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A widely used method to create a continuous representation of a discretedata-set is regression analysis. When the regression model is not based on amathematical description of the physics underlying the data, heuristictechniques play a crucial role and the model choice can have a significantimpact on the result. In this paper, the problem of identifying the mostappropriate model is formulated and solved in terms of Bayesian selection.Besides, probability calculus is the best way to choose among differentalternatives. The results obtained are applied to the case of both univariateand bivariate polynomials used as trial solutions of systems of thermodynamicpartial differential equations.

Bayesian estimate of the degree of a polynomial given a noisy data sample