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 methods for solving complicated estimation problems that arise in causal inference. His application areas of interest include health economics and, more recently, cancer therapies.

**Abstract**

Bayesian nonparametrics combines the flexibility often associated with machine learning with principled uncertainty quantification required for inference. Popular priors in this class include Gaussian Processes, Bayesian Additive Regression Trees, Chinese Restaurant Processes, and more. But what exactly are “nonparametric” priors? How can we compute posteriors under such priors? And how can we use them for flexible modeling? This talk will explore these questions by introducing nonparametric Bayes at a conceptual level and walking through a few common priors, with a particular focus on the Dirichlet Process prior for regression.

If this sounds interesting to you, please join us this Wednesday, 18 November at 12 noon ET.

P.S. Last month we had Matthew Kay from Northwestern University discussing his research on visualizing and communicating uncertainty. Here is the link to the video.

I must admit, I have no idea what this is. How can a Bayesian analysis be non-parametric? Perhaps the distributions, prior or posterior, might not be standard easily quantifiable distributions but it seems to me that if you want to do anything with the Bayesian model you have to take whatever distribution you end up with, or start with, as being about parameters of the population (whether they can be easily defined or not).

“Nonparametric” is one of the most confusing term in Statistics. Its related to Gaussian processes and stuff, and it used quite a lot of parameters to be honest.

Yes! As the abstract says, a good portion of the talk will be addressing the question: But what exactly are “nonparametric” priors?

As Mikhail suggests, it often involves introducing quite a lot of parameters (often more parameters than observations, in fact) and then trying to come up with reasonable priors over this high-dimensional set.

There are many working definitions of nonparametric. Parametric models are often described as having finitely many unknowns/parameters. On the other extreme, nonparametric models are often described as having unknowns that live in infinite-dimensional spaces. Loosely speaking , we can understand nonparametric Bayesian models as a class of models that make few restrictions on the structure of the unknown.

Join us and find out… Seriously, nonparametric is a bit of a misnomer; it usually means that parameters are not finite so you can not write down the functional form for the conditional mean. Here is one example from the Stan manual: https://mc-stan.org/docs/2_25/stan-users-guide/gaussian-processes-chapter.html

Bayesian: non-parametric means we don’t know the number of parameters, or exact parameterization a priori. We infer the parameterization after conditioning on the data.

I’ve always been curious about the white-person McDonalds process, myself.