Importance Sampling: Approaches and Misconceptions

Additional author information --J.R.G.: Also Ph.D. Candidate at the Electrical Engineering Department, School of Engineering and Applied Science, The George Washington University, Ashburn, VA, USA 20147. ABSTRACT A brief introduction to the widely spread theory of Importance Sampling is given. Several approaches to the optimization of the twisted density function are described, such as: i) using the ideal (zero-variance) estimator as a guideline, ii) increasing the probability of the event to be analyzed, iii) splitting the random process trajectory, iv) sequentially adapting the twisted density, and v) using uniformly bounded likelihood ratios. A brief description of the regenerative approach to simulations is given as well. Some details that should be taken into consideration when applying these techniques, in order to avoid a poor performance of the estimator, are also explained.