10.6084/M9.FIGSHARE.21215884.V1
Shuang Zhou
Shuang
Zhou
Pallavi Ray
Pallavi
Ray
Debdeep Pati
Debdeep
Pati
Anirban Bhattacharya
Anirban
Bhattacharya
A mass-shifting phenomenon of truncated multivariate normal priors
<p>We show that lower-dimensional marginal densities of dependent zero-mean normal distributions truncated to the positive orthant exhibit a <i>mass-shifting</i> phenomenon. Despite the truncated multivariate normal density having a mode at the origin, the marginal density assigns increasingly small mass near the origin as the dimension increases. The phenomenon accentuates with stronger correlation between the random variables. This surprising behavior has serious implications towards Bayesian constrained estimation and inference, where the prior, in addition to having a full support, is required to assign a substantial probability near the origin to capture flat parts of the true function of interest. A precise quantification of the mass-shifting phenomenon for both the prior and the posterior, characterizing the role of the dimension as well as the dependence, is provided under a variety of correlation structures. Without further modification, we show that truncated normal priors are not suitable for modeling flat regions and propose a novel alternative strategy based on shrinking the coordinates using a multiplicative scale parameter. The proposed shrinkage prior is shown to achieve optimal posterior contraction around true functions with potentially flat regions. Synthetic and real data studies demonstrate how the modification guards against the mass shifting phenomenon while retaining computational efficiency.</p>
Physiology
Pharmacology
Biotechnology
Ecology
Mathematical Sciences not elsewhere classified
Computational Biology
Taylor & Francis
2022
2022-09-27
2024-02-14
Dataset
9088640 Bytes
10.6084/m9.figshare.21215884
10.1080/01621459.2022.2129059
CC BY 4.0