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

TL;DR

This paper introduces a Bayesian approach to estimate the degree of a polynomial from noisy data, improving model selection in regression analysis for physical systems.

Contribution

It formulates polynomial degree estimation as a Bayesian model selection problem, applying probability calculus to choose the best model for thermodynamic PDEs.

Findings

Effective Bayesian method for polynomial degree estimation

Application to univariate and bivariate polynomial models

Enhanced model selection accuracy in thermodynamics

Abstract

A widely used method to create a continuous representation of a discrete data-set is regression analysis. When the regression model is not based on a mathematical description of the physics underlying the data, heuristic techniques play a crucial role and the model choice can have a significant impact on the result. In this paper, the problem of identifying the most appropriate model is formulated and solved in terms of Bayesian selection. Besides, probability calculus is the best way to choose among different alternatives. The results obtained are applied to the case of both univariate and bivariate polynomials used as trial solutions of systems of thermodynamic partial differential equations.