BAYES ESTIMATION - A NOVEL-APPROACH TO DERIVATION OF INTERNALLY CONSISTENT THERMODYNAMIC DATA FOR MINERALS, THEIR UNCERTAINTIES, AND CORRELATIONS .1. THEORY

Computation of phase diagrams in mineral systems and quantitative geot hermobarometry thrive on the availability and accuracy of internally c onsistent thermodynamic datasets for minerals. The prevailing two meth odologies applied to derive them, mathematical programming (MAP) and l east squares regression (REG), have their very specific advantages and deficiencies which are to some extent complementary. Bayes estimation (BE), the novel technique proposed here for obtaining internally cons istent thermodynamic databases, can combine the advantages of both MAP and REG but avoid their drawbacks. It optimally uses the information on thermochemical, thermophysical, and volumetric properties of phases and experimental reaction reverals to refine the thermodynamic data a nd returns their uncertainties and correlations. Therefore, BE emerges as the method of choice. The theoretical background of BE, and its re lation to MAP and REG, is explained. Although BE is conceptually simpl e, it can be computationally demanding. Fortunately, modern computer t echnology and new stochastic methods such as Gibbs sampling help surmo unt those difficulties. The basic ideas behind these methods are explo red and recommendations for their use are made using the Al2SiO5 unary as an example. The potential of BE and its future perspective for app lication to multicomponent-multiphase systems appear very promising. F or the convenience of readers not interested in the mathematical detai ls of BE, an illustrative example is given in the Appendix to promote an intuitive understanding of what BE is all about.