Multicanonical Monte Carlo Method And Its Optimization

We consider the model Y=g(X) in the paper,where g is a uncertainty real scalar function of a random vector X.We could produce samples of Y by inputting samples of X,however this procedure may be time-consuming.Our goal is to estimate the probability density function of Y when the distribution of the variable X is known.We introduce one of the importance sampling methods which is optimized on the basis of the Monte Carlo method(MC)—Multicanonical Monte Carlo method(MMC)to achieve the goal.The Multicanonical Monte Carlo method can help us to estimate the probability density function by dividing the value interval of the target random variable and generating the histogram by putting samples into the target value interval.Thus the Multicanonical Monte Carlo estimation is discontinuous and the estimation will be greatly affected by the partition of the value interval.The paper provides an improved method for the Multicanonical Monte Carlo method: GP-MMC method,which replaces histogram estimation with density function estimation of Gaussian process regression in every cycle of the Multicanonical Monte Carlo method and finally the discontinuous density function estimation becomes continuous.Moreover,compared with the Multicanonical Monte Carlo method,the GP-MMC method is more efficient.