Archive of posts filed under the Bayesian Statistics category.

## Static sensitivity analysis: Computing robustness of Bayesian inferences to the choice of hyperparameters

Ryan Giordano wrote: Last year at StanCon we talked about how you can differentiate under the integral to automatically calculate quantitative hyperparameter robustness for Bayesian posteriors. Since then, I’ve packaged the idea up into an R library that plays nice with Stan. You can install it from this github repo. I’m sure you’ll be pretty […]

## A Python program for multivariate missing-data imputation that works on large datasets!?

Alex Stenlake and Ranjit Lall write about a program they wrote for imputing missing data: Strategies for analyzing missing data have become increasingly sophisticated in recent years, most notably with the growing popularity of the best-practice technique of multiple imputation. However, existing algorithms for implementing multiple imputation suffer from limited computational efficiency, scalability, and capacity […]

## Three new domain-specific (embedded) languages with a Stan backend

One is an accident. Two is a coincidence. Three is a pattern. Perhaps it’s no coincidence that there are three new interfaces that use Stan’s C++ implementation of adaptive Hamiltonian Monte Carlo (currently an updated version of the no-U-turn sampler). ScalaStan embeds a Stan-like language in Scala. It’s a Scala package largely (if not entirely […]

## How does probabilistic computation differ in physics and statistics?

[image of Schrodinger’s cat, of course] Stan collaborator Michael Betancourt wrote an article, “The Convergence of Markov chain Monte Carlo Methods: From the Metropolis method to Hamiltonian Monte Carlo,” discussing how various ideas of computational probability moved from physics to statistics. Three things I wanted to add to Betancourt’s story: 1. My paper with Rubin […]

## Stopping rules and Bayesian analysis

This is an old one but i think there still may be interest in the topic. In this post, I explain how to think about stopping rules in Bayesian inference and why, from a Bayesian standpoint, it’s not cheating to run an experiment until you get statistical significance and then stop. If the topic interests […]

## “Handling Multiplicity in Neuroimaging through Bayesian Lenses with Hierarchical Modeling”

Donald Williams points us to this new paper by Gang Chen, Yaqiong Xiao, Paul Taylor, Tracy Riggins, Fengji Geng, Elizabeth Redcay, and Robert Cox: In neuroimaging, the multiplicity issue may sneak into data analysis through several channels . . . One widely recognized aspect of multiplicity, multiple testing, occurs when the investigator fits a separate […]

## The failure of null hypothesis significance testing when studying incremental changes, and what to do about it

A few months ago I wrote a post, “Cage match: Null-hypothesis-significance-testing meets incrementalism. Nobody comes out alive.” I soon after turned it into an article, published in Personality and Social Psychology Bulletin, with the title given above and the following abstract: A standard mode of inference in social and behavioral science is to establish stylized […]

## Setting up a prior distribution in an experimental analysis

Baruch Eitam writes: My colleague and I have gotten into a slight dispute about prior selection. Below are our 3 different opinions, the first is the uniform (will get to that in a sec) and the other two are the priors of dispute. The parameter we are trying to estimate is people’s reporting ability under […]

## R-squared for Bayesian regression models

Ben, Jonah, Imad, and I write: The usual definition of R-squared (variance of the predicted values divided by the variance of the data) has a problem for Bayesian fits, as the numerator can be larger than the denominator. We propose an alternative definition similar to one that has appeared in the survival analysis literature: the […]

## We need to stop sacrificing women on the altar of deeply mediocre men (ISBA edition)

(This is not Andrew. I would ask you not to speculate in the comments who S is, this is not a great venue for that.) Kristian Lum just published an essay about her experiences being sexually assaulted at statistics conferences.  You should read the whole thing because it’s important, but there’s a sample paragraph. I […]

## The Night Riders

Gilbert Chin writes: After reading this piece [“How one 19-year-old Illinois man Is distorting national polling averages,” by Nate Cohn] and this Nature news story [“Seeing deadly mutations in an new light,” by Erika Hayden], I wonder if you might consider blogging about how this appears to be the same issue in two different disciplines. […]

## Ed Jaynes outta control!

A commmenter points to a chapter of E. T. Jaynes’s book on probability and inference that contains the following amazing bit: The information we get from the TV evening news is not that a certain event actually happened in a certain way it is that some news reporter has claimed that it did. Even seeing […]

## Always crashing in the same car

“Hey, remember me?  I’ve been busy working like crazy” – Fever Ray I’m at the Banff International Research Station (BIRS) for the week, which is basically a Canadian version of Disneyland where during coffee breaks a Canadian woman with a rake politely walks around telling elk to “shoo”. The topic of this week’s workshop isn’t […]

## “Little Data” etc.: My talk at NYU this Friday, 8 Dec 2017

I’ll be talking at the NYU business school, in the department of information, operations, and management sciences, this Fri, 8 Dec 2017, at 12:30, in room KMC 4-90 (wherever that is): Little Data: How Traditional Statistical Ideas Remain Relevant in a Big-Data World; or, The Statistical Crisis in Science; or, Open Problems in Bayesian Data […]

## Oooh, I hate all talk of false positive, false negative, false discovery, etc.

A correspondent writes: I think this short post on p value, bayes, and false discovery rate contains some misinterpretations. My reply: Oooh, I hate all talk of false positive, false negative, false discovery, etc. I posted this not because I care about someone, somewhere, being “wrong on the internet.” Rather, I just think there’s so […]

## Computational and statistical issues with uniform interval priors

There are two anti-patterns* for prior specification in Stan programs that can be sourced directly to idioms developed for BUGS. One is the diffuse gamma priors that Andrew’s already written about at length. The second is interval-based priors. Which brings us to today’s post. Interval priors An interval prior is something like this in Stan […]

## Asymptotically we are all dead (Thoughts about the Bernstein-von Mises theorem before and after a Diamanda Galás concert)

They say I did something bad, then why’s it feel so good–Taylor Swift It’s a Sunday afternoon and I’m trying to work myself up to the sort of emotional fortitude where I can survive the Diamanda Galás concert that I was super excited about a few months ago, but now, as I stare down the […]

## Poisoning the well with a within-person design? What’s the risk?

I was thinking more about our recommendation that psychology researchers routinely use within-person rather than between-person designs. The quick story is that a within-person design is more statistically efficient because, when you compare measurements within a person, you should get less variation than when you compare different groups. But researchers often use between-person designs out […]

## Using output from a fitted machine learning algorithm as a predictor in a statistical model

Fred Gruber writes: I attended your talk at Harvard where, regarding the question on how to deal with complex models (trees, neural networks, etc) you mentioned the idea of taking the output of these models and fitting a multilevel regression model. Is there a paper you could refer me to where I can read about […]

## Stan is a probabilistic programming language

See here: Stan: A Probabilistic Programming Language. Journal of Statistical Software. (Bob Carpenter, Andrew Gelman, Matthew D. Hoffman, Daniel Lee, Ben Goodrich, Michael Betancourt, Marcus Brubaker, Jiqiang Guo, Peter Li, Allen Riddell) And here: Stan is Turing Complete. So what? (Bob Carpenter) And, the pre-stan version: Fully Bayesian computing. (Jouni Kerman and Andrew Gelman) Apparently […]