Optimal predictive model selection

Abstract

Often the goal of model selection is to choose a model for future prediction, and it is natural to measure the accuracy of a future prediction by squared error loss. Under the Bayesian approach, it is commonly perceived that the optimal predictive model is the model with highest posterior probability, but this is not necessarily the case. In this paper we show that, for selection among normal linear models, the optimal predictive model is often the median probability model, which is defined as the model consisting of those variables which have overall posterior probability greater than or equal to 1/2 of being in a model. The median probability model often differs from the highest probability model.

Cited by in corpus (65)

• Spike and slab variable selection: Frequentist and Bayesian strategies
• Bayes and empirical-Bayes multiplicity adjustment in the variable-selection problem
• Bayesian variable selection regression for genome-wide association studies and other large-scale problems
• Comparison of Bayesian predictive methods for model selection
• Bayesian variable selection with shrinking and diffusing priors
• Bayesian Variable Selection and Estimation for Group Lasso
• Spike-and-Slab Priors for Function Selection in Structured Additive Regression Models
• Consistency of Bayesian procedures for variable selection
• Projective Inference in High-dimensional Problems: Prediction and Feature Selection
• Empirical Bayes posterior concentration in sparse high-dimensional linear models
• Hyper-g Priors for Generalized Linear Models
• On spike-and-slab priors for Bayesian equation discovery of nonlinear dynamical systems via sparse linear regression
• Bayesian Gaussian Copula Graphical Modeling for Dupuytren Disease
• Using the bayesmeta R package for Bayesian random-effects meta-regression
• Statistical Significance of the Netflix Challenge
• Anisotropic function estimation using multi-bandwidth Gaussian processes
• Power-Expected-Posterior Priors for Variable Selection in Gaussian Linear Models
• Compatibility of Prior Specifications Across Linear Models
• Improving exoplanet detection capabilities with the false inclusion probability. Comparison with other detection criteria in the context of radial velocities
• Bayesian variable selection using cost-adjusted BIC, with application to cost-effective measurement of quality of health care
• Clouds form on the hot Saturn JWST ERO target WASP-96b
• Bayesian Variable Selection For Survival Data Using Inverse Moment Priors
• A Bayesian Time-Varying Effect Model for Behavioral mHealth Data
• Tutorial on survival modeling with applications to omics data
• Approximate Bayesian Model Selection with the Deviance Statistic
• Analysing the SEDs of protoplanetary disks with machine learning
• Mode jumping MCMC for Bayesian variable selection in GLMM
• Performance of variable and function selection methods for estimating the non-linear health effects of correlated chemical mixtures: a simulation study
• Efficient inference for genetic association studies with multiple outcomes
• Joint Specification of Model Space and Parameter Space Prior Distributions
• Simple Bayesian testing of scientific expectations in linear regression models
• Rejoinder: One-step sparse estimates in nonconcave penalized likelihood models
• Bayesian multinomial regression with class-specific predictor selection
• Empirical priors and coverage of posterior credible sets in a sparse normal mean model
• Bayesian Inference of Networks Across Multiple Sample Groups and Data Types
• Bayesian Effect Selection in Structured Additive Distributional Regression Models
• Bayesian Space-time SIR modeling of Covid-19 in two US states during the 2020-2021 pandemic
• A novel algorithmic approach to Bayesian Logic Regression
• Bayesian Inference in Nonparanormal Graphical Models
• Efficient estimation and correction of selection-induced bias with order statistics
• Concentration of posterior probabilities and normalized L0 criteria
• Scalable marginalization of correlated latent variables with applications to learning particle interaction kernels
• Semi-parametric dynamic time series modelling with applications to detecting neural dynamics
• Variable Selection with ABC Bayesian Forests
• Multivariate Bayesian structured variable selection for pharmacogenomic studies
• Robust and Parallel Bayesian Model Selection
• Empirical Bayes inference in sparse high-dimensional generalized linear models
• Bayesian Learning of Graph Substructures
• Learning block structured graphs in Gaussian graphical models
• Learning Bayesian networks: a copula approach for mixed-type data
• A Bayesian Joint Model for Compositional Mediation Effect Selection in Microbiome Data
• Bayesian high-dimensional covariate selection in non-linear mixed-effects models using the SAEM algorithm
• The Sensitivity of Bayesian Kernel Machine Regression (BKMR) to Data Distribution: A Comprehensive Simulation Analysis
• Comment on García-Donato et al. (2025) "Model uncertainty and missing data: An objective Bayesian perspective"
• Invited Discussion of "Model Uncertainty and Missing Data: An Objective Bayesian Perspective" by Gonzalo García-Donato , María Eugenia Castellanos , Stefano Cabras Alicia Quirós , and Anabel Forte
• A continuous multiple hypothesis testing framework for optimal exoplanet detection
• A Metropolized adaptive subspace algorithm for high-dimensional Bayesian variable selection
• Directed Cyclic Graph for Causal Discovery from Multivariate Functional Data
• Bayesian Stability Selection and Inference on Selection Probabilities
• Bayesian Modeling of Multiple Structural Connectivity Networks During the Progression of Alzheimer's Disease
• Approximate Laplace approximations for scalable model selection
• A robust Bayesian analysis of variable selection under prior ignorance
• Robust Bayesian causal estimation for causal inference in medical diagnosis
• Bayesian Centroid Estimation for Motif Discovery
• Flexible Bayesian Multiple Comparison Adjustment Using Dirichlet Process and Beta-Binomial Model Priors