Related papers: Copula Processes
Copulas have now become ubiquitous statistical tools for describing, analysing and modelling dependence between random variables. Sklar's theorem, "the fundamental theorem of copulas", makes a clear distinction between the continuous case…
This article proposes copula-based dependence quantification between multiple groups of random variables of possibly different sizes via the family of $Phi$-divergences. An axiomatic framework for this purpose is provided, after which we…
Deep Gaussian Processes learn probabilistic data representations for supervised learning by cascading multiple Gaussian Processes. While this model family promises flexible predictive distributions, exact inference is not tractable.…
In this paper, we establish sample path large and moderate deviation principles for log-price processes in Gaussian stochastic volatility models, and study the asymptotic behavior of exit probabilities, call pricing functions, and the…
Use copula to model dependency of variable extends multivariate gaussian assumption. In this paper we first empirically studied copula regression model with continous response. Both simulation study and real data study are given. Secondly…
We develop adaptive estimation and inference methods for high-dimensional Gaussian copula regression that achieve the same performance without the knowledge of the marginal transformations as that for high-dimensional linear regression.…
This tutorial aims to provide an intuitive introduction to Gaussian process regression (GPR). GPR models have been widely used in machine learning applications due to their representation flexibility and inherent capability to quantify…
We introduce Latent Gaussian Process Regression which is a latent variable extension allowing modelling of non-stationary multi-modal processes using GPs. The approach is built on extending the input space of a regression problem with a…
This paper addresses the problem of quantification and propagation of uncertainties associated with dependence modeling when data for characterizing probability models are limited. Practically, the system inputs are often assumed to be…
We show how to construct the implied copula process of response values from a Bayesian additive regression tree (BART) model with prior on the leaf node variances. This copula process, defined on the covariate space, can be paired with any…
Recent financial disasters have emphasised the need to accurately predict extreme financial losses and their consequences for the institutions belonging to a given financial market. The ability of econometric models to predict extreme…
In this article, we develop fully Bayesian, copula-based, spatial-statistical models for large, noisy, incomplete, and non-Gaussian spatial data. Our approach includes novel constructions of copulas that accommodate a spatial-random-effects…
Finding parametric models that accurately describe the dependence structure of observed data is a central task in the analysis of time series. Classical frequency domain methods provide a popular set of tools for fitting and diagnostics of…
We introduce a copula mixture model to perform dependency-seeking clustering when co-occurring samples from different data sources are available. The model takes advantage of the great flexibility offered by the copulas framework to extend…
The Gaussian process (GP) is a popular way to specify dependencies between random variables in a probabilistic model. In the Bayesian framework the covariance structure can be specified using unknown hyperparameters. Integrating over these…
This paper presents a unified treatment of Gaussian process models that extends to data from the exponential dispersion family and to survival data. Our specific interest is in the analysis of data sets with predictors that have an a priori…
We study an unbiased estimator for the density of a sum of random variables that are simulated from a computer model. A numerical study on examples with copula dependence is conducted where the proposed estimator performs favourably in…
Many inferential tasks involve fitting models to observed data and predicting outcomes at new covariate values, requiring interpolation or extrapolation. Conventional methods select a single best-fitting model, discarding fits that were…
We develop a scalable class of models for latent variable estimation using composite Gaussian processes, with a focus on derivative Gaussian processes. We jointly model multiple data sources as outputs to improve the accuracy of latent…
Diffusion processes are a class of stochastic differential equations (SDEs) providing a rich family of expressive models that arise naturally in dynamic modelling tasks. Probabilistic inference and learning under generative models with…