  This paper presents a new approach to conditional inference, based on the
simulation of samples conditioned by a statistics of the data. Also an explicit
expression for the approximation of the conditional likelihood of long runs of
the sample given the observed statistics is provided. It is shown that when the
conditioning statistics is sufficient for a given parameter, the approximating
density is still invariant with respect to the parameter. A new
Rao-Blackwellisation procedure is proposed and simulation shows that Lehmann
Scheff\'{e} Theorem is valid for this approximation. Conditional inference for
exponential families with nuisance parameter is also studied, leading to Monte
carlo tests. Finally the estimation of the parameter of interest through
conditional likelihood is considered. Comparison with the parametric bootstrap
method is discussed.
