The simNonlin function simulates data from the models used
in link{pfNonlinBS} and link{nonLinPMMH}.
simNonlin(len = 50, var_init = 10, var_evol = 10, var_obs = 1,
cosSeqOffset = -1)The simNonlin function returns a list containing the state and data sequences.
The length of data sequence to simulate.
The variance of the noise for the initial state.
The variance of the noise for the state evolution .
The variance of the observation noise.
This is related to the indexing in the cosine function in the evoluation equation. A value of -1 can be used to follow the specification of Gordon, Salmond and Smith (1993) and 0 can be used to follow Andrieu, Doucet and Holenstein (2010).
Adam M. Johansen, Dirk Eddelbuettel and Leah F. South
The simNonlin function simulates from
a simple nonlinear state space model with
state evolution and observation equations:
\(x(n) = 0.5 x(n-1) + 25 x(n-1) / (1+x(n-1)^2) + 8 cos(1.2(n+cosSeqOffset))+ e(n)\) and
\(y(n) = x(n)^2 / 20 + f(n)\)
where \(e(n)\) and \(f(n)\) are mutually-independent normal random variables of variances var_evol and var_obs, respectively, and \(x(0) ~ N(0,var_init)\).
Different variations of this model can be found in Gordon, Salmond and Smith (1993) and Andrieu, Doucet and Holenstein (2010). A cosSeqOffset of -1 is consistent with the former and 0 is consistent with the latter.
C. Andrieu, A. Doucet, and R. Holenstein. Particle Markov chain Monte Carlo methods. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 72(3):269-342, 2010.
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.
pfNonlinBS for a simple bootrap particle filter
applied to this model and nonLinPMMH for particle
marginal Metropolis Hastings applied to estimating the standard
deviation of the state evolution and observation noise.