  The sampling importance resampling method is widely utilized in various
fields, such as numerical integration and statistical simulation. In this
paper, two modified methods are presented by incorporating two variance
reduction techniques commonly used in Monte Carlo simulation, namely antithetic
sampling and Latin hypercube sampling, into the process of sampling importance
resampling method respectively. Theoretical evidence is provided to demonstrate
that the proposed methods significantly reduce estimation errors compared to
the original approach. Furthermore, the effectiveness and advantages of the
proposed methods are validated through both numerical studies and real data
analysis.
