# PF_control

0th

Percentile

##### Auxiliary for Controlling Particle Fitting

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,
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)
##### 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.

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

tolerance passed to nloptr in mode approximation.

averaging_start

index to start averaging. Values less then or equal to zero yields no averaging.

##### 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).

##### Value

A list with components named as the arguments.

##### 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.

Briers, M., Doucet, A., and Maskell, S. (2010) Smoothing algorithms for state-space models. Annals of the Institute of Statistical Mathematics, 62(1), 61.

PF_EM