In this work we consider a class of uncertainty quantification problems where
the system performance or reliability is characterized by a scalar parameter
y. The performance parameter y is random due to the presence of various
sources of uncertainty in the system, and our goal is to estimate the
probability density function (PDF) of y. We propose to use the multicanonical
Monte Carlo (MMC) method, a special type of adaptive importance sampling
algorithm, to compute the PDF of interest. Moreover, we develop an adaptive
algorithm to construct local Gaussian process surrogates to further accelerate
the MMC iterations. With numerical examples we demonstrate that the proposed
method can achieve several orders of magnitudes of speedup over the standard
Monte Carlo method
