We investigate the shape of the extinction law in two 1-degree square fields of the Perseus Molecular Cloud complex. We combine deep red-optical (r, i, and z-band) observations obtained using Megacam on the MMT with UKIDSS near-infrared (J, H, and K-band) data to measure the colours of background stars. We develop a new hierarchical Bayesian statistical model, including measurement error, intrinsic colour variation, spectral type, and dust reddening, to simultaneously infer parameters for individual stars and characteristics of the population. We implement an efficient MCMC algorithm utilising generalised Gibbs sampling to compute coherent probabilistic inferences. We find a strong correlation between the extinction (Av) and the slope of the extinction law (parameterized by Rv). Because the majority of the extinction toward our stars comes from the Perseus molecular cloud, we interpret this correlation as evidence of grain growth at moderate optical depths. The extinction law changes from the diffuse value of Rv = 3 to the dense cloud value of Rv = 5 as the column density rises from Av = 2 mags to Av = 10 mags. This relationship is similar for the two regions in our study, despite their different physical conditions, suggesting that dust grain growth is a fairly universal process.
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