First, we present some examples of calculations of polarized multiply scattered return signals of a space-based multichannel LIDAR (such as the LITE) and compare them to return signals of a ground-based LIDAR. These methods are variance reduction Monte Carlo algorithms allowing for controlling the empirical variance. Second, we recall the method of random search briefly. Random search procedures are Monte Carlo algorithms which are designed to solve deterministic or stochastic optimization problems and, hence, also deterministic or stochastic equations. Third, we show how variance reduction Monte Carlo methods may be combined with properly chosen random search procedures to retrieve one or more environmental parameters from a given (measured or calculated) LIDAR return signal. Such a procedure is time consuming, of course, but it will allow for the retrieval of several parameters simultaneously and for a sensitivity analysis. Hence, a retrieval procedure based on the combination of variance reduction Monte Carlo methods and random search including such a sensitivity analysis gives much more information than the usual inversion procedures (e.g. based on integral equations and often uncheckable environmental assumptions). Fourth, we present some examples of the (simultaneous) retrieval of the extinction coefficient and the particle size distribution of a cloud from the multiply scattered return signal of a space-based LIDAR and a sensitivity analysis of this retrieval.