Nick Whiteley
Stability properties of some particle filters.
Mon, 10/03/2011 - 15:01 — SomNambulAuthors: Nick Whiteley
Subjects: Computation
AbstractUnder multiplicative drift and other regularity conditions, it is established
that the asymptotic variance associated with a particle filter approximation of
the prediction filter is bounded uniformly in time, and the non-asymptotic,
relative variance associated with the particle approximation of the normalizing
constant is bounded linearly in time. The conditions are demonstrated to hold
for some hidden Markov models on non-compact state spaces.Linear Variance Bounds for Particle Approximations of Time-Homogeneous Feynman-Kac Formulae.
Mon, 08/22/2011 - 15:01 — SomNambulAuthors: Ajay Jasra, Nick Whiteley, Nikolas Kantas
Subjects: Computation
AbstractThis article establishes sufficient conditions for a linear-in-time bound on
the non-asymptotic variance of particle approximations of time-homogeneous
Feynman-Kac formulae. These formulae appear in a wide variety of applications
including option pricing in finance and risk sensitive control in engineering.
In direct Monte Carlo approximation of these formulae, the non-asymptotic
variance typically increases at an exponential rate in the time parameter.Sequential Monte Carlo samplers: error bounds and insensitivity to initial conditions.
Tue, 03/22/2011 - 16:01 — SomNambulAuthors: Nick Whiteley
Subjects: Computation
AbstractThis paper addresses finite sample stability properties of sequential Monte
Carlo methods for approximating sequences of probability distributions. The
results presented herein are applicable in the scenario where the start and end
distributions in the sequence are fixed and the number of intermediate steps is
a parameter of the algorithm. Under assumptions which hold on non-compact
spaces, it is shown that the effect of the initial distribution decays
exponentially fast in the number of intermediate steps and the corresponding
stochastic error is stable in \mathbb{L}_{p} norm.Efficient Bayesian Inference for Switching State-Space Models using Discrete Particle Markov Chain Monte Carlo Methods.
Thu, 11/11/2010 - 16:01 — SomNambulAuthors: Arnaud Doucet, Christophe Andrieu, Nick Whiteley
Subjects: Computation
AbstractSwitching state-space models (SSSM) are a very popular class of time series
models that have found many applications in statistics, econometrics and
advanced signal processing. Bayesian inference for these models typically
relies on Markov chain Monte Carlo (MCMC) techniques. However, even
sophisticated MCMC methods dedicated to SSSM can prove quite inefficient as
they update potentially strongly correlated discrete-valued latent variables
one-at-a-time (Carter and Kohn, 1996; Gerlach et al., 2000; Giordani and Kohn,
2008).
User login
