Related papers: Bayesian Estimation Approach for Linear Regression…
Motivated by big data and the vast parameter spaces in modern machine learning models, optimisation approaches to Bayesian inference have seen a surge in popularity in recent years. In this paper, we address the connection between the…
In high-dimensional Bayesian statistics, various methods have been developed, including prior distributions that induce parameter sparsity to handle many parameters. Yet, these approaches often overlook the rich spectral structure of the…
The paper addresses joint sparsity selection in the regression coefficient matrix and the error precision (inverse covariance) matrix for high-dimensional multivariate regression models in the Bayesian paradigm. The selected sparsity…
We study linear regressions in a context where the outcome of interest and some of the covariates are observed in two different datasets that cannot be matched. Traditional approaches obtain point identification by relying, often…
This paper investigates the high-dimensional linear regression with highly correlated covariates. In this setup, the traditional sparsity assumption on the regression coefficients often fails to hold, and consequently many model selection…
Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the…
It is generally believed that ensemble approaches, which combine multiple algorithms or models, can outperform any single algorithm at machine learning tasks, such as prediction. In this paper, we propose Bayesian convex and linear…
This paper develops a novel Bayesian approach for nonlinear regression with symmetric matrix predictors, often used to encode connectivity of different nodes. Unlike methods that vectorize matrices as predictors that result in a large…
We propose the Bayesian adaptive Lasso (BaLasso) for variable selection and coefficient estimation in linear regression. The BaLasso is adaptive to the signal level by adopting different shrinkage for different coefficients. Furthermore, we…
We study the convergence properties of the Gibbs Sampler in the context of posterior distributions arising from Bayesian analysis of conditionally Gaussian hierarchical models. We develop a multigrid approach to derive analytic expressions…
Gaussian graphical models are widely used to infer dependence structures. Bayesian methods are appealing to quantify uncertainty associated with structural learning, i.e., the plausibility of conditional independence statements given the…
Estimation of the mean vector and covariance matrix is of central importance in the analysis of multivariate data. In the framework of generalized linear models, usually the variances are certain functions of the means with the normal…
We deal with Bayesian inference for Beta autoregressive processes. We restrict our attention to the class of conditionally linear processes. These processes are particularly suitable for forecasting purposes, but are difficult to estimate…
In covariance matrix estimation, one of the challenges lies in finding a suitable model and an efficient estimation method. Two commonly used modelling approaches in the literature involve imposing linear restrictions on the covariance…
Regression models are used for inference and prediction in a wide range of applications providing a powerful scientific tool for researchers and analysts from different fields. In many research fields the amount of available data as well as…
Bayesian methods are developed for the multivariate nonparametric regression problem where the domain is taken to be a compact Riemannian manifold. In terms of the latter, the underlying geometry of the manifold induces certain symmetries…
In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…
We consider a framework for determining and estimating the conditional pairwise relationships of variables when the observed samples are contaminated with measurement error in high dimensional settings. Assuming the true underlying…
Conditional forecasts, i.e. projections of a set of variables of interest on the future paths of some other variables, are used routinely by empirical macroeconomists in a number of applied settings. In spite of this, the existing…
We consider chance constrained optimization where it is sought to optimize a function while complying with constraints, both of which are affected by uncertainties. The high computational cost of realistic simulations strongly limits the…