Estimating a Common Period for a Set of Irregularly Sampled Functions with Applications to Periodic Variable Star Data

TL;DR

This paper introduces two novel methods, MGLS and PGLS, for estimating a common period in irregularly sampled functions, especially effective when data is sparse across all filters, with applications to variable star observations.

Contribution

The paper presents two new period estimation methods that improve accuracy in poorly-sampled data, extending existing techniques with a penalized likelihood approach and efficient optimization algorithms.

Findings

PGLS outperforms MGLS in extremely poorly-sampled scenarios.

Both methods improve period estimation accuracy over existing techniques.

Methods validated on synthetic and real astronomical data.

Abstract

We consider the estimation of a common period for a set of functions sampled at irregular intervals. The problem arises in astronomy, where the functions represent a star's brightness observed over time through different photometric filters. While current methods can estimate periods accurately provided that the brightness is well--sampled in at least one filter, there are no existing methods that can provide accurate estimates when no brightness function is well--sampled. In this paper we introduce two new methods for period estimation when brightnesses are poorly--sampled in all filters. The first, multiband generalized Lomb-Scargle (MGLS), extends the frequently used Lomb-Scargle method in a way that na\"{i}vely combines information across filters. The second, penalized generalized Lomb-Scargle (PGLS), builds on the first by more intelligently borrowing strength across filters. Specifically, we incorporate constraints on the phases and amplitudes across the different functions using a non--convex penalized likelihood function. We develop a fast algorithm to optimize the penalized likelihood by combining block coordinate descent with the majorization-minimization (MM) principle. We illustrate our methods on synthetic and real astronomy data. Both advance the state-of-the-art in period estimation; however, PGLS significantly outperforms MGLS when all functions are extremely poorly--sampled.