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

Regression analysis is widely used to create continuous representations of discrete data-sets. When the regression model is not based on the physics underlying the data, heuristic models play a crucial role and the model choice affects the data analysis. This paper identifies the most appropriate model in terms of Bayesian selection. The result is applied to two practical examples, one of which is taken from a problem of chemical thermodynamics.