## UC Berkeley / Lawrence Berkeley Laboratory

#### The Implicit Particle Filter: Overview and Application

**Ethan Atkins, UC Berkeley**

##### March 9th, 2011 at 4PM–5PM in 939 Evans Hall [Map]

There are many problems in science, for example in meteorology, oceanography
and geomagnetism, in which the state of a system must be identified from an
uncertain equation supplemented by noisy data. The implicit filter is a new
sequential Monte Carlo approach (SMC) to approximating the solution of the
Bayesian filtering problem that improves upon existing SMC methods. It finds
the regions of high probability with respect to the posterior density
(determined by both the model and its observations) and disproportionally
generates samples in the high probability regions. Traditional filters, *e.g.*
Sequential Importance Resampling (SIR), don't take the observations into
account, leading to many samples with negligible contributions to the
statistics. We apply the filter to the Lorenz 63 attractor, a chaotic system of
stochastic differential equations and demonstrate numerically the increased
efficiency of the implicit filter compared to SIR.