  The uncertainty quantifications of theoretical results are of great
importance to make meaningful comparisons of those results with experimental
data and to make predictions in experimentally unknown regions. By quantifying
uncertainties, one can make more solid statements about, e.g., origins of
discrepancy in some quantities between theory and experiment. We propose a
novel method for uncertainty quantification for the effective interactions of
nuclear shell-model calculations as an example. The effective interaction is
specified by a set of parameters, and its probability distribution in the
multi-dimensional parameter space is considered. This enables us to quantify
the agreement with experimental data in a statistical manner and the resulting
confidence intervals show unexpectedly large variations. Moreover, we point out
that a large deviation of the confidence interval for the energy in shell-model
calculations from the corresponding experimental data can be used as an
indicator of some exotic property, e.g. alpha clustering, etc. Other possible
applications and impacts are also discussed.
