Auxiliary particle implementation of the probability hypothesis density filter

Optimal Bayesian multi-target filtering is, in general, computationally impractical owing to the high dimensionality of the multi-target state. The Probability Hypothesis Density (PHD) filter propagates the first moment of the multi-target posterior distribution. While this reduces the dimensionality of the problem, the PHD filter still involves intractable integrals in many cases of interest. Several authors have proposed Sequential Monte Carlo (SMC) implementations of the PHD filter. However, these implementations are the equivalent of the Bootstrap Particle Filter, and the latter is well known to be inefficient. Drawing on ideas from the Auxiliary Particle Filter (APF), we present a SMC implementation of the PHD filter which employs auxiliary variables to enhance its efficiency. Numerical examples are presented for two scenarios, including a challenging nonlinear observation model.

A probability-based approach to setting annual catch levels.

The requirement of setting annual catch limits to prevent overfishing has been added to the Magnuson-Stevens Fishery Conservation and Management Reauthorization Act of 2006 (MSRA). Because this requirement is new, a body of applied scientific practice for deriving annual catch limits and accompanying targets does not yet exist. This article demonstrates an approach to setting levels of catch that is intended to keep the probability of future overfishing at a preset low level. The proposed framework is based on stochastic projection with uncertainty in population dynamics. The framework extends common projection methodology by including uncertainty in the limit reference point and in management implementation, and by making explicit the risk of overfishing that managers consider acceptable. The approach is illustrated with application to gag (Mycteroperca microlepis), a grouper that inhabits the waters off the southeastern United States. Although devised to satisfy new legislation of the MSRA, the framework has potential application to any fishery where the management goal is to limit the risk of overfishing by controlling catch.