Flexible Prior Elicitation for Bayesian Analysis

Entejar Alam Chair
University of Texas at Austin
 
Wednesday, Aug 6: 8:30 AM - 10:20 AM
4145 
Contributed Papers 
Music City Center 
Room: CC-Davidson Ballroom A2 

Main Sponsor

Section on Bayesian Statistical Science

Presentations

A Framework for Robust Information Borrowing via Ensembling Priors and Models

Oncology clinical trials often involve time-to-event outcomes, where censoring can delay decision-making. Bayesian methods improve precision by borrowing historical data through informative priors, but improper borrowing can inflate type I error rates if historical and current data are incompatible. Nevertheless, regulatory guidelines require the borrowing approach to be pre-specified in the trial protocol, making prior selection difficult. While existing priors offer different advantages, no single approach is optimal in all cases. We illustrate this challenge using E1690 (current study) and E1684 (historical study), where the current data alone provide insufficient evidence of treatment efficacy, yet borrowing may increase the risk of a false discovery. To address this, we propose an ensemble framework that combines multiple informative priors using Bayesian model averaging or stacking techniques. Our method also accommodates different outcome models, incorporating propensity score-based approaches and distinct survival models. Rigorous simulations shows that our approach offers greater flexibility and robustness than selecting a single model-prior combination. 

Keywords

Information borrowing

Prior Elicitation

Bayesian analysis 

Co-Author(s)

Ethan Alt, GSK
Joseph Ibrahim, University of North Carolina

First Author

Xinxin Chen, University of North Carolina at Chapel Hill

Presenting Author

Xinxin Chen, University of North Carolina at Chapel Hill

Automated Prior Elicitation for Bayesian Metabolomics Analysis

Modern metabolomics experiments generate rich, high-dimensional data that capture complex biochemical relationships. While public databases like KEGG, HMDB, and Reactome contain extensive prior knowledge about metabolic networks, incorporating this information systematically into statistical analyses remains challenging. We present a novel framework for automatically constructing informative prior distributions from metabolic databases for Bayesian analysis of metabolomics data. Our method extracts network topology, reaction directionality, and uses modern NLP techniques to utilize qualitative information to build hierarchical prior distributions. We demonstrate our approach on both targeted and untargeted LC-MS data, showing improved power for differential abundance testing and more biologically plausible pathway-level effect estimates compared to standard methods. This work provides a principled bridge between accumulated biochemical knowledge and modern Bayesian methods for metabolomics. 

Keywords

Bayesian Statistics

Metabolomics

Prior Solicitation

Differential Abundance

Pathway Analysis

Biomarker Discovery 

Co-Author

Ali Rahnavard, The George Washington University

First Author

Chiraag Gohel, The George Washington University

Presenting Author

Chiraag Gohel, The George Washington University

Informative Variance Priors for Bayesian Multilevel Modeling with Large and Small Samples

Frequentist multilevel models (MLMs) often struggle with unstable variance estimates when the number of clusters (L2 units) is small, leading to imprecise inferences. Bayesian MLMs provide a solution by incorporating informative variance priors, which stabilize random effects and improve small-sample estimation. This study applies Bayesian MLM with strongly informative inverse-gamma priors to cross-sectional child trafficking data from Sierra Leone, examining individual- and household-level predictors of trafficking vulnerabilities while addressing challenges related to small L2 clusters and missing data.

Using R (brms) with Hamiltonian Monte Carlo in Stan, we specify variance priors based on empirical variance distributions, aligning prior mode with realistic estimates to reduce bias, improve precision, and yield narrower credible intervals. Model validation includes posterior predictive checks, prior sensitivity analyses, and Gelman-Rubin diagnostics.

Findings confirm that informative variance priors enhance small-sample estimation, improving inference for hierarchical data. Beyond methodology, this research provides policy-relevant insights for targeted interventions. 

Keywords

Bayesian

Multilevel modeling

Informative variance priors

Inverse-gamma

Hierarchical data

Small sample estimation 

Co-Author(s)

David Okech, University of Georgia
Hui Yi, University of Georgia

First Author

Liu Liu, University of Georgia

Presenting Author

Liu Liu, University of Georgia

Power Prior Bayesian Analysis using PROC BGLIMM

The power prior, a general class of priors that are used in Bayesian analysis, provides a practical and dynamic approach to translate data information into distributional information about the model parameters. The power prior has become a popular method in many disciplines, as it increases model efficiency and prediction accuracy by borrowing information from other data sources. Implementation of the power prior can be difficult using general Bayesian software packages and often relies on programming solutions that are problem-specific, making it hard to generalize. We introduce new features in the BGLIMM procedure that enables you to fit the power prior to many models with the simplest setup. 

Keywords

Bayesian analysis

historical data

information borrowing

power prior

PROC BGLIMM 

Co-Author

Fang Chen, SAS Institute, Inc.

First Author

Yi Gong, SAS

Presenting Author

Yi Gong, SAS

Sparse inverse covariance selection with mass-nonlocal priors

To tackle the challenges of understanding complex multivariate relationships in high-dimensional settings, we develop a method for estimating the sparsity pattern of inverse covariance matrices. Our approach employs a generalized likelihood framework for scalable computation, integrating spike and slab priors with nonlocal slab components on the elements of the inverse covariance matrix. We implement the Bayesian model using an entry-wise Gibbs sampler and establish its theoretical consistency in high-dimensional settings under mild conditions. The practical utility of our method is demonstrated through extensive numerical studies and an application to neuropathy data analysis. 

Keywords

Bayesian inference

Graphical model selection

Nonlocal prior

Spike and slab prior 

Co-Author(s)

Liangliang Zhang, Department of Population and Quantitative Health Sciences, Case Western Reserve University
Xuan Cao, University of Cincinnati

First Author

Taiwo Fagbohungbe

Presenting Author

Taiwo Fagbohungbe

Bayesian Model Averaging for Linear Regression Models With Heavy-Tailed Errors

We aim to develop a Bayesian model averaging technique in linear regression models to accommodate heavier tailed error densities than the normal distribution. Motivated by the use of the Huber loss function in presence of outliers, the Bayesian Huberized lasso with hyperbolic errors has been proposed and recently implemented in the literature. Since the Huberized lasso cannot enforce regression coefficients to be exactly zero, we propose a fully Bayesian variable selection approach with spike and slab priors to address sparsity more effectively. Furthermore, the hyperbolic distribution has heavier tails than a normal distribution but thinner tails than a Cauchy distribution. Thus, we propose a novel regression model with an error distribution encompassing both hyperbolic and Student-t distributions. Our model aims to capture the benefit of using Huber loss, while adapting to heavier tails and unknown levels of sparsity, as entailed by the data. We develop an efficient Gibbs sampler with Metropolis Hastings steps for posterior computation. Through simulation studies and analyses of real datasets, we observe a superior performance of our method over various state-of-the-art methods. 

Keywords

Bayesian Huberized lasso

Gibbs sampler

Hyperbolic distribution

Spike and slab priors

Student-t distribution 

Co-Author

Joyee Ghosh, University of Iowa

First Author

Shamriddha De, The University of Iowa

Presenting Author

Shamriddha De, The University of Iowa