  We consider perfect simulation algorithms for locally stable point processes
based on dominated coupling from the past, and apply these methods in two
different contexts. A new version of the algorithm is developed which is
feasible for processes which are neither purely attractive nor purely
repulsive. Such processes include multiscale area-interaction processes, which
are capable of modelling point patterns whose clustering structure varies
across scales. The other topic considered is nonparametric regression using
wavelets, where we use a suitable area-interaction process on the discrete
space of indices of wavelet coefficients to model the notion that if one
wavelet coefficient is non-zero then it is more likely that neighbouring
coefficients will be also. A method based on perfect simulation within this
model shows promising results compared to the standard methods which threshold
coefficients independently.
