Related papers: Asymptotic properties of Bayesian inference in lin…
A large class of problems in sciences and engineering can be formulated as the general problem of constructing random intervals with pre-specified coverage probabilities for the mean. Wee propose a general approach for statistical inference…
We consider inference from non-random samples in data-rich settings where high-dimensional auxiliary information is available both in the sample and the target population, with survey inference being a special case. We propose a regularized…
The celebrated Bernstein von-Mises theorem ensures that credible regions from Bayesian posterior are well-calibrated when the model is correctly-specified, in the frequentist sense that their coverage probabilities tend to the nominal…
In all areas of human knowledge, datasets are increasing in both size and complexity, creating the need for richer statistical models. This trend is also true for economic data, where high-dimensional and nonlinear/nonparametric inference…
In Bayesian inference, an unknown measurement uncertainty is often quantified in terms of a Gamma distributed precision parameter, which is impractical when prior information on the standard deviation of the measurement uncertainty shall be…
We propose a double robust Bayesian inference procedure on the average treatment effect (ATE) under unconfoundedness. For our new Bayesian approach, we first adjust the prior distributions of the conditional mean functions, and then correct…
In a smooth semiparametric model, the marginal posterior distribution of the finite dimensional parameter of interest is expected to be asymptotically equivalent to the sampling distribution of frequentist's efficient estimators. This is…
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…
The main goal of this paper is to study the parameter estimation problem, using the Bayesian methodology, for the drift coefficient of some linear (parabolic) SPDEs driven by a multiplicative noise of special structure. We take the spectral…
The use of standard statistical methods, such as maximum likelihood, is often justified based on their asymptotic properties. For suitably regular models, this theory is standard but, when the model is non-regular, e.g., the support depends…
We investigate the frequentist coverage properties of Bayesian credible sets in a general, adaptive, nonparametric framework. It is well known that the construction of adaptive and honest confidence sets is not possible in general. To…
This paper develops a methodology for robust Bayesian inference through the use of disparities. Metrics such as Hellinger distance and negative exponential disparity have a long history in robust estimation in frequentist inference. We…
Models with dimension more than the available sample size are now commonly used in various applications. A sensible inference is possible using a lower-dimensional structure. In regression problems with a large number of predictors, the…
We develop a semiparametric framework for inference on the mean response in missing-data settings using a corrected posterior distribution. Our approach is tailored to Bayesian Additive Regression Trees (BART), which is a powerful…
We present a Bayesian perspective on quantifying the uncertainty of graph signals estimated or reconstructed from imperfect observations. We show that many conventional methods of graph signal estimation, reconstruction and imputation, can…
In this article we investigate consistency and asymptotic normality of the maximum likelihood and the posterior distribution of the parameters in the context of state space stochastic differential equations (SDEs). We then extend our…
In this paper we study the asymptotics of linear regression in settings with non-Gaussian covariates where the covariates exhibit a linear dependency structure, departing from the standard assumption of independence. We model the covariates…
Statistical inference for extreme values of random events is difficult in practice due to low sample sizes and inaccurate models for the studied rare events. If prior knowledge for extreme values is available, Bayesian statistics can be…
One of the fundamental tasks of science is to find explainable relationships between observed phenomena. One approach to this task that has received attention in recent years is based on probabilistic graphical modelling with sparsity…
While there is an increasing amount of literature about Bayesian time series analysis, only a few Bayesian nonparametric approaches to multivariate time series exist. Most methods rely on Whittle's Likelihood, involving the second order…