Reversible Jump PDMP Samplers for Variable Selection

Chevallier, Augustin and Fearnhead, Paul and Sutton, Matthew (2023) Reversible Jump PDMP Samplers for Variable Selection. Journal of the American Statistical Association, 118 (544). pp. 2915-2927. ISSN 0162-1459

[thumbnail of 2010.11771v1]
Text (2010.11771v1)
2010.11771v1.pdf - Other

Download (834kB)
[thumbnail of RJ_PDMP_Samplers]
Text (RJ_PDMP_Samplers)
RJ_PDMP_Samplers.pdf - Accepted Version
Available under License Creative Commons Attribution.

Download (7MB)


A new class of Markov chain Monte Carlo (MCMC) algorithms, based on simulating piecewise deterministic Markov processes (PDMPs), have recently shown great promise: they are non-reversible, can mix better than standard MCMC algorithms, and can use subsampling ideas to speed up computation in big data scenarios. However, current PDMP samplers can only sample from posterior densities that are differentiable almost everywhere, which precludes their use for model choice. Motivated by variable selection problems, we show how to develop reversible jump PDMP samplers that can jointly explore the discrete space of models and the continuous space of parameters. Our framework is general: it takes any existing PDMP sampler, and adds two types of trans-dimensional moves that allow for the addition or removal of a variable from the model. We show how the rates of these trans-dimensional moves can be calculated so that the sampler has the correct invariant distribution. Simulations show that the new samplers can mix better than standard MCMC algorithms. Our empirical results show they are also more efficient than gradient-based samplers that avoid model choice through use of continuous spike-and-slab priors which replace a point mass at zero for each parameter with a density concentrated around zero.

Item Type:
Journal Article
Journal or Publication Title:
Journal of the American Statistical Association
Additional Information:
Code available from
Uncontrolled Keywords:
?? stat.costat.mlstatistics and probabilitystatistics, probability and uncertainty ??
ID Code:
Deposited By:
Deposited On:
07 Dec 2020 12:05
Last Modified:
09 May 2024 16:20