Related papers: Local Bayesian Regression
Bayesian methods are actively used for parameter identification and uncertainty quantification when solving nonlinear inverse problems with random noise. However, there are only few theoretical results justifying the Bayesian approach.…
This paper presents an approximate method for performing Bayesian inference in models with conditional independence over a decentralized network of learning agents. The method first employs variational inference on each individual learning…
Bayesian analysis is a framework for parameter estimation that applies even in uncertainty regimes where the commonly used local (frequentist) analysis based on the Cram\'er-Rao bound is not well defined. In particular, it applies when no…
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…
A nonparametric Bayes approach is proposed for the problem of estimating a sparse sequence based on Gaussian random variables. We adopt the popular two-group prior with one component being a point mass at zero, and the other component being…
In this paper we propose a semi-parametric Bayesian Generalized Least Squares estimator. In a generic setting where each error is a vector, the parametric Generalized Least Square estimator maintains the assumption that each error vector…
One of the most popular methodologies for estimating the average treatment effect at the threshold in a regression discontinuity design is local linear regression (LLR), which places larger weight on units closer to the threshold. We…
New local linear estimators are proposed for a wide class of nonparametric regression models. The estimators are uniformly consistent regardless of satisfying traditional conditions of depen\-dence of design elements. The estimators are the…
In this paper, we consider the problem of parametric empirical Bayes estimation of an i.i.d. prior in high-dimensional Bayesian linear regression, with random design. We obtain the asymptotic distribution of the variational Empirical Bayes…
Variable selection and classification are common objectives in the analysis of high-dimensional data. Most such methods make distributional assumptions that may not be compatible with the diverse families of distributions data can take. A…
We study empirical Bayes estimation in high-dimensional linear regression. To facilitate computationally efficient estimation of the underlying prior, we adopt a variational empirical Bayes approach, introduced originally in Carbonetto and…
We propose a new semi-parametric distributional regression smoother that is based on a copula decomposition of the joint distribution of the vector of response values. The copula is high-dimensional and constructed by inversion of a pseudo…
We study location-scale mixture priors for nonparametric statistical problems, including multivariate regression, density estimation and classification. We show that a rate-adaptive procedure can be obtained if the prior is properly…
It has historically been a challenge to perform Bayesian inference in a design-based survey context. The present paper develops a Bayesian model for sampling inference in the presence of inverse-probability weights. We use a hierarchical…
From a systems biology perspective the majority of cancer models, although interesting and providing a qualitative explanation of some problems, have a major disadvantage in that they usually miss a genuine connection with experimental…
This paper develops a novel approach to density estimation on a network. We formulate nonparametric density estimation on a network as a nonparametric regression problem by binning. Nonparametric regression using local polynomial…
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.…
We consider the nonparametric regression problem when the covariates are located on an unknown smooth compact submanifold of a Euclidean space. Under defining a random geometric graph structure over the covariates we analyze the asymptotic…
There is increasing interest in the problem of nonparametric regression with high-dimensional predictors. When the number of predictors $D$ is large, one encounters a daunting problem in attempting to estimate a $D$-dimensional surface…
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…