Skip to main content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.


The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Estimating the Parameters of Circles and Ellipses Using Orthogonal Distance Regression and Bayesian Errors-in-Variables Regression



Jolene D. Splett, Felix M. Jimenez, Amanda A. Koepke


In ordinary least-squares regression, independent variables are assumed to be known without error. However, in many real-life situations this assumption is not valid. Both orthogonal distance regression and Bayesian errors-in-variables regression can be used to estimate model parameters when there are errors in the dependent and independent variables. To illustrate the use of the maximum-likelihood and Bayesian approaches, we use both methods to estimate the parameters of a circle. The data used for circle fitting were taken from the cross section of an optical fiber. The shape of optical fibers is important when joining two fibers, so accurate dimensional measurements are critical to minimizing coupling loss. We then compare the results of the two techniques when fitting an ellipse to simulated data. Circle and ellipse fitting using maximum-likelihood methods have been well documented; however, Bayesian methods for these tasks are less developed. As expected, we found that the Bayesian approach for circle fitting is more intuitive and easier to implement than the maximum-likelihood approach, but generalizing the Bayesian approach to ellipse fitting was surprisingly difficult.
Proceedings Title
JSM Proceedings
Conference Dates
July 28-August 1, 2019
Conference Location
Denver, CO
Conference Title
2019 Joint Statistical Meetings


Bayesian statistics, circle fitting, ellipse fitting, errors-in-variables regression, orthogonal distance regression
Created December 5, 2019, Updated December 12, 2019