Numerical calculation of permanents

The $\alpha$-permanent of a square matrix is a determinant-style sum, with $\alpha=-1$ corresponding to the determinant, $\alpha=1$ to the ordinary permanent, and $\alpha=0$ to the Hamiltonian sum over cyclic permutations.  Exact computation of permanents is notoriously difficult; numerical computation using the best algorithm for $\alpha=1$ is feasible for matrices of order about 25--30; numerical computation for general $\alpha$ is feasible only for $n < 12$.  I will describe briefly how the $\alpha$-permanent arises in statistical work as the probability density function of the Boson point process, and I will discuss the level of numerical accuracy needed for statistical applications.  My hope is that, for sufficiently large matrices, it may be possible to develop a non-stochastic polynomial-time approximation of adequate accuracy.