A Bayesian method for fitting parametric and nonparametric models to noisy data

Michael Werman*, Daniel Keren

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

71 Scopus citations


We present a simple paradigm for fitting models, parametric and nonparametric, to noisy data, which resolves some of the problems associated with classical MSE algorithms. This is done by considering each point on the model as a possible source for each data point. The paradigm can be used to solve problems which are ill-posed in the classical MSE approach, such as fitting a segment (as opposed to a line). It is shown to be nonbiased 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, elliptic arcs, segments, rectangles, and general curves, contaminated by Gaussian and uniform noise.

Original languageAmerican English
Pages (from-to)528-534
Number of pages7
JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
Issue number5
StatePublished - May 2001

Bibliographical note

Funding Information:
The authors would like to thank Dr. Alexander Goldenshluger of the Department of Statistics in the University of Haifa, for some interesting discussions. This research was supported by the Israeli Ministry of Science.


  • Bayesian fitting
  • Nonparametric models
  • Parametric models


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