Related papers: A New Look at Bayesian Testing
Bayesian model selection provides a formal method of determining the level of support for new parameters in a model. However, if there is not a specific enough underlying physical motivation for the new parameters it can be hard to assign…
The standard Bayesian Information Criterion (BIC) is derived under regularity conditions which are not always satisfied by the graphical models with hidden variables. In this paper we derive the BIC score for Bayesian networks in the case…
New problems arise when the standard theory of joint detection and estimation is applied to a set of signals drawn from a continuous family; decision thresholds must be determined as a function of the continuous parameter x characterizing…
Despite the popularity of the false discovery rate (FDR) as an error control metric for large-scale multiple testing, its close Bayesian counterpart the local false discovery rate (lfdr), defined as the posterior probability that a…
A central problem in the theory of empirical Bayes is to control the regret (excess risk) of a learned Bayes rule by the Hellinger distance between the estimated and true marginal densities. In the normal means model, the classical result…
The aim of this paper is to discuss both higher-order asymptotic expansions and skewed approximations for the Bayesian Discrepancy Measure for testing precise statistical hypotheses. In particular, we derive results on third-order…
We study the posterior distribution of the Bayesian multiple change-point regression problem when the number and the locations of the change-points are unknown. While it is relatively easy to apply the general theory to obtain the…
The Bayes linear estimator is derived by minimizing the Bayes risk with respect to the squared loss function. Non-unbiased estimators such as ordinary ridge, typical shrinkage, fractional rank, and restricted least squares estimators, as…
Bayesian parameter inference depends on a choice of prior probability distribution for the parameters in question. The prior which makes the posterior distribution maximally sensitive to data is called the Jeffreys prior, and it is…
Adversarial examples pose a security threat to many critical systems built on neural networks. Given that deterministic robustness often comes with significantly reduced accuracy, probabilistic robustness (i.e., the probability of having…
We consider estimation of a multivariate normal mean vector under sum of squared error loss. We propose a new class of smooth estimators parameterized by \alpha dominating the James-Stein estimator. The estimator for \alpha=1 corresponds to…
Confidence sequences based on test martingales provide time-uniform uncertainty quantification for the mean of bounded IID observations without parametric distributional assumptions. Their practical efficiency, however, depends strongly on…
Measurement error occurs when a covariate influencing a response variable is corrupted by noise. This can lead to misleading inference outcomes, particularly in problems where accurately estimating the relationship between covariates and…
We give a sufficient condition for admissibility of generalized Bayes estimators of the location vector of spherically symmetric distribution under squared error loss. Compared to the known results for the multivariate normal case, our…
Towards understanding the fundamental limits of estimation from data of varied quality, we study the problem of estimating a mean parameter from heteroskedastic Gaussian observations where the variances are unknown and may vary arbitrarily…
The local false discovery rate (lfdr) of Efron et al. (2001) enjoys major conceptual and decision-theoretic advantages over the false discovery rate (FDR) as an error criterion in multiple testing, but is only well-defined in Bayesian…
Conventional Bayesian estimation requires an accurate stochastic model of a system. However, this requirement is not always met in many practical cases where the system is not completely known or may differ from the assumed model. For such…
Generalization error (also known as the out-of-sample error) measures how well the hypothesis learned from training data generalizes to previously unseen data. Proving tight generalization error bounds is a central question in statistical…
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…
We consider symmetric hypothesis testing in quantum statistics, where the hypotheses are density operators on a finite-dimensional complex Hilbert space, representing states of a finite quantum system. We prove a lower bound on the…