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Abstract:
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In preparation for the era of the LSST-driven time-domain astronomy, we propose a state-space representation of a multivariate damped random walk process as a tool to analyze irregularly-spaced multi-filter light curves of an astronomical object with heteroscedastic measurement errors. It is not necessary that the multi-band observations be measured at the same time and multiple light curves be of the same length. Thus, the proposed process is suitable for the multi-band light curves of the LSST in particular. We adopt a computationally efficient Kalman-filtering approach to evaluate the likelihood function of the proposed model, leading to O(k^3n) complexity, where k is the number of bands and n is the total number of observations across the bands. This is a significant computational advantage over a commonly used O(k^3n^3) approach based on a univariate Gaussian process that stacks up all multi-filter light curves in one vector. Using this efficient likelihood evaluation, we provide both maximum likelihood estimates and Bayesian posterior samples of the model parameters. We apply the proposed process to several astronomical data sets for numerical illustrations.
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