  We describe a simple Importance Sampling strategy for Monte Carlo simulations
based on a least squares optimization procedure. With several numerical
examples, we show that such Least Squares Importance Sampling (LSIS) provides
efficiency gains comparable to the state of the art techniques, when the latter
are known to perform well. However, in contrast to traditional approaches, LSIS
is not limited to the determination of the optimal mean of a Gaussian sampling
distribution. As a result, it outperforms other methods when the ability to
adjust higher moments of the sampling distribution, or to deal with
non-Gaussian or multi-modal densities, is critical to achieve variance
reductions.
