Auxiliary variable based particle lters

We model a time series fyt; t = 1; :::; ng using a state space framework with the fytj tg being independent and with the state f tg assumed to be Markovian. The task will be to use simulation to estimate f( tjFt), t = 1; :::; n, where Ft is contemporaneously available information. We assume a known `measurement' density f(ytj t) and the ability to simulate from the `transition' density f( t+1j t). Sometimes we will also assume that we can evaluate f( t+1j t). Filtering can be thought of as the repeated application of the iteration