  Particle filter (PF) sequential Monte Carlo (SMC) methods are very attractive
for the estimation of parameters of time dependent systems where the data is
either not all available at once, or the range of time constants is wide enough
to create problems in the numerical time propagation of the states. The need to
evolve a large number of particles makes PF-based methods computationally
challenging, the main bottlenecks being the time propagation of each particle
and the large number of particles. While parallelization is typically advocated
to speed up the computing time, vectorization of the algorithm on a single
processor may result in even larger speedups for certain problems. In this
paper we present a formulation of the PF-SMC class of algorithms proposed in
Arnold et al. (2013), which is particularly amenable to a parallel or
vectorized computing environment, and we illustrate the performance with a few
computed examples in MATLAB.

Computation