PF_control: Auxiliary for Controlling Particle Fitting

Description

Auxiliary for additional settings with PF_EM.

Usage

PF_control(
  N_fw_n_bw = NULL,
  N_smooth = NULL,
  N_first = NULL,
  eps = 0.01,
  forward_backward_ESS_threshold = NULL,
  method = "AUX_normal_approx_w_cloud_mean",
  n_max = 25,
  n_threads = getOption("ddhazard_max_threads"),
  smoother = "Fearnhead_O_N",
  Q_tilde = NULL,
  est_a_0 = TRUE,
  N_smooth_final = N_smooth,
  nu = 0L,
  covar_fac = -1,
  ftol_rel = 1e-08,
  averaging_start = -1L,
  fix_seed = TRUE
)

Value

A list with components named as the arguments.

Arguments

N_fw_n_bw: number of particles to use in forward and backward filter.
N_smooth: number of particles to use in particle smoother.
N_first: number of particles to use at time \(0\) and time \(d + 1\).
eps: convergence threshold in EM method.
forward_backward_ESS_threshold: required effective sample size to not re-sample in the particle filters.
method: method for forward, backward and smoothing filter.
n_max: maximum number of iterations of the EM algorithm.
n_threads: maximum number threads to use in the computations.
smoother: smoother to use.
Q_tilde: covariance matrix of additional error term to add to the proposal distributions. NULL implies no additional error term.
est_a_0: FALSE if the starting value of the state model should be fixed. Does not apply for type = "VAR".
N_smooth_final: number of particles to sample with replacement from the smoothed particle cloud with N_smooth particles using the particles' weights. This causes additional sampling error but decreases the computation time in the M-step.
nu: integer with degrees of freedom to use in the (multivariate) t-distribution used as the proposal distribution. A (multivariate) normal distribution is used if it is zero.
covar_fac: factor to scale the covariance matrix with. Ignored if the values is less than or equal to zero.
ftol_rel: relative convergence tolerance of the mode objective in mode approximation.
averaging_start: index to start averaging. Values less then or equal to zero yields no averaging.
fix_seed: TRUE if the same seed should be used. E.g., in PF_EM the same seed will be used in each iteration of the E-step of the MCEM algorithm.

Details

The method argument can take the following values

bootstrap_filter for a bootstrap filter.
PF_normal_approx_w_cloud_mean for a particle filter where a Gaussian approximation is used using a Taylor approximation made at the mean for the current particle given the mean of the parent particles and/or mean of the child particles.
AUX_normal_approx_w_cloud_mean for an auxiliary particle filter version of PF_normal_approx_w_cloud_mean.
PF_normal_approx_w_particles for a filter similar to PF_normal_approx_w_cloud_mean and differs by making a Taylor approximation at a mean given each sampled parent and/or child particle.
AUX_normal_approx_w_particles for an auxiliary particle filter version of PF_normal_approx_w_particles.

The smoother argument can take the following values

Fearnhead_O_N for the smoother in Fearnhead, Wyncoll, and Tawn (2010).
Brier_O_N_square for the smoother in Briers, Doucet, and Maskell (2010).

References

Gordon, N. J., Salmond, D. J., and Smith, A. F. (1993) Novel approach to nonlinear/non-Gaussian Bayesian state estimation. In IEE Proceedings F (Radar and Signal Processing), (Vol. 140, No. 2, pp. 107-113). IET Digital Library.

Pitt, M. K., and Shephard, N. (1999) Filtering via simulation: Auxiliary particle filters. Journal of the American statistical association, 94(446), 590-599.

Fearnhead, P., Wyncoll, D., and Tawn, J. (2010) A sequential smoothing algorithm with linear computational cost. Biometrika, 97(2), 447-464.