Related papers: Parameterization of Copulas and Covariance Decay o…
The main challenges that arise when adopting Gaussian Process priors in probabilistic modeling are how to carry out exact Bayesian inference and how to account for uncertainty on model parameters when making model-based predictions on…
Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…
In the paper we consider a stochastic model which called Markov Q-processes that forms a continuous-time Markov population system. Markov Q-processes are defined as stochastic Markov branching processes with trajectories continuing in the…
We provide a computationally and statistically efficient method for estimating the parameters of a stochastic covariance model observed on a regular spatial grid in any number of dimensions. Our proposed method, which we call the Debiased…
This paper develops a systematic parametric method for analyzing stochastic systems under volatility uncertainty within the $G$-expectation framework. Leveraging the dual representation of the $G$-expectation as a supremum over a family of…
We consider joint inversion for two or more unknown parameters from observational data in the Bayesian framework. Standard approaches often either treat the parameters as independent or impose structural similarity through regularisation…
This article presents factor copula approaches to model temporal dependency of non-Gaussian (continuous/discrete) longitudinal data. Factor copula models are canonical vine copulas which explain the underlying dependence structure of a…
Regular vine copulas can describe a wider array of dependency patterns than the multivariate Gaussian copula or the multivariate Student's t copula. This paper presents two contributions related to model selection of regular vine copulas.…
Although copulas are used and defined for various infinite-dimensional objects (e.g. Gaussian processes and Markov processes), there is no prevalent notion of a copula that unifies these concepts. We propose a unified approach and define…
Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…
In this paper, we analyze the relative errors in various reliability measures due to the tacit assumption that the components associated with a $n$-component series system or a parallel system are independently working where the components…
This chapter presents specific aspects of Gaussian process modeling in the presence of complex noise. Starting from the standard homoscedastic model, various generalizations from the literature are presented: input varying noise variance,…
An approach to the modelling of volatile time series using a class of uniformity-preserving transforms for uniform random variables is proposed. V-transforms describe the relationship between quantiles of the stationary distribution of the…
We consider estimation of the parameters of a Gaussian Stochastic Process (GaSP), in the context of emulation (approximation) of computer models for which the outcomes are real-valued scalars. The main focus is on estimation of the GaSP…
Some problems in the theory and applications of stochastic processes can be reduced to solving integral equations. While explicit solutions for these equations are often elusive, valuable insights can be gained through their asymptotic…
The PC algorithm uses conditional independence tests for model selection in graphical modeling with acyclic directed graphs. In Gaussian models, tests of conditional independence are typically based on Pearson correlations, and…
Nonparanormal models describe the joint distribution of multivariate responses via latent Gaussian, and thus parametric, copulae while allowing flexible nonparametric marginals. Some aspects of such distributions, for example conditional…
We propose to model multivariate volatility processes based on the newly defined conditionally uncorrelated components (CUCs). This model represents a parsimonious representation for matrix-valued processes. It is flexible in the sense that…
We analyze a method to produce pairs of non independent Poisson processes $M(t),N(t)$ from positively correlated, self-decomposable, exponential renewals. In particular the present paper provides the family of copulas pairing the renewals,…
This paper presents an algorithm for sampling random variables that allows to separation of the sampling process into subproblems by dividing the sample space into overlapping parts. The subproblems can be solved independently of each other…