State-space representation of Mat\'ern and Damped Simple Harmonic Oscillator Gaussian processes

TL;DR

This paper derives analytic state-space models for specific Gaussian processes, including the damped harmonic oscillator and certain Matérn processes, enabling more efficient likelihood evaluation in astronomical time series analysis.

Contribution

It provides new analytic state-space representations for these Gaussian processes, improving computational efficiency for their application.

Findings

Derived explicit state-space models for damped harmonic oscillator and Matérn processes.

Enables O(n) likelihood evaluation for these Gaussian processes.

Facilitates more efficient analysis of astronomical time series data.

Abstract

Gaussian processes (GPs) are used widely in the analysis of astronomical time series. GPs with rational spectral densities have state-space representations which allow O(n) evaluation of the likelihood. We calculate analytic state space representations for the damped simple harmonic oscillator and the Mat\'ern 1/2, 3/2 and 5/2 processes.