## Electronic Journal of Statistics

### Scalable Bayesian nonparametric regression via a Plackett-Luce model for conditional ranks

#### Abstract

We present a novel Bayesian nonparametric regression model for covariates $X$ and continuous response variable $Y\in\mathbb{R}$. The model is parametrized in terms of marginal distributions for $Y$ and $X$ and a regression function which tunes the stochastic ordering of the conditional distributions $F(y|x)$. By adopting an approximate composite likelihood approach, we show that the resulting posterior inference can be decoupled for the separate components of the model. This procedure can scale to very large datasets and allows for the use of standard, existing, software from Bayesian nonparametric density estimation and Plackett-Luce ranking estimation to be applied. As an illustration, we show an application of our approach to a US Census dataset, with over 1,300,000 data points and more than 100 covariates.

#### Article information

Source
Electron. J. Statist., Volume 10, Number 2 (2016), 1807-1828.

Dates
First available in Project Euclid: 18 July 2016

https://projecteuclid.org/euclid.ejs/1468849964

Digital Object Identifier
doi:10.1214/15-EJS1032

Mathematical Reviews number (MathSciNet)
MR3522661

Zentralblatt MATH identifier
06624502

#### Citation

Gray-Davies, Tristan; Holmes, Chris C.; Caron, François. Scalable Bayesian nonparametric regression via a Plackett-Luce model for conditional ranks. Electron. J. Statist. 10 (2016), no. 2, 1807--1828. doi:10.1214/15-EJS1032. https://projecteuclid.org/euclid.ejs/1468849964

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