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We study the problem of estimating the mode and maximum of an unknown regression function in the presence of noise. We adopt the Bayesian approach by using tensor-product B-splines and endowing the coefficients with Gaussian priors. In the…

Statistics Theory · Mathematics 2018-03-16 William Weimin Yoo , Subhashis Ghosal

We introduce constrained Gaussian process (CGP), a Gaussian process model for random functions that allows easy placement of mathematical constrains (e.g., non-negativity, monotonicity, etc) on its sample functions. CGP comes with…

Statistics Theory · Mathematics 2019-04-23 Jeremiah Zhe Liu

We put forward a new Bayesian modeling strategy for spatiotemporal count data that enables efficient posterior sampling. Most previous models for such data decompose logarithms of the response Poisson rates into fixed effects and spatial…

Methodology · Statistics 2025-07-29 Yifan Cheng , Cheng Li

Gaussian Process regression is a kernel method successfully adopted in many real-life applications. Recently, there is a growing interest on extending this method to non-Euclidean input spaces, like the one considered in this paper,…

Machine Learning · Computer Science 2022-12-05 Antonio Candelieri , Andrea Ponti , Francesco Archetti

We consider a combined state and drift estimation problem for the linear stochastic heat equation. The infinite-dimensional Bayesian inference problem is formulated in terms of the Kalman-Bucy filter over an extended state space, and its…

Statistics Theory · Mathematics 2020-08-18 Sebastian Reich , Paul Rozdeba

This paper aims at developing a quasi-Bayesian analysis of the nonparametric instrumental variables model, with a focus on the asymptotic properties of quasi-posterior distributions. In this paper, instead of assuming a distributional…

Statistics Theory · Mathematics 2013-11-21 Kengo Kato

We introduce a scalable Gaussian process (GP) framework with deep product kernels for data-driven learning of parametrized spatio-temporal fields over fixed or parameter-dependent domains. The proposed framework learns a continuous…

Machine Learning · Computer Science 2026-03-03 Srinath Dama , Prasanth B. Nair

We consider inverse problems in Hilbert spaces under correlated Gaussian noise and use a Bayesian approach to find their regularised solution. We focus on mildly ill-posed inverse problems with the noise being generalised derivative of…

Statistics Theory · Mathematics 2023-11-21 Natalia Bochkina , Jenovah Rodrigues

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…

Statistics Theory · Mathematics 2017-08-17 Mengyang Gu , Xiaojing Wang , James O. Berger

Approximate Bayesian computation allows for statistical analysis in models with intractable likelihoods. In this paper we consider the asymptotic behaviour of the posterior distribution obtained by this method. We give general results on…

Methodology · Statistics 2018-05-09 David T. Frazier , Gael M. Martin , Christian P. Robert , Judith Rousseau

This paper develops methodology for local sensitivity analysis based on directional derivatives associated with spatial processes. Formal gradient analysis for spatial processes was elaborated in previous papers, focusing on distribution…

Statistics Theory · Mathematics 2015-03-31 Maria A. Terres , Alan E. Gelfand

In this article, we consider the general task of performing Gaussian process regression (GPR) on pointwise observations of solutions of the 3 dimensional homogeneous free space wave equation.In a recent article, we obtained promising…

Analysis of PDEs · Mathematics 2023-11-10 Iain Henderson , Pascal Noble , Olivier Roustant

This paper studies large sample properties of a Bayesian approach to inference about slope parameters $\gamma$ in linear regression models with a structural break. In contrast to the conventional approach to inference about $\gamma$ that…

Econometrics · Economics 2023-08-15 Kenichi Shimizu

In this work we deal with the stochastic homogenization of the initial boundary value problems of monotone type. The models of monotone type under consideration describe the deformation behaviour of inelastic materials with a microstructure…

Analysis of PDEs · Mathematics 2017-01-16 Martin Heida , Sergiy Nesenenko

We study frequentist properties of a Bayesian high-dimensional multivariate linear regression model with correlated responses. The predictors are separated into many groups and the group structure is pre-determined. Two features of the…

Statistics Theory · Mathematics 2019-06-13 Bo Ning , Seonghyun Jeong , Subhashis Ghosal

Due to spatial dependence -- often characterized as complex and non-linear -- model misspecification is a prevalent and critical issue in spatial data analysis and prediction. As the data, and thus model performance, is heterogeneous,…

Model selection for regression problems with an increasing number of covariates continues to be an important problem both theoretically and in applications. Model selection consistency and mean structure reconstruction depend on the…

Statistics Theory · Mathematics 2019-05-16 Zikun Yang , Andrew Womack

We consider non-parametric Bayesian estimation of the drift coefficient of a one-dimensional stochastic differential equation from discrete-time observations on the solution of this equation. Under suitable regularity conditions that are…

Statistics Theory · Mathematics 2014-07-15 Shota Gugushvili , Peter Spreij

In application areas where data generation is expensive, Gaussian processes are a preferred supervised learning model due to their high data-efficiency. Particularly in model-based control, Gaussian processes allow the derivation of…

Machine Learning · Computer Science 2021-01-15 Armin Lederer , Jonas Umlauft , Sandra Hirche

Given a sample from a discretely observed multidimensional compound Poisson process, we study the problem of nonparametric estimation of its jump size density $r_0$ and intensity $\lambda_0$. We take a nonparametric Bayesian approach to the…

Statistics Theory · Mathematics 2015-06-08 Shota Gugushvili , Frank van der Meulen , Peter Spreij