A guided intermediate resampling particle filter for inference on high dimensional systems

28 Aug 2017  ·  Joonha Park, Edward L. Ionides ·

Particle filter methods are a basic tool for inference on nonlinear partially observed Markov process (POMP) models. However, the performance of standard particle filter algorithms quickly deteriorates as the model dimension increases. We introduce guided intermediate resampling filter (GIRF) methodology to address this issue. GIRF methodology requires that the latent Markov process has a continuous time representation, allowing particles to be assessed at times intermediate to the observation times. We obtain theoretical results showing improved scaling of a GIRF algorithm, relative to widely used particle filters, as the model dimension increases. We present numerical comparisons with alternative methods on toy examples, including a stochastic version of the Lorenz 96 atmospheric circulation model. As predicted by the theoretical results, we find empirically that our GIRF algorithm greatly out-performs an auxiliary particle filter and an ensemble Kalman filter on nonlinear systems of moderately high dimension. Our GIRF algorithm is applicable to a broad range of models thanks to its plug-and-play property of not requiring the evaluation of the transition density of the process. We demonstrate the scientific applicability of GIRF methodology by solving a scientific challenge, carrying out likelihood based inference on epidemic coupling between forty cities from spatiotemporal infectious disease case reports.

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