  The framework of Stein's method for Poisson process approximation is
presented from the point of view of Palm theory, which is used to construct
Stein identities and define local dependence. A general result (Theorem
\refimportantproposition) in Poisson process approximation is proved by taking
the local approach.
  It is obtained without reference to any particular metric, thereby allowing
wider applicability. A Wasserstein pseudometric is introduced for measuring the
accuracy of point process approximation. The pseudometric provides a
generalization of many metrics used so far, including the total variation
distance for random variables and the Wasserstein metric for processes as in
Barbour and Brown [Stochastic Process. Appl. 43 (1992) 9-31]. Also, through the
pseudometric, approximation for certain point processes on a given carrier
space is carried out by lifting it to one on a larger space, extending an idea
of Arratia, Goldstein and Gordon [Statist. Sci. 5 (1990)
  403-434]. The error bound in the general result is similar in form to that
for Poisson approximation. As it yields the Stein factor 1/\lambda as in
  Poisson approximation, it provides good approximation, particularly in cases
where \lambda is large. The general result is applied to a number of problems
including Poisson process modeling of rare words in a DNA sequence.
