This document presents a method for parameter estimation in statistical models when data is uncertain and represented as belief functions. The method maximizes a generalized likelihood criterion to estimate parameters, which measures the agreement between the statistical model and uncertain observations. An EM algorithm is proposed to iteratively maximize this criterion. The method is demonstrated on uncertain data clustering using finite mixture models for categorical and continuous attributes.

1. MAXIMUM LIKELIHOOD ESTIMATION FROM UNCERTAIN DATA IN THE
BELIEF FUNCTION FRAMEWORK
ABSTRACT:
We consider the problem of parameter estimation in statistical models in the case where data are
uncertain and represented as belief functions. The proposed method is based on the maximization
of a generalized likelihood criterion, which can be interpreted as a degree of agreement between
the statistical model and the uncertain observations. We propose a variant of the EM algorithm
that iteratively maximizes this criterion. As an illustration, the method is applied to uncertain
data clustering using finite mixture models, in the cases of categorical and continuous attributes.
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