Suppose we wish to carry out likelihood based inference but we solely have an unbiased simulation based estimator of the likelihood.  We note that unbiasedness is enough when the estimated likelihood is used inside a Metropolis-Hastings algorithm.  This result has recently been introduced in...

A key ingredient of many particle filters is the use of the sampling importance resampling algorithm (SIR), which transforms a sample of weighted draws from a prior distribution into equally weighted draws from a posterior distribution.  We give a novel analysis of the SIR algorithm and analyse...