Maximum Likelihood from Evidential Data: An Extension of the EM Algorithm

Abstract

AbstractWe consider the problem of statistical parameter estimation when the data are uncertain and described by belief functions. An extension of the Expectation-Maximization (EM) algorithm, called the Evidential EM (E2M) algorithm, is described and shown to maximize a generalized likelihood function. This general procedure provides a simple mechanism for estimating the parameters in statistical models when observed data are uncertain. The method is illustrated using the problem of univariate normal mean and variance estimation from uncertain data.KeywordsBelief functionsDempster-Shafer theoryStatistical inferenceUncertain data