Monte Carlo analysis has so far been the corner stone for analog statistical simulations. Fast and accurate simulations are necessary for stringent time-to-market, design for manufacturability and yield concerns in the analog domain. Although Monte Carlo attains accuracy, it does so with a sacrifice in run-time for analog simulations. In this paper, we propose a fast and accurate probabilistic simulation method alternative to Monte Carlo using deterministic sampling and weight propagation. We furthermore propose accuracy improvement algorithms and a fast yield calculation method. The proposed method shows accuracy improvement combined with a 100-fold reduction in run-time with respect to a 1000-sample Monte Carlo analysis.