We present a robust statistical analysis of the white dwarf coolingsequence in 47 Tucanae. We combine Hubble Space Telescope UV and opticaldata in the core of the cluster, Modules for Experiments in StellarEvolution (MESA) white dwarf cooling models, white dwarf atmospheremodels, artificial star tests, and a Markov Chain Monte Carlo samplingmethod to fit white dwarf cooling models to our data directly. We use atechnique known as the unbinned maximum likelihood to fit these modelsto our data without binning. We use these data to constrain neutrinoproduction and the thickness of the hydrogen layer in these whitedwarfs. The data prefer thicker hydrogen layers({q}{{H}}=3.2× {10}-5) and we can stronglyrule out thin layers ({q}{{H}}={10}-6). Theneutrino rates currently in the models are consistent with the data.This analysis does not provide a constraint on the number of neutrinospecies.