Related papers: Consistent Bayesian Information Criterion Based on…
Model selection is a cornerstone of statistical inference, where information criteria are widely employed to balance model fit and complexity. However, classical likelihood-based criteria are often highly sensitive to contamination,…
Uncovering genuine relationships between a response variable of interest and a large collection of covariates is a fundamental and practically important problem. In the context of Gaussian linear models, both the Bayesian and non-Bayesian…
Varying coefficient models have numerous applications in a wide scope of scientific areas. While enjoying nice interpretability, they also allow flexibility in modeling dynamic impacts of the covariates. But, in the new era of big data, it…
Mixture models are well-known for their versatility, and the Bayesian paradigm is a suitable platform for mixture analysis, particularly when the number of components is unknown. Bhattacharya (2008) introduced a mixture model based on the…
Integrating high-dimensional, heterogeneous data from multi-site cohort studies with complex hierarchical structures poses significant feature selection and prediction challenges. We extend the Bayesian Integrative Analysis and Prediction…
A statistical model or a learning machine is called regular if the map taking a parameter to a probability distribution is one-to-one and if its Fisher information matrix is always positive definite. If otherwise, it is called singular. In…
Most of the regularization methods such as the LASSO have one (or more) regularization parameter(s), and to select the value of the regularization parameter is essentially equal to select a model. Thus, to obtain a model suitable for the…
Bayesian predictive densities when the observed data $x$ and the target variable $y$ to be predicted have different distributions are investigated by using the framework of information geometry. The performance of predictive densities is…
We introduce a novel Information Criterion (IC), termed Learning under Singularity (LS), designed to enhance the functionality of the Widely Applicable Bayes Information Criterion (WBIC) and the Singular Bayesian Information Criterion…
Watanabe-Akaike information criterion (WAIC; Watanabe, 2010) and leave-one-out cross validation (LOO) are two fully Bayesian model selection methods that have been shown to perform better than other traditional information-criterion based…
Modern variable selection procedures make use of penalization methods to execute simultaneous model selection and estimation. A popular method is the LASSO (least absolute shrinkage and selection operator), the use of which requires…
Traditional probabilistic methods for the simulation of advection-diffusion equations (ADEs) often overlook the entropic contribution of the discretization, e.g., the number of particles, within associated numerical methods. Many times, the…
Multivariate pattern analyses approaches in neuroimaging are fundamentally concerned with investigating the quantity and type of information processed by various regions of the human brain; typically, estimates of classification accuracy…
Information Bottleneck (IB) based multi-view learning provides an information theoretic principle for seeking shared information contained in heterogeneous data descriptions. However, its great success is generally attributed to estimate…
Bayesian model selection is a tool to decide whether the introduction of a new parameter is warranted by data. I argue that the usual sampling statistic significance tests for a null hypothesis can be misleading, since they do not take into…
Motivated by examples from genetic association studies, this paper considers the model selection problem in a general complex linear model system and in a Bayesian framework. We discuss formulating model selection problems and incorporating…
Spatial regression models have a variety of applications in several fields ranging from economics to public health. Typically, it is of interest to select important exogenous predictors of the spatially autocorrelated response variable. In…
This thesis responds to the challenges of using a large number, such as thousands, of features in regression and classification problems. There are two situations where such high dimensional features arise. One is when high dimensional…
Bayesian model comparison (BMC) offers a principled probabilistic approach to study and rank competing models. In standard BMC, we construct a discrete probability distribution over the set of possible models, conditional on the observed…
Mixed modeling of extreme values and random effects is relatively unexplored topic. Computational difficulties in using the maximum likelihood method for mixed models and the fact that maximum likelihood method uses available data and does…