Following up on our discussions here and here of poststratified models of coronavirus risk, Jon Zelner writes: Here’s a paper [by Robert Verity et al.] that I think shows what could be done with an MRP approach. From the abstract: We used individual-case data from mainland China and cases detected outside mainland China to estimate […]

**Bayesian Statistics**category.

## Prior predictive, posterior predictive, and cross-validation as graphical models

I just wrote up a bunch of chapters for the Stan user’s guide on prior predictive checks, posterior predictive checks, cross-validation, decision analysis, poststratification (with the obligatory multilevel regression up front), and even bootstrap (which has a surprisingly elegant formulation in Stan now that we have RNGs in trnasformed data). Andrew then urged me to […]

## Coronavirus model update: Background, assumptions, and room for improvement

Julien Riou, coauthor of one of the models we discussed here, writes: Here is an overview of the current state of the project, so that it is easier for everyone to quickly grasp what is the potential room for improvement. Background on the epidemic: COVID-19 just passed 100,000 confirmed cases all over the world, and […]

## Coronavirus age-specific fatality ratio, estimated using Stan, and (attempting) to account for underreporting of cases and the time delay to death. Now with data and code. And now a link to another paper (also with data and code).

Julien Riou writes: Stan epidemiologist here. We actually just released a preprint [estimating death rates of people infected with coronavirus, breaking down the population by age and then poststratifying] using Stan (https://www.medrxiv.org/content/10.1101/2020.03.04.20031104v1). Crude estimates of case fatality ratio obtained by dividing observed deaths by observed cases are biased in two ways: 1) Deaths are underestimated […]

## Conditioning on a statistical method as a “meta” version of conditioning on a statistical model

When I do applied statistics, I follow Bayesian workflow: Construct a model, ride it hard, assess its implications, add more information, and so on. I have lots of doubt in my models, but when I’m fitting any particular model, I condition on it. The idea is we take our models seriously as that’s the best […]

## The Great Society, Reagan’s revolution, and generations of presidential voting

> Continuing our walk through the unpublished papers list: This one’s with Yair and Jonathan: We build a model of American presidential voting in which the cumulative impression left by political events determines the preferences of voters. This impression varies by voter, depending on their age at the time the events took place. We find […]

## What can we do with complex numbers in Stan?

I’m wrapping up support for complex number types in the Stan math library. Now I’m wondering what we can do with complex numbers in statistical models. Functions operating in the complex domain The initial plan is to add some matrix functions that use complex numbers internally: fast fourier transforms asymmetric eigendecomposition Schur decomposition The eigendecomposition […]

## How to embrace variation and accept uncertainty in linguistic and psycholinguistic data analysis

I don’t have much to say about this one, as Shravan wrote pretty much all of it. It’s a study of how to apply our general advice to “accept uncertainty,” in a specific area of research in linguistics:

## Deep learning workflow

Ido Rosen points us to this interesting and detailed post by Andrej Karpathy, “A Recipe for Training Neural Networks.” It reminds me a lot of various things that Bob Carpenter has said regarding the way that some fitting algorithms are often oversold because the presenters don’t explain the tuning that was required to get good […]

## Rank-normalization, folding, and localization: An improved R-hat for assessing convergence of MCMC

With Aki, Dan, Bob, and Paul: Markov chain Monte Carlo is a key computational tool in Bayesian statistics, but it can be challenging to monitor the convergence of an iterative stochastic algorithm. In this paper we show that the convergence diagnostic R-hat of Gelman and Rubin (1992) has serious flaws. R-hat will fail to correctly […]

## Holes in Bayesian Statistics

With Yuling: Every philosophy has holes, and it is the responsibility of proponents of a philosophy to point out these problems. Here are a few holes in Bayesian data analysis: (1) the usual rules of conditional probability fail in the quantum realm, (2) flat or weak priors lead to terrible inferences about things we care […]

## How good is the Bayes posterior for prediction really?

It might not be common courtesy of this blog to make comments on a very-recently-arxiv-ed paper. But I have seen two copies of this paper entitled “how good is the Bayes posterior in deep neural networks really” left on the tray of the department printer during the past weekend, so I cannot underestimate the popularity of […]

## MRP Conference at Columbia April 3rd – April 4th 2020

The Departments of Statistics and Political Science and Institute for Social and Economic Research and Policy at Columbia University are delighted to invite you to our Spring conference on Multilevel Regression and Poststratification. Featuring Andrew Gelman, Beth Tipton, Jon Zelner, Shira Mitchell, Qixuan Chen and Leontine Alkema, the conference will combine a mix of cutting […]

## Abuse of expectation notation

I’ve been reading a lot of statistical and computational literature and it seems like expectation notation is absued as shorthand for integrals by decorating the expectation symbol with a subscripted distribution like so: This is super confusing, because expectations are properly defined as functions of random variables. For example, the square bracket convention arises because […]

## Fugitive and cloistered virtues

There’s a new revolution, a loud evolution that I saw. Born of confusion and quiet collusion of which mostly I’ve known. — Lana Del Ray While an unexamined life seems like an excellent idea, an unexamined prior distribution probably isn’t. And, I mean, I write and talk and think and talk and write and talk and talk and […]

## Forget about multiple testing corrections. Actually, forget about hypothesis testing entirely.

Tai Huang writes: I am reading this paper [Why we (usually) don’t have to worry about multiple comparisons, by Jennifer, Masanao, and myself]. I am searching how to do multiple comparisons correctly under Bayesian inference for A/B/C testing. For the traditional t-test approach, Bonferroni correction is needed to correct alpha value. I am confused with […]

## Rao-Blackwellization and discrete parameters in Stan

I’m reading a really dense and beautifully written survey of Monte Carlo gradient estimation for machine learning by Shakir Mohamed, Mihaela Rosca, Michael Figurnov, and Andriy Mnih. There are great explanations of everything including variance reduction techniques like coupling, control variates, and Rao-Blackwellization. The latter’s the topic of today’s post, as it relates directly to […]

## Causal inference in AI: Expressing potential outcomes in a graphical-modeling framework that can be fit using Stan

David Rohde writes: We have been working on an idea that attempts to combine ideas from Bayesian approaches to causality developed by you and your collaborators with Pearl’s do calculus. The core idea is simple, but we think powerful and allows some problems previously that only had known solutions with the do calculus to be […]

## In Bayesian inference, do people cheat by rigging the prior?

Ulrich Atz writes in with a question: A newcomer to Bayesian inference may argue that priors seem sooo subjective and can lead to any answer. There are many counter-arguments (e.g., it’s easier to cheat in other ways), but are there any pithy examples where scientists have abused the prior to get to the result they […]

## Steven Pinker on torture

I’ve recently been thinking about that expression, “A liberal is a conservative who’s been arrested.” Linguist and public intellectual Steven Pinker got into some trouble recently when it turned out that he’d been offering expert advice to the legal team of now-disgraced financier Jeffrey Epstein. I would not condemn Pinker for this. After all, everybody […]