  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.
