Auxiliary Variable Based Particle Filters

We model a time series {y t , t = 1, ..., n} using a state-space framework with the {y t |α t } being independent and with the state {α t } assumed to be Markovian. The task will be to use simulation to estimate f(α t |F t ), t = 1, ..., n, where F t is contemporaneously available information. We assume a known measurement density f(y t |α t ) and the ability to simulate from the transition density f(α t+1|α t ). Sometimes we will also assume that we can evaluate f(α t+1|α t ).

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