Active Galactic Nuclei (AGN) vary in their brightness across all wavelengths. Moreover, longer wavelength ultraviolet - optical continuum light curves appear to be delayed with respect to shorter wavelength light curves. A simple way to model these delays is by assuming thermal reprocessing of a variable point source (a lamp post) by a blackbody accretion disc. We introduce a new method, CREAM (textbf{C}ontinuum textbf{RE}processed textbf{A}GN textbf{M}arkov Chain Monte Carlo), that models continuum variations using this lamp post model. The disc light curves lag the lamp post emission with a time delay distribution sensitive to the disc temperature-radius profile and inclination. We test CREAMs ability to recover both inclination and product of black hole mass and accretion rate $mmdot$, and show that the code is also able to infer the shape of the driving light curve. CREAM is applied to synthetic light curves expected from 1000 second exposures of a 17th magnitude AGN with a 2m telescope in Sloan g and i bands with signal to noise of 500 - 900 depending on the filter and lunar phase. We also tests CREAM on poorer quality g and i light curves with SNR = 100. We find in the high SNR case that CREAM can recover the accretion disc inclination to within an uncertainty of 5 degrees and an $mmdot$ to within 0.04 dex.
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