Bayesian constraint relaxation.
Journal Article (Journal Article)
Prior information often takes the form of parameter constraints. Bayesian methods include such information through prior distributions having constrained support. By using posterior sampling algorithms, one can quantify uncertainty without relying on asymptotic approximations. However, sharply constrained priors are not necessary in some settings and tend to limit modelling scope to a narrow set of distributions that are tractable computationally. We propose to replace the sharp indicator function of the constraint with an exponential kernel, thereby creating a close-to-constrained neighbourhood within the Euclidean space in which the constrained subspace is embedded. This kernel decays with distance from the constrained space at a rate depending on a relaxation hyperparameter. By avoiding the sharp constraint, we enable use of off-the-shelf posterior sampling algorithms, such as Hamiltonian Monte Carlo, facilitating automatic computation in a broad range of models. We study the constrained and relaxed distributions under multiple settings and theoretically quantify their differences. Application of the method is illustrated through several novel modelling examples.
Full Text
Duke Authors
Cited Authors
- Duan, LL; Young, AL; Nishimura, A; Dunson, DB
Published Date
- March 2020
Published In
Volume / Issue
- 107 / 1
Start / End Page
- 191 - 204
PubMed ID
- 32089562
Pubmed Central ID
- PMC7017863
Electronic International Standard Serial Number (EISSN)
- 1464-3510
International Standard Serial Number (ISSN)
- 0006-3444
Digital Object Identifier (DOI)
- 10.1093/biomet/asz069
Language
- eng