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Detecting periodic variable stars is critical for many astronomical pursuits including determining distances to clusters. An important step in detecting periodic variable stars is estimating the period of a light curve. In this talk, we generalize the Lomb-Scargle period finding algorithm to multiband light curves. We incorporate constraints on phases and amplitudes across the different bands using a penalized likelihood function. We show how the penalized likelihood function is equivalent to a Bayesian prior probability distribution on phase and amplitude. We test our algorithm on I and V band Cepheid data collected by the Optical Gravitational Lensing Experiment (OGLE).

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