Related papers: Some Results on Tighter Bayesian Lower Bounds on t…

In many practical parameter estimation problems, such as coefficient estimation of polynomial regression, the true model is unknown and thus, a model selection step is performed prior to estimation. The data-based model selection step…

In this paper we analyze, for a model of linear regression with gaussian covariates, the performance of a Bayesian estimator given by the mean of a log-concave posterior distribution with gaussian prior, in the high-dimensional limit where…

Contemporary sample size calculations for external validation of risk prediction models require users to specify fixed values of assumed model performance metrics alongside target precision levels (e.g., 95% CI widths). However, due to the…

Approximate Bayesian computation (ABC) is a widely used inference method in Bayesian statistics to bypass the point-wise computation of the likelihood. In this paper we develop theoretical bounds for the distance between the statistics used…

The standard asymmetric Laplace framework for Bayesian quantile regression (BQR) suffers from a fundamental decision-theoretic misalignment, yielding biased finite-sample estimates, and precludes gradient-based computation due to…

The Bayesian lasso is well-known as a Bayesian alternative for Lasso. Although the advantage of the Bayesian lasso is capable of full probabilistic uncertain quantification for parameters, the corresponding posterior distribution can be…

Regularized system identification has become a significant complement to more classical system identification. It has been numerically shown that kernel-based regularized estimators often perform better than the maximum likelihood estimator…

In some applied scenarios, the availability of complete data is restricted, often due to privacy concerns; only aggregated, robust and inefficient statistics derived from the data are made accessible. These robust statistics are not…

Using differential geometry, I derive a form of the Bayesian Cram\'er-Rao bound that remains invariant under reparametrization. With the invariant formulation at hand, I find the optimal and naturally invariant bound among the Gill-Levit…

Clustering procedures typically estimate which data points are clustered together, a quantity of primary importance in many analyses. Often used as a preliminary step for dimensionality reduction or to facilitate interpretation, finding…

In this article we perform an asymptotic analysis of parallel Bayesian logspline density estimators. Such estimators are useful for the analysis of datasets that are partitioned into subsets and stored in separate databases without the…

Bayesian nonparametric mixture models are widely used to cluster observations. However, one major drawback of the approach is that the estimated partition often presents unbalanced clusters' frequencies with only a few dominating clusters…

McDiarmid's inequality has recently been proposed as a tool for setting margin requirements for complex systems. If $F$ is the bounded output of a complex system, depending on a vector of $n$ bounded inputs, this inequality provides a bound…

This paper derives lower bounds for the mean square errors of parameter estimators in the case of Poisson distributed data subjected to multiple abrupt changes. Since both change locations (discrete parameters) and parameters of the Poisson…

We consider the problem of estimating a random state vector when there is information about the maximum distances between its subvectors. The estimation problem is posed in a Bayesian framework in which the minimum mean square error (MMSE)…

An empirical Bayes approach to the estimation of possibly sparse sequences observed in Gaussian white noise is set out and investigated. The prior considered is a mixture of an atom of probability at zero and a heavy-tailed density \gamma,…

Model averaging methods have become an increasingly popular tool for improving predictions and dealing with model uncertainty, especially in Bayesian settings. Recently, frequentist model averaging methods such as information theoretic and…

Manifold-valued parameters routinely arise in modern statistical applications such as in medical imaging, robotics, and computer vision, to name a few. While traditional Bayesian approaches are applicable to such settings by considering an…

We compute a variance lower bound for unbiased estimators in specified statistical models. The construction of the bound is related to the original Cram\'er-Rao bound, although it does not require the differentiability of the model.…

Bayesian Neural Networks (BNNs) provide a tool to estimate the uncertainty of a neural network by considering a distribution over weights and sampling different models for each input. In this paper, we propose a method for uncertainty…