Building possibility distribution based on confidence intervals of parameters of Gaussian mixtures

International audienceIn parametric methods, building a probability distribution from data requires an a priori knowledge about the shape of the distribution. Once the shape is known, we can estimate the optimal parameters value from the data set. However, there is always a gap between the estimated parameters from the sample sets and true parameters, and this gap depends on the number of observations. Even if an exact estimation of parameters values might not be performed, confidence intervals for these parameters can be built. One interpretation of the quantitative possibility theory is in terms of families of probabilities that are upper and lower bounded by the associated possibility and necessity measure. In this paper, we assume that the data follow a Gaussian distribution, or a mixture of Gaussian distributions. We propose to use confidence interval parameters (computed from a sample set of data) in order to build a possibility distribution that upper approximate the family of probability distributions whose parameters are in the confidence intervals. Starting from the case of a single Gaussian distribution, we extend our approach to the case of Gaussian mixture models