Related papers: Stability of doubly-intractable distributions
We study the distributionally robust optimization (DRO) in a dynamic context where the model uncertainty is captured by penalizing potential models in function of their adapted Wasserstein distance to a given reference model. We consider…
We derive normal approximation bounds in the Wasserstein distance for sums of weighted U-statistics, based on a general distance bound for functionals of independent random variables of arbitrary distributions. Those bounds are applied to…
Ranking distributions according to a stochastic order has wide applications in diverse areas. Although stochastic dominance has received much attention, convex order, particularly in general dimensions, has yet to be investigated from a…
Doubly intractable problems occur when both the likelihood and the posterior are available only in unnormalised form, with computationally intractable normalisation constants. Bayesian inference then typically requires direct approximation…
Formulating a statistical inverse problem as one of inference in a Bayesian model has great appeal, notably for what this brings in terms of coherence, the interpretability of regularisation penalties, the integration of all uncertainties,…
If the prior probability distributions of all possible hypothetical true means and all possible observed means of a continuous variable are conditional on the universal set of all numbers (i.e., before the nature of a study is known and a…
We investigate the use of the Metropolis-Hastings algorithm to sample posterior distribution in a Bayesian inverse problem, where the likelihood function is random. Concretely, we consider the case where one has full field observations of a…
We study distributionally robust optimization (DRO) problems with uncertainty sets consisting of high-dimensional random vectors that are close in the multivariate Wasserstein distance to a reference random vector. We give conditions when…
The prior distribution on parameters of a sampling distribution is the usual starting point for Bayesian uncertainty quantification. In this paper, we present a different perspective which focuses on missing observations as the source of…
Piecewise constant priors are routinely used in the Bayesian Cox proportional hazards model for survival analysis. Despite its popularity, large sample properties of this Bayesian method are not yet well understood. This work provides a…
Inference for doubly intractable distributions is challenging because the intractable normalizing functions of these models include parameters of interest. Previous auxiliary variable MCMC algorithms are infeasible for multi-dimensional…
This short note is on a property of the $\mathcal{W}_2$ Wasserstein distance which indicates that independent elliptical distributions minimize their $\mathcal{W}_2$ Wasserstein distance from given independent elliptical distributions with…
Wasserstein distributionally robust optimization (WDRO) strengthens statistical learning under model uncertainty by minimizing the local worst-case risk within a prescribed ambiguity set. Although WDRO has been extensively studied in…
This article extends the framework of Bayesian inverse problems in infinite-dimensional parameter spaces, as advocated by Stuart (Acta Numer. 19:451--559, 2010) and others, to the case of a heavy-tailed prior measure in the family of stable…
Probability functions figure prominently in optimization problems of engineering. They may be nonsmooth even if all input data are smooth.This fact motivates the consideration of subdifferentials for such typically just continuous…
We study the weighted total variation distance between probability measures. Using Fourier-analytic tools, we present estimates in terms of Wasserstein distances between the respective probabilities, under appropriate smoothness and moment…
We establish a general, non-asymptotic error analysis framework for understanding the effects of incremental approximations made by practical approaches for Bayesian sequential learning (BSL) on their long-term inference performance. Our…
Multivariate extreme value statistical analysis is concerned with observations on several variables which are thought to possess some degree of tail-dependence. In areas such as the modeling of financial and insurance risks, or as the…
The sliced Wasserstein (SW) distances between two probability measures are defined as the expectation of the Wasserstein distance between two one-dimensional projections of the two measures. The randomness comes from a projecting direction…
In many applications in statistics and machine learning, the availability of data samples from multiple possibly heterogeneous sources has become increasingly prevalent. On the other hand, in distributionally robust optimization, we seek…