  Full likelihood inference under Kingman's coalescent is a computationally
challenging problem to which importance sampling (IS) and the product of
approximate conditionals (PAC) method have been applied successfully. Both
methods can be expressed in terms of families of intractable conditional
sampling distributions (CSDs), and rely on principled approximations for
accurate inference. Recently, more general $\Lambda$- and $\Xi$-coalescents
have been observed to provide better modelling fits to some genetic data sets.
We derive families of approximate CSDs for finite sites $\Lambda$- and
$\Xi$-coalescents, and use them to obtain "approximately optimal" IS and PAC
algorithms for $\Lambda$-coalescents, yielding substantial gains in efficiency
over existing methods.
