Distribution type uncertainty due to sparse and imprecise data

This paper proposes a likelihood-based methodology to quantify the distribution type uncertainty while fitting probability distributions to sparse and imprecise data. In probabilistic representation of uncertainty, it is common to assume a particular type of probability distribution (e.g. normal, lognormal, etc.) while fitting distributions to available data; once this type is chosen, the distribution parameters and the uncertainty in the distribution parameters are estimated. This paper analyzes the effect of the choice of the distribution type and quantifies the resulting uncertainty in the probabilistic characterization. Two approaches – Bayesian model averaging and Bayesian hypothesis testing – are investigated for the quantification of distribution type uncertainty. Two cases – competing distribution types and uncertainty regarding a single distribution type – are considered. Once the distribution type uncertainty in a particular random variable is quantified, the uncertainty in the distribution parameters is also quantified. Further, the three types of uncertainty – variability, distribution type uncertainty, and distribution parameter uncertainty – are propagated through a response function to calculate the effect of overall input distribution uncertainty on the response uncertainty.

► Sparse and imprecise data leads to uncertainty in distribution type.
► Methods to quantify uncertainty in distribution type and parameters are developed.
► Both single model form and multiple model forms are considered.
► Bayesian model averaging and hypothesis testing methods are investigated.
► Both aleatory and epistemic uncertainties are propagated through the system model.