Optimal extinction measurements: I. Single-object extinction inference

In this paper we present XNICER, an optimized multi-band extinction technique based on the extreme deconvolution of the intrinsic colors of objects observed through a molecular cloud. XNICER follows a rigorous statistical approach and provides the full Bayesian inference of the extinction for each observed object. Photometric errors in both the training control field and in the science field are properly taken into account. XNICER improves over the known extinction methods and is computationally fast enough to be used on large datasets of objects. Our tests and simulations show that this method is able to reduce the noise associated with extinction measurements by a factor 2 with respect to the previous NICER algorithm, and it has no evident bias even at high extinctions.