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Archive of posts filed under the Bayesian Statistics category.

“We’ve got to look at the analyses, the real granular data. It’s always tough when you’re looking at a press release to figure out what’s going on.”

Chris Arderne writes: Surprised to see you hadn’t yet discussed the Oxford/AstraZeneca 60%/90% story on the blog. They accidentally changed the dose for some patients without an hypothesis, saw that it worked out better and are now (sort of) claiming 90% as a result… Sounds like your kind of investigation? I hadn’t heard about this […]

2 PhD student positions on Bayesian workflow! With Paul Bürkner!

Paul Bürkner writes: The newly established work group for Bayesian Statistics of Dr. Paul-Christian Bürkner at the Cluster of Excellence SimTech, University of Stuttgart (Germany), is looking for 2 PhD students to work on Bayesian workflow and Stan-related topics. The positions are fully funded for at least 3 years and people with a Master’s degree […]

Mister P for the 2020 presidential election in Belarus

An anonymous group of authors writes: Political situation Belarus is often called the “last dictatorship” in Europe. Rightly so, Aliaskandr Lukashenka has served as the country’s president since 1994. In the 26 years of his rule, Lukashenka has consolidated and extended his power, which is today absolute. Rigging referendums has been an effective means of […]

Nonparametric Bayes webinar

This post is by Eric. A few months ago we started running monthly webinars focusing on Bayes and uncertainty. Next week, we will be hosting Arman Oganisian, a 5th-year biostatistics PhD candidate at the University of Pennsylvania and Associate Fellow at the Leonard Davis Institute for Health Economics. His research focuses on developing Bayesian nonparametric […]

You don’t need a retina specialist to know which way the wind blows

Jayakrishna Ambati writes: I am a retina specialist and vision scientist at the University of Virginia. I am writing to you with a question on Bayesian statistics. I am performing a meta analysis of 5 clinical studies. In addition to a random effects meta analysis model, I am running Bayesian meta analysis models using half […]

How to describe Pfizer’s beta(0.7, 1) prior on vaccine effect?

Now it’s time for some statistical semantics. Specifically, how do we describe the prior that Pfizer is using for their COVID-19 study? Here’s a link to the report. A PHASE 1/2/3, PLACEBO-CONTROLLED, RANDOMIZED, OBSERVER-BLIND, DOSE-FINDING STUDY TO EVALUATE THE SAFETY, TOLERABILITY, IMMUNOGENICITY, AND EFFICACY OF SARS-COV-2 RNA VACCINE CANDIDATES AGAINST COVID-19 IN HEALTHY INDIVIDUALS Way […]

Bayesian Workflow

Aki Vehtari, Daniel Simpson, Charles C. Margossian, Bob Carpenter, Yuling Yao, Paul-Christian Bürkner, Lauren Kennedy, Jonah Gabry, Martin Modrák, and I write: The Bayesian approach to data analysis provides a powerful way to handle uncertainty in all observations, model parameters, and model structure using probability theory. Probabilistic programming languages make it easier to specify and […]

What would would mean to really take seriously the idea that our forecast probabilities were too far from 50%?

Here’s something I’ve been chewing on that I’m still working through. Suppose our forecast in a certain state is that candidate X will win 0.52 of the two-party vote, with a forecast standard deviation of 0.02. Suppose also that the forecast has a normal distribution. (We’ve talked about the possible advantages of long-tailed forecasts, but […]

Here’s why rot13 text looks so cool.

To avoid spoilers, I posted some text in rot13: V yvxrq gung ovg arne gur ortvaavat jurer Qnavry Penvt gnyxrq nobhg tbvat gb gur raq bs gur envaobj jurer gurer vf gehgu, naq gura jnvgvat sbe gur riragf bs gur fgbel gb trg gurer. Guvf frrzf gb zr gb qrfpevor n ybg bs jung erfrnepu […]

Don’t kid yourself. The polls messed up—and that would be the case even if we’d forecasted Biden losing Florida and only barely winning the electoral college

To continue our post-voting, pre-vote-counting assessment (see also here and here), I want to separate two issues which can get conflated:

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 […]