# Bayesian Nonparametric Quasi Likelihood

arXiv: https://arxiv.org/abs/2405.20601 · HTML: https://mlsanity.com/paper/2405.20601/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 May 2024.

## Built on by (most cited first, 1 of 1)

- [Bayesian Additive Distribution Regression](https://mlsanity.com/paper/2603.06462/) (2026)

## Abstract (arXiv)

A recent trend in Bayesian research has been revisiting generalizations of the likelihood that enable Bayesian inference without requiring the specification of a model for the data generating mechanism. This paper focuses on a Bayesian nonparametric extension of Wedderburn's quasi-likelihood, using Bayesian additive regression trees to model the mean function. Here, the analyst posits only a structural relationship between the mean and variance of the outcome. We show that this approach provides a unified, computationally efficient, framework for extending Bayesian decision tree ensembles to many new settings, including simplex-valued and heavily heteroskedastic data. We also introduce Bayesian strategies for inferring the dispersion parameter of the quasi-likelihood, a task which is complicated by the fact that the quasi-likelihood itself does not contain information about this parameter; despite these challenges, we are able to inject updates for the dispersion parameter into a Markov chain Monte Carlo inference scheme in a way that, in the parametric setting, leads to a Bernstein-von Mises result for the stationary distribution of the resulting Markov chain. We illustrate the utility of our approach on a variety of both synthetic and non-synthetic datasets.