Related papers: Power Reserve Procurement Considering Dependent Ra…
We propose a flexible Bayesian approach for estimating the joint density of a multivariate outcome of interest in the presence of categorical covariates. Leveraging a Gaussian copula framework, our method effectively captures the dependence…
Variational language models seek to estimate the posterior of latent variables with an approximated variational posterior. The model often assumes the variational posterior to be factorized even when the true posterior is not. The learned…
We propose a new method for estimating the extreme quantiles for a function of several dependent random variables. In contrast to the conventional approach based on extreme value theory, we do not impose the condition that the tail of the…
We present a joint copula-based model for insurance claims and sizes. It uses bivariate copulae to accommodate for the dependence between these quantities. We derive the general distribution of the policy loss without the restrictive…
The intermittent nature of renewable power availability is one of the major sources of uncertainty in power systems. While markets can guarantee that the demand is covered by the available generation, transmission system operators have to…
We consider a class of parameter-dependent optimal control problems of elliptic PDEs with constraints of general type on the control variable. Applying the concept of variational discretization, [4], together with techniques from the…
Modeling distributions of covariates, or density estimation, is a core challenge in unsupervised learning. However, the majority of work only considers the joint distribution, which has limited utility in practical situations. A more…
In this paper we study rare events associated to solutions of elliptic partial differential equations with spatially varying random coefficients. The random coefficients follow the lognormal distribution, which is determined by a Gaussian…
Longitudinal and survival sub-models are two building blocks for joint modelling of longitudinal and time to event data. Extensive research indicates separate analysis of these two processes could result in biased outputs due to their…
We are studying the problems of modeling and inference for multivariate count time series data with Poisson marginals. The focus is on linear and log-linear models. For studying the properties of such processes we develop a novel conceptual…
Gaussian process (GP) regression has been widely used in supervised machine learning due to its flexibility and inherent ability to describe uncertainty in function estimation. In the context of control, it is seeing increasing use for…
We present a combination technique based on mixed differences of both spatial approximations and quadrature formulae for the stochastic variables to solve efficiently a class of Optimal Control Problems (OCPs) constrained by random partial…
Research on Poisson regression analysis for dependent data has been developed rapidly in the last decade. One of difficult problems in a multivariate case is how to construct a cross-correlation structure and at the meantime make sure that…
In the context of uncertainty quantification, computational models are required to be repeatedly evaluated. This task is intractable for costly numerical models. Such a problem turns out to be even more severe for stochastic simulators, the…
We consider the problem of inferring a latent function in a probabilistic model of data. When dependencies of the latent function are specified by a Gaussian process and the data likelihood is complex, efficient computation often involve…
We describe a general strategy for sampling configurations from a given distribution, NOT based on the standard Metropolis (Markov chain) strategy. It uses the fact that nontrivial problems in statistical physics are high dimensional and…
The Polynomial Chaos Expansion (PCE) technique recovers a finite second order random variable exploiting suitable linear combinations of orthogonal polynomials which are functions of a given stochas- tic quantity {\xi}, hence acting as a…
A method for estimating the Shannon differential entropy of multidimensional random variables using independent samples is described. The method is based on decomposing the distribution into a product of the marginal distributions and the…
By the classical Martingale Representation Theorem, replication of random vectors can be achieved via stochastic integrals or solutions of stochastic differential equations. We introduce a new approach to replication of random vectors via…
We introduce a novel perspective by linking ordered probabilistic choice to copula theory, a mathematical framework for modeling dependencies in multivariate distributions. Each representation of ordered probabilistic choice behavior can be…