# Bayesian and Maximum Likelihood Estimation for Gaussian Processes on an Incomplete Lattice

arXiv: https://arxiv.org/abs/1402.4281 · HTML: https://mlsanity.com/paper/1402.4281/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Feb 2014.

## Built on by (most cited first, 7 of 7)

- [Faster Kernel Interpolation for Gaussian Processes](https://mlsanity.com/paper/2101.11751/) (2021)
- [Iterative Methods for Full-Scale Gaussian Process Approximations for Large Spatial Data](https://mlsanity.com/paper/2405.14492/) (2024)
- [Learning particle swarming models from data with Gaussian processes](https://mlsanity.com/paper/2106.02735/) (2021)
- [Lattice partition recovery with dyadic CART](https://mlsanity.com/paper/2105.13504/) (2021)
- [Modeling Massive Spatial Datasets Using a Conjugate Bayesian Linear Regression Framework](https://mlsanity.com/paper/2109.04447/) (2021)
- [Physics-Informed Statistical Modeling for Wildfire Aerosols Process Using Multi-Source Geostationary Satellite Remote-Sensing Data Streams](https://mlsanity.com/paper/2206.11766/) (2022)
- [Spatial Process Approximations: Assessing Their Necessity](https://mlsanity.com/paper/2311.03201/) (2023)

## Abstract (arXiv)

This paper proposes a new approach for Bayesian and maximum likelihood parameter estimation for stationary Gaussian processes observed on a large lattice with missing values. We propose an MCMC approach for Bayesian inference, and a Monte Carlo EM algorithm for maximum likelihood inference. Our approach uses data augmentation and circulant embedding of the covariance matrix, and provides exact inference for the parameters and the missing data. Using simulated data and an application to satellite sea surface temperatures in the Pacific Ocean, we show that our method provides accurate inference on lattices of sizes up to 512 x 512, and outperforms two popular methods: composite likelihood and spectral approximations.