Related papers: New approaches to Bayesian consistency

(This is the third version of a working paper.) We develop a family of self-normalized concentration inequalities for marginal mean under martingale-difference structure and $\phi/\tilde{\phi}$-mixing conditions, where the latter includes…

We consider the problem of parameter estimation in a Bayesian setting and propose a general lower-bound that includes part of the family of $f$-Divergences. The results are then applied to specific settings of interest and compared to other…

A Berry-Esseen bound is obtained for self-normalized martingales under the assumption of finite moments. The bound coincides with the classical Berry-Esseen bound for standardized martingales. An example is given to show the optimality of…

We consider the use of randomised forward models and log-likelihoods within the Bayesian approach to inverse problems. Such random approximations to the exact forward model or log-likelihood arise naturally when a computationally expensive…

In an empirical Bayesian setting, we provide a new multiple testing method, useful when an additional covariate is available, that influences the probability of each null hypothesis being true. We measure the posterior significance of each…

This paper introduces and reviews some of the principles and methods used in Bayesian reliability. It specifically discusses methods used in the analysis of success/no-success data and then reminds the reader of a simple Monte Carlo…

Complementing the analysis in [41], we investigate the well-posedness of SPDEs problems of doubly nonlinear type. These arise ubiquitously in the modelization of dissipative media and correspond to generalized balance laws between…

In this survey we borrow from Coskun and Huizenga an example of application of Bridgeland stability conditions to birational geometry and we rephrase it without assuming any previous knowledge about derived categories.

We propose one and a half criteria for determining how many measurements are needed to quantify entanglement reliably. We base these criteria on Bayesian analysis of measurement results, and apply our methods to four-qubit entanglement, but…

We investigate stability conditions related to the existence of solutions of the Hull-Strominger system with prescribed balanced class. We build on recent work by the authors, where the Hull-Strominger system is recasted using non-Hermitian…

The sample mean is often used to aggregate different unbiased estimates of a parameter, producing a final estimate that is unbiased but possibly high-variance. This paper introduces the Bayesian median of means, an aggregation rule that…

With the advent of high-performance computing, Bayesian methods are increasingly popular tools for the quantification of uncertainty throughout science and industry. Since these methods impact the making of sometimes critical decisions in…

We present three tiers of Bayesian consistency tests for the general case of $correlated$ datasets. Building on duplicates of the model parameters assigned to each dataset, these tests range from Bayesian evidence ratios as a global summary…

Necessary and sufficient conditions for bipartite entanglement are derived, which apply to arbitrary Hilbert spaces. Motivated by the concept of witnesses, optimized entanglement inequalities are formulated solely in terms of arbitrary…

Stacking is a widely used model averaging technique that asymptotically yields optimal predictions among linear averages. We show that stacking is most effective when model predictive performance is heterogeneous in inputs, and we can…

In this note, we shortly survey some recent approaches on the approximation of the Bayes factor used in Bayesian hypothesis testing and in Bayesian model choice. In particular, we reassess importance sampling, harmonic mean sampling, and…

Using Bridgeland stability conditions we give sufficient criteria for a stable vector bundle on a surface to remain stable when restricted to a curve. We give a stronger criterion when the vector bundle is a general vector bundle on the…

Bayesian statistics is concerned with conducting posterior inference for the unknown quantities in a given statistical model. Conventional Bayesian inference requires the specification of a probabilistic model for the observed data, and the…

This paper shows that large nonparametric classes of conditional multivariate densities can be approximated in the Kullback--Leibler distance by different specifications of finite mixtures of normal regressions in which normal means and…

In this paper we consider the problem of multiple testing when the hypotheses are dependent. In most of the existing literature, either Bayesian or non-Bayesian, the decision rules mainly focus on the validity of the test procedure rather…