A novel Bayesian method for fitting parametric and non-parametric models to noisy data

Abstract

We offer a simple paradigm for fitting models, parametric and non-parametric, to noisy data, which resolves some of the problems associated with classic MSE algorithms. This is done by considering each point on the model as a possible source for each data point. The paradigm also allows to solve problems which are not defined in the classical MSE approach, such as fitting a segment (as opposed to a line). It is shown to be non-biased, and to achieve excellent results for general curves, even in the presence of strong discontinuities. Results are shown for a number of fitting problems, including lines, circles, segments, and general curves, contaminated by Gaussian and uniform noise.