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The Period--Luminosity relation (PLR) of Mira variable stars is an importanttool to determine astronomical distances. The common approach of estimating thePLR is a two-step procedure that first estimates the Mira periods and then runsa linear regression of magnitude on log period. When the light curves aresparse and noisy, the accuracy of period estimation decreases and can sufferfrom aliasing effects. Some methods improve accuracy by incorporating complexmodel structures at the expense of significant computational costs. Anotherdrawback of existing methods is that they only provide point estimation withoutproper estimation of uncertainty. To overcome these challenges, we develop ahierarchical Bayesian model that simultaneously models the quasi-periodicvariations for a collection of Mira light curves while estimating their commonPLR. By borrowing strengths through the PLR, our method automatically reducesthe aliasing effect, improves the accuracy of period estimation, and is capableof characterizing the estimation uncertainty. We develop a scalable stochasticvariational inference algorithm for computation that can effectively deal withthe multimodal posterior of period. The effectiveness of the proposed method isdemonstrated through simulations, and an application to observations of Mirasin the Local Group galaxy M33. Without using ad-hoc period correction tricks,our method achieves a distance estimate of M33 that is consistent withpublished work. Our method also shows superior robustness to downsampling ofthe light curves.

Simultaneous inference of periods and period-luminosity relations for Mira variable stars