  Many random processes can be simulated as the output of a deterministic model
accepting random inputs. Such a model usually describes a complex mathematical
or physical stochastic system and the randomness is introduced in the input
variables of the model. When the statistics of the output event are known,
these input variables have to be chosen in a specific way for the output to
have the prescribed statistics. Because the probability distribution of the
input random variables is not directly known but dictated implicitly by the
statistics of the output random variables, this problem is usually intractable
for classical sampling methods. Based on Markov Chain Monte Carlo we propose a
novel method to sample random inputs to such models by introducing a
modification to the standard Metropolis-Hastings algorithm. As an example we
consider a system described by a stochastic differential equation (sde) and
demonstrate how sample paths of a random process satisfying this sde can be
generated with our technique.
