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We develop a non-linear semi-parametric Gaussian process model to estimateperiods of Miras with sparsely-sampled light curves. The model uses asinusoidal basis for the periodic variation and a Gaussian process for thestochastic changes. We use maximum likelihood to estimate the period and theparameters of the Gaussian process, while integrating out the effects of othernuisance parameters in the model with respect to a suitable prior distributionobtained from earlier studies. Since the likelihood is highly multimodal forperiod, we implement a hybrid method that applies the quasi-Newton algorithmfor Gaussian process parameters and search the period/frequency parameter overa dense grid.  A large-scale, high-fidelity simulation is conducted to mimic the samplingquality of Mira light curves obtained by the M33 Synoptic Stellar Survey. Thesimulated data set is publicly available and can serve as a testbed for futureevaluation of different period estimation methods. The semi-parametric modeloutperforms an existing algorithm on this simulated test data set as measuredby period recovery rate and quality of the resulting Period-Luminosityrelations.

Period estimation for sparsely-sampled quasi-periodic light curves applied to Miras