  Monte Carlo methods are widely used for approximating complicated,
multidimensional integrals for Bayesian inference. Population Monte Carlo (PMC)
is an important class of Monte Carlo methods, which utilizes a population of
proposals to generate weighted samples that approximate the target
distribution. The generic PMC framework iterates over three steps: samples are
simulated from a set of proposals, weights are assigned to such samples to
correct for mismatch between the proposal and target distributions, and the
proposals are then adapted via resampling from the weighted samples. When the
target distribution is expensive to evaluate, the PMC has its computational
limitation since the convergence rate is $\mathcal{O}(N^{-1/2})$. To address
this, we propose in this paper a new Population Quasi-Monte Carlo (PQMC)
framework, which integrates Quasi-Monte Carlo ideas within the sampling and
adaptation steps of PMC. A key novelty in PQMC is the idea of importance
support points resampling, a deterministic method for finding an "optimal"
subsample from the weighted proposal samples. Moreover, within the PQMC
framework, we develop an efficient covariance adaptation strategy for
multivariate normal proposals. Lastly, a new set of correction weights is
introduced for the weighted PMC estimator to improve the efficiency from the
standard PMC estimator. We demonstrate the improved empirical convergence of
PQMC over PMC in extensive numerical simulations and a friction drilling
application.
