Related papers: Bayesian model selection for linear regression

Motivation: Gene selection has become a common task in most gene expression studies. The objective of such research is often to identify the smallest possible set of genes that can still achieve good predictive performance. The problem of…

The aim of reduced rank regression is to connect multiple response variables to multiple predictors. This model is very popular, especially in biostatistics where multiple measurements on individuals can be re-used to predict multiple…

Spike-and-slab and horseshoe regression are arguably the most popular Bayesian variable selection approaches for linear regression models. However, their performance can deteriorate if outliers and heteroskedasticity are present in the…

A widely used method to create a continuous representation of a discrete data-set is regression analysis. When the regression model is not based on a mathematical description of the physics underlying the data, heuristic techniques play a…

Bayesian models provide recursive inference naturally because they can formally reconcile new data and existing scientific information. However, popular use of Bayesian methods often avoids priors that are based on exact posterior…

Linear mixed models (LMMs) are instrumental for regression analysis with structured dependence, such as grouped, clustered, or multilevel data. However, selection among the covariates--while accounting for this structured…

Bayesian methods - either based on Bayes Factors or BIC - are now widely used for model selection. One property that might reasonably be demanded of any model selection method is that if a model ${M}_{1}$ is preferred to a model ${M}_{0}$,…

We propose a new variable selection procedure for a functional linear model with multiple scalar responses and multiple functional predictors. This method is based on basis expansions of the involved functional predictors and coefficients…

In all areas of human knowledge, datasets are increasing in both size and complexity, creating the need for richer statistical models. This trend is also true for economic data, where high-dimensional and nonlinear/nonparametric inference…

Subset selection in multiple linear regression aims to choose a subset of candidate explanatory variables that tradeoff fitting error (explanatory power) and model complexity (number of variables selected). We build mathematical programming…

Double descent is a phenomenon of over-parameterized statistical models such as deep neural networks which have a re-descending property in their risk function. As the complexity of the model increases, risk exhibits a U-shaped region due…

Approximate Bayesian computation (ABC) methods provide an elaborate approach to Bayesian inference on complex models, including model choice. Both theoretical arguments and simulation experiments indicate, however, that model posterior…

Theories can be represented as statistical models for empirical testing. There is a vast literature on model selection and multimodel inference that focuses on how to assess which statistical model, and therefore which theory, best fits the…

We consider constructing model selection criteria for evaluating nonlinear mixed effects models via basis expansions. Mean functions and random functions in the mixed effects model are expressed by basis expansions, then they are estimated…

When applying Machine Learning techniques to problems, one must select model parameters to ensure that the system converges but also does not become stuck at the objective function's local minimum. Tuning these parameters becomes a…

A reciprocal LASSO (rLASSO) regularization employs a decreasing penalty function as opposed to conventional penalization approaches that use increasing penalties on the coefficients, leading to stronger parsimony and superior model…

This introduction to Bayesian statistics presents the main concepts as well as the principal reasons advocated in favour of a Bayesian modelling. We cover the various approaches to prior determination as well as the basis asymptotic…

Bayesian models quantify uncertainty and facilitate optimal decision-making in downstream applications. For most models, however, practitioners are forced to use approximate inference techniques that lead to sub-optimal decisions due to…

Considering the context of functional data analysis, we developed and applied a new Bayesian approach via Gibbs sampler to select basis functions for a finite representation of functional data. The proposed methodology uses Bernoulli latent…

Variable selection for a multiple regression model (Noisy Linear Perceptron) is studied with a mean field approximation. In our Bayesian framework, variable selection is formulated as estimation of discrete parameters that indicate a subset…