Large Spatial Data Modeling and Analysis: A Krylov Subspace Approach

Event status:

You are welcome to attend the following Statistics and Stochastic colloquium (part of the Colloquium Series of the Department of Mathematics and Statistics) at La Trobe University.

Thursday 15 October 2020 12:00 pm (Add to calendar)
Andriy Olenko
Presented by:
Dr Tingjin Chu, University of Melbourne
Type of Event:

Abstract: Estimating the parameters of spatial models for large spatial datasets can be computationally challenging, as it involves repeated evaluation of sizable spatial covariance matrices. In this paper, we aim to develop Krylov subspace based methods that are computationally efficient for large spatial data. Specifically, we approximate the inverse and the log-determinant of the spatial covariance matrix in the log-likelihood function via conjugate gradient and stochastic Lanczos on a Krylov subspace. These methods reduce the computational complexity from $O(N^3)$ to $O(N^2)$ and $O(N\log N)$ for dense and sparse matrices, respectively. Moreover, we quantify the difference between the approximated log-likelihood function and the original log-likelihood function and establish the consistency of parameter estimates.  Simulation studies are conducted to examine the computational efficiency as well as the finite-sample properties. For illustration, our methodology is applied to analyze a large LiDAR dataset.

This is joint work with Jialuo Liu, Jun Zhu and Haonan Wang.




20th Oct 2020 2:27pm

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