Wavelet Monte Carlo: a principle for sampling from complex distributions

Abstract We present Wavelet Monte Carlo (WMC), a new method for generating independent samples from complex target distributions. The methodology is based on wavelet decomposition of the difference between density and user-specified initial density, exploits both theory survival analysis. In practice, WMC can process only finite range scales. prove that resulting $$L_1$$ L 1 approximation error converges to zero geometrically as scale tends $$(-\infty ,+\infty )$$ ( - ∞ , + ) . This provides principled approach trading off accuracy against computational efficiency. offer practical suggestions addressing some issues implementation, but further development needed computationally efficient methodology. illustrate in one- two-dimensional examples, discuss challenges opportunities application higher dimensions.