Title: Efficient sampling of conditioned Markov jump processes,
Abstract: We consider the task of generating draws from a Markov jump process (MJP)
between two time points at which the process is known. Resulting draws are
typically termed bridges and the generation of such bridges plays a key role in
simulation-based inference algorithms for MJPs. The problem is challenging due
to the intractability of the conditioned process, necessitating the use of
computationally intensive methods such as weighted resampling or Markov chain
Monte Carlo. An efficient implementation of such schemes requires an
approximation of the intractable conditioned hazard/propensity function that is
both cheap and accurate. In this paper, we review some existing approaches to
this problem before outlining our novel contribution. Essentially, we leverage
the tractability of a Gaussian approximation of the MJP and suggest a
computationally efficient implementation of the resulting conditioned hazard
approximation. We compare and contrast our approach with existing methods using
three examples.