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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…
We investigate the small deviation probabilities of a class of very smooth stationary Gaussian processes playing an important role in Bayesian statistical inference. Our calculations are based on the appropriate modification of the entropy…
We develop a practical framework for distinguishing diffusive stochastic processes from deterministic signals using only a single discrete time series. Our approach is based on classical excursion and crossing theorems for continuous…
Gaussian processes (GPs) are a Bayesian machine learning approach widely used to construct surrogate models for the uncertainty quantification of computer simulation codes in industrial applications. It provides both a mean predictor and an…
We study maximum likelihood estimation for spatial generalized linear mixed models with Gaussian process approximations using a stochastic Newton-Raphson algorithm. We consider two Gaussian Process approximations in this context: spectral…
A stochastic theory for the toppling activity in sandpile models is developed, based on a simple mean-field assumption about the toppling process. The theory describes the process as an anti-persistent Gaussian walk, where the diffusion…
In this paper approximation methods for infinite-dimensional Levy processes, also called (time-dependent) Levy fields, are introduced. For square integrable fields beyond the Gaussian case, it is no longer given that the one-dimensional…
Via constructing an asymptotic coupling by reflection, in this paper we establish uniform-in-time estimates on probability distances for mean-field type SDEs, where the drift terms under consideration are dissipative merely in the long…
A variational inference-based framework for training a multi-output Gaussian process latent variable model, specifically tailored to the tails-up spatio-temporal stream network, is developed. Training, given a censored observational data…
Self-similar processes are useful in modeling diverse phenomena that exhibit scaling properties. Operator scaling allows a different scale factor in each coordinate. This paper develops practical methods for modeling and simulating…
This paper studies a problem of Bayesian parameter estimation for a sequence of scaled counting processes whose weak limit is a Brownian motion with an unknown drift. The main result of the paper is that the limit of the posterior…
We compute exactly the distribution of the occupation time in a discrete {\em non-Markovian} toy sequence which appears in various physical contexts such as the diffusion processes and Ising spin glass chains. The non-Markovian property…
We study pathwise approximation of scalar stochastic differential equations at a single point. We provide the exact rate of convergence of the minimal errors that can be achieved by arbitrary numerical methods that are based (in a…
We consider the case of performing Bayesian inference for stochastic epidemic compartment models, using incomplete time course data consisting of incidence counts that are either the number of new infections or removals in time intervals of…
Bayesian optimal experimental design provides a principled framework for selecting experimental settings that maximize obtained information. In this work, we focus on estimating the expected information gain in the setting where the…
A new method called "variational sampling" is proposed to estimate integrals under probability distributions that can be evaluated up to a normalizing constant. The key idea is to fit the target distribution with an exponential family model…
We present elliptical processes, a family of non-parametric probabilistic models that subsume Gaussian processes and Student's t processes. This generalization includes a range of new heavy-tailed behaviors while retaining computational…
In applications spaning from image analysis and speech recognition, to energy dissipation in turbulence and time-to failure of fatigued materials, researchers and engineers want to calculate how often a stochastic observable crosses a…
This work aims at making a comprehensive contribution in the general area of parametric inference for discretely observed diffusion processes. Established approaches for likelihood-based estimation invoke a time-discretisation scheme for…
Gaussian couplings of partial sum processes are derived for the high-dimensional regime $d=o(n^{1/3})$. The coupling is derived for sums of independent random vectors and subsequently extended to nonstationary time series. Our inequalities…