Modelling Function-Valued Processes with Nonseparable Covariance Structure

03/24/2019
by   Evandro Konzen, et al.
0

We discuss a general Bayesian framework on modelling multidimensional function-valued processes by using a Gaussian process or a heavy-tailed process as a prior, enabling us to handle nonseparable and/or nonstationary covariance structure. The nonstationarity is introduced by a convolution-based approach through a varying kernel, whose parameters vary along the input space and are estimated via a local empirical Bayesian method. For the varying anisotropy matrix, we propose to use a spherical parametrisation, leading to unconstrained and interpretable parameters. The unconstrained nature allows the parameters to be modelled as a nonparametric function of time, spatial location or other covariates. Furthermore, to extract important information in data with complex covariance structure, the Bayesian framework can decompose the function-valued processes using the eigenvalues and eigensurfaces calculated from the estimated covariance structure. The results are demonstrated by simulation studies and by an application to real data.

READ FULL TEXT

page 14

page 16

page 18

page 20

research
07/21/2022

Fixed-domain Posterior Contraction Rates for Spatial Gaussian Process Model with Nugget

Spatial Gaussian process regression models typically contain finite dime...
research
01/29/2019

GPMatch: A Bayesian Doubly Robust Approach to Causal Inference with Gaussian Process Covariance Function As a Matching Tool

Gaussian process (GP) covariance function is proposed as a matching tool...
research
04/11/2020

Covariance Estimation for Matrix-valued Data

Covariance estimation for matrix-valued data has received an increasing ...
research
01/13/2019

Learning Temporal Evolution of Spatial Dependence with Generalized Spatiotemporal Gaussian Process Models

Spatiotemporal processes are ubiquitous in our life and have been a tren...
research
02/15/2018

Modelling spatial heterogeneity and discontinuities using Voronoi tessellations

Many methods for modelling spatial processes assume global smoothness pr...
research
07/25/2014

Efficient Bayesian Nonparametric Modelling of Structured Point Processes

This paper presents a Bayesian generative model for dependent Cox point ...

Please sign up or login with your details

Forgot password? Click here to reset