相关论文: On the behavior of Bayesian credible intervals for…

We address the problem of producing a lower bound for the mean of a discrete probability distribution, with known support over a finite set of real numbers, from an iid sample of that distribution. Up to a constant, this is equivalent to…

A rigorous lower bound is obtained for the average resolution of any estimate of a shift parameter, such as an optical phase shift or a spatial translation. The bound has the asymptotic form k_I/<2|G|> where G is the generator of the shift…

Say $X_1,X_2,\ldots$ are independent identically distributed Bernoulli random variables with mean $p$. This paper builds a new estimate $\hat p$ of $p$ that has the property that the relative error, $\hat p /p - 1$, of the estimate does not…

For ill-posed inverse problems, a regularised solution can be interpreted as a mode of the posterior distribution in a Bayesian framework. This framework enriches the set the solutions, as other posterior estimates can be used as a solution…

In random parameter estimation, Bayesian lower bounds (BLBs) for the mean-square error have been noticed to not be tight in a number of cases, even when the sample size, or the signal-to-noise ratio, grow to infinity. In this paper, we…

Bootstrap smoothed (bagged) parameter estimators have been proposed as an improvement on estimators found after preliminary data-based model selection. The key result of Efron (2014) is a very convenient and widely applicable formula for a…

We study nonparametric Bayesian binary classification, in the case where the unknown probability response function is possibly spatially inhomogeneous, for example, being generally flat across the domain but presenting localized sharp…

The high energy physics unfolding problem is an important statistical inverse problem in data analysis at the Large Hadron Collider (LHC) at CERN. The goal of unfolding is to make nonparametric inferences about a particle spectrum from…

We establish sparse Hanson-Wright inequalities for quadratic forms of sparse $\alpha$-sub-exponential random vectors with exponent parameter $\alpha\in(0, 2]$. In the regime $0< \alpha\le 1$ we derive a refined inequality that is optimal in…

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…

A reasonable confidence interval should have a confidence coefficient no less than the given nominal level and a small expected length to reliably and accurately estimate the parameter of interest, and the bootstrap interval is considered…

We show that lower-dimensional marginal densities of dependent zero-mean normal distributions truncated to the positive orthant exhibit a mass-shifting phenomenon. Despite the truncated multivariate normal density having a mode at the…

We perform accurate numerical experiments with fully-connected (FC) one-hidden layer neural networks trained with a discretized Langevin dynamics on the MNIST and CIFAR10 datasets. Our goal is to empirically determine the regimes of…

We provide finite-sample distribution approximations, that are uniform in the parameter, for inference in linear mixed models. Focus is on variances and covariances of random effects in cases where existing theory fails because their…

Modeled along the truncated approach in Panigrahi (2016), selection-adjusted inference in a Bayesian regime is based on a selective posterior. Such a posterior is determined together by a generative model imposed on data and the selection…

The ratio of Bayesian evidences is a popular tool in cosmology to compare different models. There are however several issues with this method: Bayes' ratio depends on the prior even in the limit of non-informative priors, and Jeffrey's…

We provide lower error bounds for randomized algorithms that approximate integrals of functions depending on an unrestricted or even infinite number of variables. More precisely, we consider the infinite-dimensional integration problem on…

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…

A fundamental issue in real-world systems, such as sensor networks, is the selection of observations which most effectively reduce uncertainty. More specifically, we address the long standing problem of nonmyopically selecting the most…

We study high-dimensional Bayesian linear regression with a general beta prime distribution for the scale parameter. Under the assumption of sparsity, we show that appropriate selection of the hyperparameters in the beta prime prior leads…