Physical Sciences and Mathematics Commons^™

Interval Methods For Data Fitting Under Uncertainty: A Probabilistic Treatment, Vladik Kreinovich, Sergey P. Shary

Departmental Technical Reports (CS)

How to estimate parameters from observations subject to errors and uncertainty? Very often, the measurement errors are random quantities that can be adequately described by the probability theory. When we know that the measurement errors are normally distributed with zero mean, then the (asymptotically optimal) Maximum Likelihood Method leads to the popular least squares estimates. In many situations, however, we do not know the shape of the error distribution, we only know that the measurement errors are located on a certain interval. Then the maximum entropy approach leads to a uniform distribution on this interval, and the Maximum Likelihood Method …