Related papers: Bayesian Variable Selection with Related Predictor…

In epidemiological research, causal models incorporating potential mediators along a pathway are crucial for understanding how exposures influence health outcomes. This work is motivated by integrated epidemiological and blood biomarker…

Most of the consistency analyses of Bayesian procedures for variable selection in regression refer to pairwise consistency, that is, consistency of Bayes factors. However, variable selection in regression is carried out in a given class of…

We introduce a novel Bayesian approach for variable selection using Gaussian process regression, which is crucial for enhancing interpretability and model regularization. Our method employs nearest neighbor Gaussian processes, serving as…

We discuss Bayesian model uncertainty analysis and forecasting in sequential dynamic modeling of multivariate time series. The perspective is that of a decision-maker with a specific forecasting objective that guides thinking about relevant…

Variable selection for Gaussian process models is often done using automatic relevance determination, which uses the inverse length-scale parameter of each input variable as a proxy for variable relevance. This implicitly determined…

We consider a Bayesian approach to variable selection in the presence of high dimensional covariates based on a hierarchical model that places prior distributions on the regression coefficients as well as on the model space. We adopt the…

It can be important in Bayesian analyses of complex models to construct informative prior distributions which reflect knowledge external to the data at hand. Nevertheless, how much prior information an analyst can elicit from an expert will…

In many practices, scientists are particularly interested in detecting which of the predictors are truly associated with a multivariate response. It is more accurate to model multiple responses as one vector rather than separating each…

In the popular approach of "Bayesian variable selection" (BVS), one uses prior and posterior distributions to select a subset of candidate variables to enter the model. A completely new direction will be considered here to study BVS with a…

Bayesian variable selection is a powerful tool for data analysis, as it offers a principled method for variable selection that accounts for prior information and uncertainty. However, wider adoption of Bayesian variable selection has been…

In the context of a high-dimensional linear regression model, we propose the use of an empirical correlation-adaptive prior that makes use of information in the observed predictor variable matrix to adaptively address high collinearity,…

This paper describes a Bayesian method for learning causal networks using samples that were selected in a non-random manner from a population of interest. Examples of data obtained by non-random sampling include convenience samples and…

High-dimensional variable selection, with many more covariates than observations, is widely documented in standard regression models, but there are still few tools to address it in non-linear mixed-effects models where data are collected…

Factors are categorical variables, and the values which these variables assume are called levels. In this paper, we consider the variable selection problem where the set of potential predictors contains both factors and numerical variables.…

For a Bayesian, real-time forecasting with the posterior predictive distribution can be challenging for a variety of time series models. First, estimating the parameters of a time series model can be difficult with sample-based approaches…

We develop a Bayesian approach for selecting the model which is the most supported by the data within a class of marginal models for categorical variables formulated through equality and/or inequality constraints on generalised logits…

Bayesian model selection poses two main challenges: the specification of parameter priors for all models, and the computation of the resulting Bayes factors between models. There is now a large literature on automatic and objective…

Regression models are used in a wide range of applications providing a powerful scientific tool for researchers from different fields. Linear, or simple parametric, models are often not sufficient to describe complex relationships between…

We propose a new approach to Bayesian prediction that caters for models with a large number of parameters and is robust to model misspecification. Given a class of high-dimensional (but parametric) predictive models, this new approach…

The Bayesian approach to machine learning amounts to computing posterior distributions of random variables from a probabilistic model of how the variables are related (that is, a prior distribution) and a set of observations of variables.…