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

The period-luminosity relation (PLR) of Mira variable stars is an important tool to determine astronomical distances. common approach estimating the PLR a two-step procedure that first estimates periods and then runs linear regression magnitude on log period. When light curves are sparse noisy, accuracy period estimation decreases can suffer from aliasing effects. Some methods improve by incorporating complex model structures at expense significant computational costs. Another drawback existing they only provide point without proper uncertainty. To overcome these challenges, we develop hierarchical Bayesian simultaneously models quasi-periodic variations for collection while their PLR. By borrowing strengths through PLR, our method automatically reduces effect, improves capable characterizing We scalable stochastic variational inference algorithm computation effectively deal with multimodal posterior effectiveness proposed demonstrated simulations application observations Miras in Local Group galaxy M33. Without using ad hoc correction tricks, achieves distance estimate M33 consistent published work. Our also shows superior robustness downsampling curves.