Related papers: An Empirical Bayes approach to ARX Estimation

We consider a prior for nonparametric Bayesian estimation which uses finite random series with a random number of terms. The prior is constructed through distributions on the number of basis functions and the associated coefficients. We…

Bayesian models often involve a small set of hyperparameters determined by maximizing the marginal likelihood. Bayesian optimization is a popular iterative method where a Gaussian process posterior of the underlying function is sequentially…

A new methodology for model determination in decomposable graphical Gaussian models is developed. The Bayesian paradigm is used and, for each given graph, a hyper inverse Wishart prior distribution on the covariance matrix is considered.…

Bayesian variable selection methods are powerful techniques for fitting and inferring on sparse high-dimensional linear regression models. However, many are computationally intensive or require restrictive prior distributions on model…

The empirical Bayes $g$-modeling approach via the nonparametric maximum likelihood estimator (NPMLE) is widely used for large-scale estimation and inference in the normal means problem, yet theoretical guarantees for uncertainty…

The first-order autoregressive process, AR (1), has been widely used and implemented in time series analysis. Different estimation methods have been employed in order to estimate the autoregressive parameter. This article focuses on…

Bayesian computational strategies for inference can be inefficient in approximating the posterior distribution in models that exhibit some form of periodicity. This is because the probability mass of the marginal posterior distribution of…

One of the main goals of mathematical modeling in systems medicine related to medical applications is to obtain patient-specific parameterizations and model predictions. In clinical practice, however, the number of available measurements…

Bayesian inference is attractive for its coherence and good frequentist properties. However, it is a common experience that eliciting a honest prior may be difficult and, in practice, people often take an {\em empirical Bayes} approach,…

Bayesian inference provides a flexible way of combining data with prior information. However, quantile regression is not equipped with a parametric likelihood, and therefore, Bayesian inference for quantile regression demands careful…

Random effects model can account for the lack of fitting a regression model and increase precision of estimating area-level means. However, in case that the synthetic mean provides accurate estimates, the prior distribution may inflate an…

Empirical Bayes estimators are based on minimizing the average risk with the hyper-parameters in the weighting function being estimated from observed data. The performance of an empirical Bayes estimator is typically evaluated by its mean…

Gaussian process regression has proven very powerful in statistics, machine learning and inverse problems. A crucial aspect of the success of this methodology, in a wide range of applications to complex and real-world problems, is…

A method for sequential Bayesian inference of the static parameters of a dynamic state space model is proposed. The method is based on the observation that many dynamic state space models have a relatively small number of static parameters…

We propose an empirical Bayes estimator based on Dirichlet process mixture model for estimating the sparse normalized mean difference, which could be directly applied to the high dimensional linear classification. In theory, we build a…

We study Bayesian inference methods for solving linear inverse problems, focusing on hierarchical formulations where the prior or the likelihood function depend on unspecified hyperparameters. In practice, these hyperparameters are often…

We propose a new empirical Bayes approach for inference in the $p \gg n$ normal linear model. The novelty is the use of data in the prior in two ways, for centering and regularization. Under suitable sparsity assumptions, we establish a…

In this article we provide a formulation of empirical bayes described by Atchade (2011) to tune the hyperparameters of priors used in bayesian set up of collaborative filter. We implement the same in MovieLens small dataset. We see that it…

Empirical likelihood is a popular nonparametric statistical tool that does not require any distributional assumptions. In this paper, we explore the possibility of conducting variable selection via Bayesian empirical likelihood. We show…

We discuss the use of empirical Bayes for data integration, in the sense of transfer learning. Our main interest is in settings where one wishes to learn structure (e.g. feature selection) and one only has access to incomplete data from…