  Conditional Monte Carlo refers to sampling from the conditional distribution
of a random vector X given the value T(X) = t for a function T(X). Classical
conditional Monte Carlo methods were designed for estimating conditional
expectations of functions of X by sampling from unconditional distributions
obtained by certain weighting schemes. The basic ingredients were the use of
importance sampling and change of variables. In the present paper we
reformulate the problem by introducing an artificial parametric model,
representing the conditional distribution of X given T(X)=t within this new
model. The key is to provide the parameter of the artificial model by a
distribution. The approach is illustrated by several examples, which are
particularly chosen to illustrate conditional sampling in cases where such
sampling is not straightforward. A simulation study and an application to
goodness-of-fit testing of real data are also given.
