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We describe how to consistently incorporate solar model uncertainties, alongwith experimental errors and correlations, when analyzing solar neutrino datato derive confidence limits on parameter space for proposed solutions of thesolar neutrino problem. Our work resolves ambiguities and inconsistencies inthe previous literature. As an application of our methods we calculate themasses and mixing angles allowed by the current data for the proposed MSWsolution using both Bayesian and frequentist methods, allowing purely for solarmodel flux variations, to compare with previous work. We consider the effectsof including metal diffusion in the solar models and also discuss implicationsfor future experiments.Comment: 29 pages (incl figs), latex, 6 figures (appended as separate  uuencoded file. To embed figures in text, uncomment 6 \epsfysize lines which  appear before bibliography), CWRU-P5-94, CfPA-94-TTH-29,  Fermilab-Pub-94/176-

Treating solar model uncertainties: A consistent statistical analysis of solar neutrino models and data