Two- and Multi-dimensional Curve Fitting using Bayesian Inference

TL;DR

This paper develops a Bayesian inference framework for fitting curves in data, introducing a metric embedding approach that generalizes existing methods and compares favorably to frequentist and Bayesian alternatives.

Contribution

It introduces a novel formalism for Bayesian curve fitting that incorporates metric embeddings, extending previous approaches and providing a unified framework.

Findings

The formalism naturally derives the metric used in curve embedding.

Comparison shows advantages over traditional frequentist methods.

Framework generalizes existing Bayesian and frequentist curve fitting techniques.

Abstract

Fitting models to data using Bayesian inference is quite common, but when each point in parameter space gives a curve, fitting the curve to a data set requires new nuisance parameters, which specify the metric embedding the one-dimensional curve into the higher-dimensional space occupied by the data. A generic formalism for curve fitting in the context of Bayesian inference is developed which shows how the aforementioned metric arises. The result is a natural generalization of previous works, and is compared to oft-used frequentist approaches and similar Bayesian techniques.