Preprint
Posterior shrinkage towards linear subspaces
ArXiv.org
Cornell University
01/15/2024
DOI: 10.48550/arxiv.2401.07820
Abstract
It is common to hold prior beliefs that are not characterized by points in the parameter space but instead are relational in nature and can be described by a linear subspace. While some previous work has been done to account for such prior beliefs, the focus has primarily been on point estimators within a regression framework. We argue, however, that prior beliefs about parameters ought to be encoded into the prior distribution rather than in the formation of a point estimator. In this way, the prior beliefs help shape \textit{all} inference. Through exponential tilting, we propose a fully generalizable method of taking existing prior information from, e.g., a pilot study, and combining it with additional prior beliefs represented by parameters lying on a linear subspace. We provide computationally efficient algorithms for posterior inference that, once inference is made using a non-tilted prior, does not depend on the sample size. We illustrate our proposed approach on an antihypertensive clinical trial dataset where we shrink towards a power law dose-response relationship, and on monthly influenza and pneumonia data where we shrink moving average lag parameters towards smoothness. Software to implement the proposed approach is provided in the R package \verb+SUBSET+ available on GitHub.
Details
- Title: Subtitle
- Posterior shrinkage towards linear subspaces
- Creators
- Daniel K Sewell
- Resource Type
- Preprint
- Publication Details
- ArXiv.org
- DOI
- 10.48550/arxiv.2401.07820
- ISSN
- 2331-8422
- Publisher
- Cornell University; Ithaca, NY
- Language
- English
- Date posted
- 01/15/2024
- Academic Unit
- Biostatistics; Public Policy Center (Archive)
- Record Identifier
- 9984548288802771
Metrics
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