives, while many establishment…

The above sketch shows a decision tree. The circles are uncertainty nodes and the squares are decision nodes. Read the tree from left to right: to start, there is uncertainty of which of the strata i=1,…,I you will be in. In any given stratum, you will have to decide between options 1 and 2, and for each of these decision options there is uncertainty about the payoff. The goals are: (a) Conditional on the stratum, pick the best decision. This is the local decision problem. (b) Averaging over…

Yesterday Nate Cohn wrote about The Big Changes Coming to the Times/Siena Poll, with more details in their poll of Maine. Say we want to estimate average Platner support in Maine’s likely electorate, E(Y). But we only have survey respondents, R = 1. The NYT uses survey weights to weight respondents, E(YW | R = 1). In contrast, some pollsters use MRP, fitting a Multilevel Regression model for Platner support, then applying it to the population, E(E_model(Y | X, R = 1)). Nate discusses 2 Big…

The former Arizona State University physicist reported in 2018 this advice from his “religious right wing law professor brother” [that’s Krauss’s description, not mine]: Therefore i think you should pursue a mixed strategy. On the one hand, you should non-aggressively, soberly, suggest that the groping allegation is exaggerated but likely the result of a good faith misunderstanding. At the same time you should acknowledge that all these accusations have woken you up. You had never fully…

OK, this one was funny. I searched the Epstein files for “statistician” and found this receipt from biologist Robert Trivers: Only $1000 for the statistician??? What a cheapskate! Especially given that he said the statistician “did an outstanding job.” Given all the statistical problems in evolutionary biology, maybe he should’ve allocated more of his research budget to the statistician. Some background on Trivers is here.