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A Bayesian non-parametric framework for studying time-to-event data is proposed, where the prior distribution is allowed to depend on an additional random source, and may update with the sample size. Such scenarios are natural, for…
Gaussian processes constitute a very powerful and well-understood method for non-parametric regression and classification. In the classical framework, the training data consists of deterministic vector-valued inputs and the corresponding…
The logistic specification has been used extensively in non-Bayesian statistics to model the dependence of discrete outcomes on the values of specified covariates. Because the likelihood function is globally weakly concave estimation by…
Approximate numerical methods are one of the most used strategies to extract information from many-interacting-agents systems. In particular, numerical approximations are of extended use to deal with epidemic, ecological and biological…
A method for sequential inference of the fixed parameters of a dynamic latent Gaussian models is proposed and evaluated that is based on the iterated Laplace approximation. The method provides a useful trade-off between computational…
This paper presents a novel approach to level set estimation for any function/simulation with an arbitrary number of continuous inputs and arbitrary numbers of continuous responses. We present a method that uses existing data from computer…
This paper proposes approaches for the analysis of multiple changepoint models when dependency in the data is modelled through a hierarchical Gaussian Markov random field. Integrated nested Laplace approximations are used to approximate…
Many records in environmental sciences exhibit asymmetric trajectories and there is a need for simple and tractable models which can reproduce such features. In this paper we explore an approach based on applying both a time change and a…
Statistical inference for time series such as curve estimation for time-varying models or testing for existence of change-point have garnered significant attention. However, these works are generally restricted to the assumption of…
We introduce a scalable approach to Gaussian process inference that combines spatio-temporal filtering with natural gradient variational inference, resulting in a non-conjugate GP method for multivariate data that scales linearly with…
We study discrete-time stochastic processes $(X_t)$ on $[0,\infty)$ with asymptotically zero mean drifts. Specifically, we consider the critical (Lamperti-type) situation in which the mean drift at $x$ is about $c/x$. Our focus is the…
The paper deals with the asymptotic behavior of the bridge of a Gaussian process conditioned to stay in $n$ fixed points at $n$ fixed past instants. In particular, functional large deviation results are stated for small time. Several…
The growing availability of large and complex datasets has increased interest in temporal stochastic processes that can capture stylized facts such as marginal skewness, non-Gaussian tails, long memory, and even non-Markovian dynamics.…
We obtain an optimal bound for a Gaussian approximation of a large class of vector-valued random processes. Our results provide a substantial generalization of earlier results that assume independence and/or stationarity. Based on the decay…
Process-oriented theories of cognition must be evaluated against time-ordered observations. Here we present a representative example for data assimilation of the SWIFT model, a dynamical model of the control of spatial fixation position and…
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…
We focus on the problem of estimating and quantifying uncertainties on the excursion set of a function under a limited evaluation budget. We adopt a Bayesian approach where the objective function is assumed to be a realization of a Gaussian…
We study the small deviation probabilities of a family of very smooth self-similar Gaussian processes. The canonical process from the family has the same scaling property as standard Brownian motion and plays an important role in the study…
The results of a series of theoretical studies are reported, examining the convergence rate for different approximate representations of $\alpha$-stable distributions. Although they play a key role in modelling random processes with jumps…
For a sensor network, a tractable spatially-dependent node deployment model is presented with the property that the density is inversely proportional to the sink distance. A stochastic model is formulated to examine message advancements…