  We describe a simple method of umbrella trajectory sampling for Markov
chains. The method allows the estimation of large-deviation rate functions, for
path-extensive dynamic observables, for an arbitrary number of models within a
certain family. The general relationship between probability distributions of
dynamic observables of members of this family is an extended fluctuation
relation. When the dynamic observable is chosen to be entropy production,
members of this family include the forward Markov chain and its time reverse,
whose probability distributions are related by the expected simple fluctuation
relation.
