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

arXiv: https://arxiv.org/abs/1704.06988 · HTML: https://mlsanity.com/paper/1704.06988/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Apr 2017.

## Built on by (most cited first, 10 of 10)

- [Auto-differentiable Ensemble Kalman Filters](https://mlsanity.com/paper/2107.07687/) (2021)
- [Learning Dynamical Systems from Data: A Simple Cross-Validation Perspective, Part V: Sparse Kernel Flows for 132 Chaotic Dynamical Systems](https://mlsanity.com/paper/2301.10321/) (2023)
- [Scaling Up Bayesian Uncertainty Quantification for Inverse Problems using Deep Neural Networks](https://mlsanity.com/paper/2101.03906/) (2021)
- [Uncertainty quantification for deeponets with ensemble kalman inversion](https://mlsanity.com/paper/2403.03444/) (2024)
- [Iterated Block Particle Filter for High-dimensional Parameter Learning: Beating the Curse of Dimensionality](https://mlsanity.com/paper/2110.10745/) (2021)
- [Gaussian Ensemble Belief Propagation for Efficient Inference in High-Dimensional Systems](https://mlsanity.com/paper/2402.08193/) (2024)
- [Physics-Informed Statistical Modeling for Wildfire Aerosols Process Using Multi-Source Geostationary Satellite Remote-Sensing Data Streams](https://mlsanity.com/paper/2206.11766/) (2022)
- [Adaptive LASSO estimation for functional hidden dynamic geostatistical model](https://mlsanity.com/paper/2208.05528/) (2022)
- [Warped Dynamic Linear Models for Time Series of Counts](https://mlsanity.com/paper/2110.14790/) (2021)
- [Adversarial Transform Particle Filters](https://mlsanity.com/paper/2502.06165/) (2025)

## Abstract (arXiv)

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.