Using an unified framework, we integrate the two major Monte Carlo techniques currently available: Efficient Importance Sampling (EIS) and Markov Chain Monte Carlo (MCMC). We do so for two reasons. First, the two methods complement one another. Loosely, EIS is effective for integrating...

The sine and cosine functions used as the bases in Fourier analysis are very smooth (infinitely differentiable) and very broad (nonzero almost everywhere on the real line), and hence they are not effective for representing functions that change abruptly (jumps) or have highly localized support...