Marginally Parametrized Spatio-Temporal Models and Stepwise Maximum Likelihood Estimation

TL;DR

This paper introduces marginally parametrized models and stepwise maximum likelihood estimation for efficient inference in large spatio-temporal datasets, significantly reducing computational costs while maintaining accuracy.

Contribution

The paper proposes a new class of models and an estimation method that enable fast, scalable inference for complex spatio-temporal data with large parameter sets.

Findings

SMLE is at least three orders of magnitude faster than MLE.

The proposed models are applicable to large climate datasets with over five million data points.

SMLE achieves near-equivalent statistical efficiency compared to traditional MLE.

Abstract

In order to learn the complex features of large spatio-temporal data, models with large parameter sets are often required. However, estimating a large number of parameters is often infeasible due to the computational and memory costs of maximum likelihood estimation (MLE). We introduce the class of marginally parametrized (MP) models, where inference can be performed efficiently with a sequence of marginal (estimated) likelihood functions via stepwise maximum likelihood estimation (SMLE). We provide the conditions under which the stepwise estimators are consistent, and we prove that this class of models includes the diagonal vector autoregressive moving average model. We demonstrate that the parameters of this model can be obtained at least three orders of magnitude faster using SMLE compared to MLE, with only a small loss in statistical efficiency. We apply an MP model to a spatio-temporal global climate data set (in order to learn complex features of interest to climate scientists) consisting of over five million data points, and we demonstrate how estimation can be performed in less than an hour on a laptop.