Related papers: Asymptotics of Bayesian Uncertainty Estimation in …
In Bayesian nonparametric inference, random discrete probability measures are commonly used as priors within hierarchical mixture models for density estimation and for inference on the clustering of the data. Recently, it has been shown…
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…
Bayesian model comparison is often based on the posterior distribution over the set of compared models. This distribution is often observed to concentrate on a single model even when other measures of model fit or forecasting ability…
We obtain an asymptotic normality result that reveals the precise asymptotic behavior of the maximum likelihood estimators of parameters for a very general class of linear mixed models containing cross random effects. In achieving the…
Bayesian statistics has two common measures of central tendency of a posterior distribution: posterior means and Maximum A Posteriori (MAP) estimates. In this paper, we discuss a connection between MAP estimates and posterior means. We…
We consider the sparse high-dimensional linear regression model $Y=Xb+\epsilon$ where $b$ is a sparse vector. For the Bayesian approach to this problem, many authors have considered the behavior of the posterior distribution when, in truth,…
Consider semiparametric models that display local asymptotic exponentiality (Ibragimov and Has'minskii (1981)), an asymptotic property of the likelihood associated with discontinuities of densities. Our interest goes to estimation of the…
Bayesian inference and the use of posterior or posterior predictive probabilities for decision making have become increasingly popular in clinical trials. The current practice in Bayesian clinical trials relies on a hybrid…
We present asymptotic results for the regression-adjusted version of approximate Bayesian computation introduced by Beaumont(2002). We show that for an appropriate choice of the bandwidth, regression adjustment will lead to a posterior…
We study the properties of variational Bayes approximations for exponential family models with missing values. It is shown that the iterative algorithm for obtaining the variational Bayesian estimator converges locally to the true value…
The Peaks Over Threshold (POT) method is the most popular statistical method for the analysis of univariate extremes. Even though there is a rich applied literature on Bayesian inference for the POT, the asymptotic theory for such proposals…
We study the consistency of sample mean-variance portfolios of arbitrarily high dimension that are based on Bayesian or shrinkage estimation of the input parameters as well as weighted sampling. In an asymptotic setting where the number of…
The autoregressive moving average (ARMA) model is one of the most important models in time series analysis.We consider the Bayesian estimation of an unknown spectral density in the ARMA model.In the i.i.d. cases, Komaki showed that Bayesian…
We study Bayesian linear regression models with skew-symmetric scale mixtures of normal error distributions. These kinds of models can be used to capture departures from the usual assumption of normality of the errors in terms of heavy…
We derive the precise asymptotic distributional behavior of Gaussian variational approximate estimators of the parameters in a single-predictor Poisson mixed model. These results are the deepest yet obtained concerning the statistical…
Asymptotic equivalence results for nonparametric regression experiments have always assumed that the variances of the observations are known. In practice, however the variance of each observation is generally considered to be an unknown…
Contemporary focus on selective inference has renewed interest in the theory of selection models. In this paper, we analyze the asymptotic properties of selection models built on independent and identically distributed observations. We show…
Asymptotic equivalence in Le Cam's sense for nonparametric regression experiments is extended to the case of non-regular error densities, which have jump discontinuities at their endpoints. We prove asymptotic equivalence of such regression…
Mathematical models of real life phenomena are highly nonlinear involving multiple parameters and often exhibiting complex dynamics. Experimental data sets are typically small and noisy, rendering estimation of parameters from such data…
Many modern experiments, such as microarray gene expression and genome-wide association studies, present the problem of estimating a large number of parallel effects. Bayesian inference is a popular approach for analyzing such data by…