Related papers: On the Simulation of General Multivariate Gamma Di…
Gaussian Processes (GPs) are a powerful tool for probabilistic modeling, but their performance is often constrained in complex, large-scale real-world domains due to the limited expressivity of classical kernels. Quantum computing offers…
In this article, we present some specific aspects of symmetric Gamma process mixtures for use in regression models. We propose a new Gibbs sampler for simulating the posterior and we establish adaptive posterior rates of convergence related…
This article provides a general expression for infinitely divisible multivariate gamma distributions defined by their Laplace transforms, as well as the conditional Laplace transform of infinitely divisible multivariate gamma…
We provide a new approach to approximate emulation of large computer experiments. By focusing expressly on desirable properties of the predictive equations, we derive a family of local sequential design schemes that dynamically define the…
We consider Bayesian inference problems with computationally intensive likelihood functions. We propose a Gaussian process (GP) based method to approximate the joint distribution of the unknown parameters and the data. In particular, we…
We propose a family of multivariate Gaussian process models for correlated outputs, based on assuming that the likelihood function takes the generic form of the multivariate exponential family distribution (EFD). We denote this model as a…
A multivariate extension of the Dickman distribution was recently introduced, but very few properties have been studied. We discuss several properties with an emphasis on simulation. Further, we introduce and study a multivariate extension…
Bayesian analysis for Markov jump processes is a non-trivial and challenging problem. Although exact inference is theoretically possible, it is computationally demanding thus its applicability is limited to a small class of problems. In…
Deep Gaussian Processes (DGPs) compose GP layers to warp inputs, enabling improved emulation of computer models with nonstationary input-output behavior compared with ordinary GPs. In contrast to GPs, the predictive uncertainty for DGP…
We present a class of L\'evy processes for modelling financial market fluctuations: Bilateral Gamma processes. Our starting point is to explore the properties of bilateral Gamma distributions, and then we turn to their associated L\'evy…
We introduce an approach to quickly and accurately approximate the cumulative distribution function of multivariate Gaussian distributions arising from spatial Gaussian processes. This approximation is trivially parallelizable and simple to…
In this paper, we propose decentralized and scalable algorithms for Gaussian process (GP) training and prediction in multi-agent systems. To decentralize the implementation of GP training optimization algorithms, we employ the alternating…
Deep Gaussian processes (DGPs) are multi-layer hierarchical generalisations of Gaussian processes (GPs) and are formally equivalent to neural networks with multiple, infinitely wide hidden layers. DGPs are nonparametric probabilistic models…
We study the Stochastic Gradient Descent (SGD) method in nonconvex optimization problems from the point of view of approximating diffusion processes. We prove rigorously that the diffusion process can approximate the SGD algorithm weakly…
The Darwin approximation is investigated for its possible use in simulation of electromagnetic effects in large size, high frequency capacitively coupled discharges. The approximation is utilized within the framework of two different fluid…
In this paper we propose an objective Bayesian estimation approach for the parameters of the generalized gamma distribution. Various reference priors are obtained, but showing that they lead to improper posterior distributions. We overcome…
Gaussian process (GP) regression with 1D inputs can often be performed in linear time via a stochastic differential equation formulation. However, for non-Gaussian likelihoods, this requires application of approximate inference methods…
We propose simple methods for multivariate diffusion bridge simulation, which plays a fundamental role in simulation-based likelihood and Bayesian inference for stochastic differential equations. By a novel application of classical coupling…
Approximating complex probability distributions, such as Bayesian posterior distributions, is of central interest in many applications. We study the expressivity of geometric Gaussian approximations. These consist of approximations by…
Gaussian processes are a powerful class of non-linear models, but have limited applicability for larger datasets due to their high computational complexity. In such cases, approximate methods are required, for example, the recently…