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The purpose of this paper is to estimate the limiting variance of asymptotically stationary Gaussian processes observed at high frequency, using the second moment estimator (SME). We study rates of convergence of the central limit theorem…
The performance of Gaussian Process (GP) regression is often hampered by the curse of dimensionality, which inflates computational cost and reduces predictive power in high-dimensional problems. Variable selection is thus crucial for…
Deep Gaussian process models typically employ discrete hierarchies, but recent advancements in differential Gaussian processes (DiffGPs) have extended these models to infinite depths. However, existing DiffGP approaches often overlook the…
Nested error regression models are useful tools for analysis of grouped data, especially in the case of small area estimation. This paper suggests a nested error regression model using uncertain random effects in which the random effect in…
We study learning problems in which the conditional distribution of the output given the input varies as a function of additional task variables. In varying-coefficient models with Gaussian process priors, a Gaussian process generates the…
We perform a Bayesian parameter inference in the context of resonantly damped transverse coronal loop oscillations. The forward problem is solved in terms of parametric results for kink waves in one-dimensional flux tubes in the thin tube…
Sparse variational Gaussian processes (GPs) construct tractable posterior approximations to GP models. At the core of these methods is the assumption that the true posterior distribution over training function values ${\bf f}$ and inducing…
We study the behavior of the posterior distribution in high-dimensional Bayesian Gaussian linear regression models having $p\gg n$, with $p$ the number of predictors and $n$ the sample size. Our focus is on obtaining quantitative finite…
We consider the problem of scalable sampling algorithms to fit Bayesian generalized linear mixed models on large datasets. Stochastic gradient Langevin dynamics, coupled with smooth re-parameterizations of variance parameters, produces…
In the usual Bayesian setting, a full probabilistic model is required to link the data and parameters, and the form of this model and the inference and prediction mechanisms are specified via de Finetti's representation. In general, such a…
Gaussian variational approximation is a popular methodology to approximate posterior distributions in Bayesian inference especially in high dimensional and large data settings. To control the computational cost while being able to capture…
Parameter identification and comparison of dynamical systems is a challenging task in many fields. Bayesian approaches based on Gaussian process regression over time-series data have been successfully applied to infer the parameters of a…
Contemporary focus on selective inference has renewed interest in the theory of selection models. In this paper, we analyze the asymptotic properties of selection models built on independent and identically distributed observations. We show…
We introduce a novel Bayesian estimator for the class proportion in an unlabeled dataset, based on the targeted learning framework. Our procedure requires the specification of a prior (and outputs a posterior) only for the target of…
This article discusses prior distributions for the parameters of Gaussian processes (GPs) that are widely used as surrogate models to emulate expensive computer simulations. The parameters typically involve mean parameters, a variance…
We study high-dimensional asymptotic performance limits of binary supervised classification problems where the class conditional densities are Gaussian with unknown means and covariances and the number of signal dimensions scales faster…
We present a new approach to semiparametric inference using corrected posterior distributions. The method allows us to leverage the adaptivity, regularization and predictive power of nonparametric Bayesian procedures to estimate…
Bayesian inference and the use of posterior or posterior predictive probabilities for decision making have become increasingly popular in clinical trials. The current practice in Bayesian clinical trials relies on a hybrid…
This paper proposes a new formulation of functional Gaussian Process regression in manifolds, based on an Empirical Bayes approach, in the spatiotemporal random field context. We apply the machinery of tight Gaussian measures in separable…
In this paper, we introduce the notion of Gaussian processes indexed by probability density functions for extending the Mat\'ern family of covariance functions. We use some tools from information geometry to improve the efficiency and the…