  The problem of drawing samples from a discrete distribution can be converted
into a discrete optimization problem. In this work, we show how sampling from a
continuous distribution can be converted into an optimization problem over
continuous space. Central to the method is a stochastic process recently
described in mathematical statistics that we call the Gumbel process. We
present a new construction of the Gumbel process and A* sampling, a practical
generic sampling algorithm that searches for the maximum of a Gumbel process
using A* search. We analyze the correctness and convergence time of A* sampling
and demonstrate empirically that it makes more efficient use of bound and
likelihood evaluations than the most closely related adaptive rejection
sampling-based algorithms.
