Likelihood-based representation of epistemic uncertainty due to sparse point data and/or interval data

This paper presents a likelihood-based methodology for a probabilistic representation of a stochastic quantity for which only sparse point data and/or interval data may be available. The likelihood function is evaluated from the probability density function (PDF) for sparse point data and the cumulative distribution function for interval data. The full likelihood function is used in this paper to calculate the entire PDF of the distribution parameters. The uncertainty in the distribution parameters is integrated to calculate a single PDF for the quantity of interest. The approach is then extended to non-parametric PDFs, wherein the entire distribution can be discretized at a finite number of points and the probability density values at these points can be inferred using the principle of maximum likelihood, thus avoiding the assumption of any particular distribution. The proposed approach is demonstrated with challenge problems from the Sandia Epistemic Uncertainty Workshop and the results are compared with those of previous studies that pursued different approaches to represent and propagate interval description of input uncertainty.