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We present a method to infer reddenings and distances to stars, based only ontheir broad-band photometry, and show how this method can be used to produce athree-dimensional dust map of the Galaxy. Our method samples from the fullprobability density function of distance, reddening and stellar type forindividual stars, as well as the full uncertainty in reddening as a function ofdistance in the 3D dust map. We incorporate prior knowledge of the distributionof stars in the Galaxy and the detection limits of the survey. For stars in thePan-STARRS 1 (PS1) 3 pi survey, we demonstrate that our reddening estimates areunbiased, and accurate to ~0.13 mag in E(B-V) for the typical star. Based oncomparisons with mock catalogs, we expect distances for main-sequence stars tobe constrained to within ~20% - 60%, although this range can vary, depending onthe reddening of the star, the precise stellar type and its position on thesky. A further paper will present a 3D map of dust over the three quarters ofthe sky surveyed by PS1. Both the individual stellar inferences and the 3D dustmap will enable a wealth of Galactic science in the plane. The method wepresent is not limited to the passbands of the PS1 survey, but may be extendedto incorporate photometry from other surveys, such as 2MASS, SDSS (whereavailable), and in the future, LSST and Gaia.

Measuring Distances and Reddenings for a Billion Stars: Towards A 3D Dust Map from Pan-STARRS 1