RcppSMC (version 0.2.7)

pfNonlinBS: Nonlinear Bootstrap Particle Filter (Univariate Non-Linear State Space Model)

Description

The pfNonlinBS function provides a simple example for RcppSMC. It is a simple “bootstrap” particle filter which employs multinomial resampling after each iteration applied to the ubiquitous "nonlinear state space model" following Gordon, Salmond and Smith (1993).

Usage

pfNonlinBS(data, particles=500, plot=FALSE)

Value

The pfNonlinBS function returns two vectors, the first containing the posterior filtering means; the second the posterior filtering standard deviations.

Arguments

data

A vector variable containing the sequence of observations.

particles

An integer specifying the number of particles.

plot

A boolean variable describing whether a plot should illustrate the (posterior mean) estimated path along with one and two standard deviation intervals.

Author

Adam M. Johansen, Dirk Eddelbuettel and Leah F. South

Details

The pfNonlinbs function provides a simple example for RcppSMC. It is based on a simple nonlinear state space model in which the state evolution and observation equations are: x(n) = 0.5 x(n-1) + 25 x(n-1) / (1+x(n-1)^2) + 8 cos(1.2(n-1))+ e(n) and y(n) = x(n)^2 / 20 + f(n) where e(n) and f(n) are mutually-independent normal random variables of variances 10.0 and 1.0, respectively. A boostrap proposal (i.e. sampling from the state equation) is used, together with multinomial resampling after each iteration.

References

N. J. Gordon, S. J. Salmond, and A. F. M. Smith. Novel approach to nonlinear/non-Gaussian Bayesian state estimation. IEE Proceedings-F, 140(2):107-113, April 1993.

See Also

simNonlin for a function to simulate from the model and nonLinPMMH for an example of particle marginal Metropolis Hastings applied to a non-linear state space model.

Examples

  sim <- simNonlin(len=50)
  res <- pfNonlinBS(sim$data,particles=500,plot=TRUE)