  Due to lack of scientific understanding, some mechanisms may be missing in
mathematical modeling of complex phenomena in science and engineering. These
mathematical models thus contain some uncertainties such as uncertain
parameters. One method to estimate these parameters is based on pathwise
observations, i.e., quantifying model uncertainty in the space of sample paths
for system evolution. Another method is devised here to estimate uncertain
parameters, or unknown system functions, based on experimental observations of
probability distributions for system evolution. This is called the
quantification of model uncertainties in the space of probability measures. A
few examples are presented to demonstrate this method, analytically or
numerically.
