Bayesian data analysis, as my colleagues and I have formulated it, has a human in the loop. Here’s how we put it on the very first page of our book: The process of Bayesian data analysis can be idealized by dividing it into the following three steps: 1. Setting up a full probability model—a joint […]

**Bayesian Statistics**category.

## More on my paper with John Carlin on Type M and Type S errors

Deborah Mayo asked me some questions about that paper (“Beyond Power Calculations: Assessing Type S (Sign) and Type M (Magnitude) Errors”), and here’s how I responded: I am not happy with the concepts of “power,” “type 1 error,” and “type 2 error,” because all these are defined in terms of statistical significance, which I am […]

## Election forecasting updating error: We ignored correlations in some of our data, thus producing illusory precision in our inferences

The election outcome is a surprise in that it contradicts two pieces of information: Pre-election polls and early-voting tallies. We knew that each of these indicators could be flawed (polls because of differential nonresponse; early-voting tallies because of extrapolation errors), but when the two pieces of evidence came to the same conclusion, they gave us […]

## What if NC is a tie and FL is a close win for Clinton?

On the TV they said that they were guessing that Clinton would win Florida in a close race and that North Carolina was too close to call. Let’s run the numbers, Kremp: > update_prob2(clinton_normal=list(“NC”=c(50,2), “FL”=c(52,2))) Pr(Clinton wins the electoral college) = 95% That’s good news for Clinton. What if both states are tied? > update_prob2(clinton_normal=list(“NC”=c(50,2), […]

## Election updating software update

When going through the Pierre-Antoine Kremp’s election forecasting updater program, we saw that it ran into difficulties when we started to supply information from lots of states. It was a problem with the program’s rejection sampling algorithm. Kremp updated the program to allow an option where you could specify the winner in each state, and […]

## Now that 7pm has come, what do we know?

(followup to this post) On TV they said that Trump won Kentucky and Indiana (no surprise), Clinton won Vermont (really no surprise), but South Carolina, Georgia, and Virginia were too close to call. I’ll run Pierre-Antoine Kremp’s program conditioning on this information, coding states that are “too close to call” as being somewhere between 45% […]

## Updating the Forecast on Election Night with R

Pierre-Antoine Kremp made this cool widget that takes his open-source election forecaster (it aggregates state and national polls using a Stan program that runs from R) and computes conditional probabilities. Here’s the starting point, based on the pre-election polls and forecast information: These results come from the fitted Stan model which gives simulations representing a […]

## What is the chance that your vote will decide the election? Ask Stan!

I was impressed by Pierre-Antoine Kremp’s open-source poll aggregator and election forecaster (all in R and Stan with an automatic data feed!) so I wrote to Kremp: I was thinking it could be fun to compute probability of decisive vote by state, as in this paper. This can be done with some not difficult but […]

## Different election forecasts not so different

Yeah, I know, I need to work some on the clickbait titles . . . Anyway, people keep asking me why different election forecasts are so different. At the time of this writing, Nate Silver gives Clinton a 66.2% [ugh! See Pedants Corner below] chance of winning the election while Drew Linzer, for example, gives […]

## Why I prefer 50% rather than 95% intervals

I prefer 50% to 95% intervals for 3 reasons: 1. Computational stability, 2. More intuitive evaluation (half the 50% intervals should contain the true value), 3. A sense that in aplications itâ€™s best to get a sense of where the parameters and predicted values will be, not to attempt an unrealistic near-certainty. This came up […]

## Michael Betancourt has made NUTS even more awesome and efficient!

In an beautiful new paper, Betancourt writes: The geometric foundations of Hamiltonian Monte Carlo implicitly identify the optimal choice of [tuning] parameters, especially the integration time. I then consider the practical consequences of these principles in both existing algorithms and a new implementation called Exhaustive Hamiltonian Monte Carlo [XMC] before demonstrating the utility of these […]

## Some modeling and computational ideas to look into

Can we implement these in Stan? Marginally specified priors for non-parametric Bayesian estimation (by David Kessler, Peter Hoff, and David Dunson): Prior specification for non-parametric Bayesian inference involves the difficult task of quantifying prior knowledge about a parameter of high, often infinite, dimension. A statistician is unlikely to have informed opinions about all aspects of […]

## “The Warriors suck”: A Bayesian exploration

A basketball fan of my close acquaintance woke up Wednesday morning and, upon learning the outcome of the first games of the NBA season, announced that “The Warriors suck.” Can we answer this question? To put it more precisely, how much information is supplied by that first-game-of-season blowout? Speaking Bayesianly, who much should we adjust […]

## “Generic and consistent confidence and credible regions”

Christian Bartels sends along this paper, which begins: A generic, consistent, efficient and exact method is proposed for set selection. The method is generic in that its definition and implementation uses only the likelihood function. The method is consistent in that the same criterion is used to select confidence and credible sets making the two […]

## Yes, despite what you may have heard, you can easily fit hierarchical mixture models in Stan

There was some confusion on the Stan list that I wanted to clear up, having to do with fitting mixture models. Someone quoted this from John Kruschke’s book, Doing Bayesian Data Analysis: The lack of discrete parameters in Stan means that we cannot do model comparison as a hierarchical model with an indexical parameter at […]

## Practical Bayesian model evaluation in Stan and rstanarm using leave-one-out cross-validation

Our (Aki, Andrew and Jonah) paper Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC was recently published in Statistics and Computing. In the paper we show why it’s better to use LOO instead of WAIC for model evaluation how to compute LOO quickly and reliably using the full posterior sample how Pareto smoothing importance […]

## Avoiding model selection in Bayesian social research

One of my favorites, from 1995. Don Rubin and I argue with Adrian Raftery. Here’s how we begin: Raftery’s paper addresses two important problems in the statistical analysis of social science data: (1) choosing an appropriate model when so much data are available that standard P-values reject all parsimonious models; and (2) making estimates and […]