# PF_control

##### 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,
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)
```

##### 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
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.

##### See Also

*Documentation reproduced from package dynamichazard, version 0.6.5, License: GPL-2*