# Ensemble Kalman methods for high-dimensional hierarchical dynamic space-time models

## TL;DR

This paper introduces a novel class of filtering and smoothing algorithms that combine ensemble Kalman methods with state-space models to enable efficient inference in high-dimensional, nonlinear, non-Gaussian spatio-temporal systems, outperforming existing methods.

## Contribution

It develops ensemble Kalman-based algorithms for high-dimensional hierarchical dynamic space-time models, integrating Bayesian inference with dimension reduction techniques.

## Key findings

- Outperforms existing ensemble Kalman, particle filters, and particle MCMC methods.
- Effective in high-dimensional, nonlinear, non-Gaussian scenarios.
- Demonstrated success with real cloud motion data.

## Abstract

We propose a new class of filtering and smoothing methods for inference in high-dimensional, nonlinear, non-Gaussian, spatio-temporal state-space models. The main idea is to combine the ensemble Kalman filter and smoother, developed in the geophysics literature, with state-space algorithms from the statistics literature. Our algorithms address a variety of estimation scenarios, including on-line and off-line state and parameter estimation. We take a Bayesian perspective, for which the goal is to generate samples from the joint posterior distribution of states and parameters. The key benefit of our approach is the use of ensemble Kalman methods for dimension reduction, which allows inference for high-dimensional state vectors. We compare our methods to existing ones, including ensemble Kalman filters, particle filters, and particle MCMC. Using a real data example of cloud motion and data simulated under a number of nonlinear and non-Gaussian scenarios, we show that our approaches outperform these existing methods.