Related papers: Posterior consistency in multi-response regression…
Recent works have shown an interest in investigating the frequentist asymptotic properties of Bayesian procedures for high-dimensional linear models under sparsity constraints. However, there exists a gap in the literature regarding…
In multivariate statistics, estimating the covariance matrix is essential for understanding the interdependence among variables. In high-dimensional settings, where the number of covariates increases with the sample size, it is well known…
Most of the consistency analyses of Bayesian procedures for variable selection in regression refer to pairwise consistency, that is, consistency of Bayes factors. However, variable selection in regression is carried out in a given class of…
This paper focuses on Bayesian shrinkage for covariance matrix estimation. We examine posterior properties and frequentist risks of Bayesian estimators based on new hierarchical inverse-Wishart priors. More precisely, we give the existence…
Covariance matrix estimation arises in multivariate problems including multivariate normal sampling models and regression models where random effects are jointly modeled, e.g. random-intercept, random-slope models. A Bayesian analysis of…
We consider Bayesian inference in inverse regression problems where the objective is to infer about unobserved covariates from observed responses and covariates. We establish posterior consistency of such unobserved covariates in Bayesian…
We investigate the asymptotic behavior of posterior distributions of regression coefficients in high-dimensional linear models as the number of dimensions grows with the number of observations. We show that the posterior distribution…
We derive conditions for posterior consistency when the responses are independent but not identically distributed ($i.n.i.d$) and the model is "misspecified" to be a family of densities parametrized by a possibly infinite dimensional…
We study frequentist properties of a Bayesian high-dimensional multivariate linear regression model with correlated responses. The predictors are separated into many groups and the group structure is pre-determined. Two features of the…
This paper develops a methodology for approximating the posterior first two moments of the posterior distribution in Bayesian inference. Partially specified probability models, which are defined only by specifying means and variances, are…
Frequentist conditions for asymptotic suitability of Bayesian procedures focus on lower bounds for prior mass in Kullback-Leibler neighbourhoods of the data distribution. The goal of this paper is to investigate the flexibility in criteria…
Non-linear latent variable models have become increasingly popular in a variety of applications. However, there has been little study on theoretical properties of these models. In this article, we study rates of posterior contraction in…
We consider a class of non-conjugate priors as a mixing family of distributions for a parameter (e.g., Poisson or gamma rate, inverse scale or precision of an inverse-gamma, inverse variance of a normal distribution) of an exponential…
Non-linear latent variable models have become increasingly popular in a variety of applications. However, there has been little study on theoretical properties of these models. In this article, we study rates of posterior contraction in…
Inverse propensity-score weighted (IPW) estimators are prevalent in causal inference for estimating average treatment effects in observational studies. Under unconfoundedness, given accurate propensity scores and $n$ samples, the size of…
We study full Bayesian procedures for high-dimensional linear regression. We adopt data-dependent empirical priors introduced in [1]. In their paper, these priors have nice posterior contraction properties and are easy to compute. Our paper…
The normal-inverse-Wishart (NIW) distribution is commonly used as a prior distribution for the mean and covariance parameters of a multivariate normal distribution. The family of NIW distributions is also a minimal exponential family. In…
This work studies the large sample properties of the posterior-based inference in the curved exponential family under increasing dimension. The curved structure arises from the imposition of various restrictions on the model, such as moment…
We derive a maximum a posteriori estimator for the linear observation model, where the signal and noise covariance matrices are both uncertain. The uncertainties are treated probabilistically by modeling the covariance matrices with prior…
In recent years, shrinkage priors have received much attention in high-dimensional data analysis from a Bayesian perspective. Compared with widely used spike-and-slab priors, shrinkage priors have better computational efficiency. But the…