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Archive of posts filed under the Bayesian Statistics category.

Post-election post

A favorite demonstration in statistics classes is to show a coin and ask what is the probability it comes up heads when flipped. Students will correctly reply 1/2. You then flip the coin high into the air, catch it, slap it on your wrist, look at it, and cover it up again with your hand. […]

So, what’s with that claim that Biden has a 96% chance of winning? (some thoughts with Josh Miller)

As indicated above, our model gives Joe Biden a 99+% chance of receiving more votes than Donald Trump and a 96% chance of winning in the electoral college. Michael Wiebe wrote in to ask: Your Economist model currently says that Biden has a 96% chance of winning the electoral college. How should we think about […]

Merlin and me talk on the Bayesian podcast about forecasting the election

Alex Androrra interviewed us, and I guess it makes sense to post the link before the election is over. A couple months ago, Alex interviewed Jennifer, Aki, and me to talk about our book, Regression and Other Stories. I can’t figure out how to directly link to that; you’ll have to follow the above link, […]

Concerns with our Economist election forecast

A few days ago we discussed some concerns with Fivethirtyeight’s election forecast. This got us thinking again about some concerns with our own forecast for The Economist (see here for more details). Here are some of our concerns with our forecast: 1. Distribution of the tails of the national vote forecast 2. Uncertainties of state […]

Prediction markets and election forecasts

Zev Berger writes: The question sounds snarky, but it’s not meant in that vein. It’s instructive to hear how modelers understand the predictions of their models, which is something I am still trying to think through. Your model has the chance of Biden being elected at 0.95. Predictit has Biden at 0.60. Given the spread, […]

Postdoc in Ann Arbor to work with clinical and cohort studies!

Jon Zelner writes: The EpiBayes research group, led by Dr. Jon Zelner in the Dept. of Epidemiology and Center for Social Epidemiology and Population Health (CSEPH) at the University of Michigan School of Public Health seeks a postdoctoral fellow to work with us on several projects relating to the transmission of SARS-CoV-2 and Influenza and […]

Birthday data!

Someone asked us for the birthday data, and Aki replied: We used 1969-1989 also in BDA3 And there we mention that the birthday data come from the National Vital Statistics System natality data and are at, provided by Robert Kern using Google BigQuery. The code for the BDA3 example is at (with […]

Reverse-engineering the problematic tail behavior of the Fivethirtyeight presidential election forecast

We’ve been writing a bit about some odd tail behavior in the Fivethirtyeight election forecast, for example that it was giving Joe Biden a 3% chance of winning Alabama (which seemed high), it was displaying Trump winning California as in “the range of scenarios our model thinks is possible” (which didn’t seem right), and it […]

Interactive analysis needs theories of inference

Jessica Hullman and I wrote an article that begins, Computer science research has produced increasingly sophisticated software interfaces for interactive and exploratory analysis, optimized for easy pattern finding and data exposure. But assuming that identifying what’s in the data is the end goal of analysis misrepresents strong connections between exploratory and confirmatory analysis and contributes […]

“Model takes many hours to fit and chains don’t converge”: What to do? My advice on first steps.

The above question came up on the Stan forums, and I replied: Hi, just to give some generic advice here, I suggest simulating fake data from your model and then fitting the model and seeing if you can recover the parameters. Since it’s taking a long time to run, I suggest just running your 4 […]

Calibration problem in tails of our election forecast

Following up on the last paragraph of this discussion, Elliott looked at the calibration of our state-level election forecasts, fitting our model retroactively to data from the 2008, 2012, and 2016 presidential elections. The plot above shows the point prediction and election outcome for the 50 states in each election, showing in red the states […]

Stan’s Within-Chain Parallelization now available with brms

The just released R package brms version 2.14.0 supports within-chain parallelization of Stan. This new functionality is based on the recently introduced reduce_sum function in Stan, which allows to evaluate sums over (conditionally) independent log-likelihood terms in parallel, using multiple CPU cores at the same time via threading. The idea of reduce_sum is to exploit […]

More on martingale property of probabilistic forecasts and some other issues with our election model

Edward Yu writes: I’m wondering if you’ve seen Nassim Taleb’s article arguing that we should price election forecasts as binary options. You seem to be generally fine with this approach, as when Nate Silver asked your colleague: On the off-chance our respective employers would allow it, which they almost certainly wouldn’t in my case, could […]

They’re looking for Stan and R programmers, and they’re willing to pay.

Tom Vladeck writes: I am one half of a company building a media mix model, primarily for online e-commerce brands. Our modeling is done in Stan, and we are looking to hire part time developers (paid, of course, at a real rate) to build and maintain our Stan models and R code. They can be […]

Postdoc in Bayesian spatiotemporal modeling at Imperial College London!

Seth Flaxman writes: We are hiring a postdoctoral research associate with a background in statistics or computer science to join a vibrant team at the cutting edge of the emerging field of spatiotemporal statistical machine learning (ST-SML). ST-SML draws in equal parts on Bayesian spatiotemporal statistics, scalable kernel methods and Gaussian processes, and recent deep […]

Election Scenario Explorer using Economist Election Model

Ric Fernholz writes: I wanted to tell you about a new website I built together with my brother Dan. The 2020 Election Scenario Explorer allows you to explore how electoral outcomes in individual states influence the national election outlook using data from your election model. The map and tables on our site reveal some interesting […]

Election forecasts: The math, the goals, and the incentives (my talk this Friday afternoon at Cornell University)

At the Colloquium for the Center for Applied Mathematics, Fri 18 Sep 3:30pm: Election forecasts: The math, the goals, and the incentives Election forecasting has increased in popularity and sophistication over the past few decades and has moved from being a hobby of some political scientists and economists to a major effort in the news […]

Information, incentives, and goals in election forecasts

Jessica Hullman, Christopher Wlezien, and I write: Presidential elections can be forecast using information from political and economic conditions, polls, and a statistical model of changes in public opinion over time. We discuss challenges in understanding, communicating, and evaluating election predictions, using as examples the Economist and Fivethirtyeight forecasts of the 2020 election. Here are […]

Post-stratified longitudinal item response model for trust in state institutions in Europe

This is a guest post by Marta Kołczyńska: Paul, Lauren, Aki, and I (Marta) wrote a preprint where we estimate trends in political trust in European countries between 1989 and 2019 based on cross-national survey data. This paper started from the following question: How to estimate country-year levels of political trust with data from surveys […]

Problem of the between-state correlations in the Fivethirtyeight election forecast

Elliott writes: I think we’re onto something with the low between-state correlations [see item 1 of our earlier post]. Someone sent me this collage of maps from Nate’s model that show: – Biden winning every state except NJ – Biden winning LA and MS but not MI and WI – Biden losing OR but winning […]