mif causes the iterated filtering algorithm to run for a specified number of iterations.
At each iteration, the particle filter is performed on a perturbed version of the model.
Specifically, parameters to be estimated are subjected to random perturbations at each observation.
This extra variability effectively smooths the likelihood surface and combats particle depletion by introducing diversity into the population of particles.
At the iterations progress, the magnitude of the perturbations is diminished according to a user-specified cooling schedule.
For most purposes, mif has been superseded by mif2.## S3 method for class 'pomp':
mif(object, Nmif = 1, start, ivps = character(0),
particles, rw.sd, Np, ic.lag, var.factor = 1,
cooling.type, cooling.fraction.50,
method = c("mif","unweighted","fp","mif2"),
tol = 1e-17, max.fail = Inf,
verbose = getOption("verbose"), transform = FALSE, ...)
## S3 method for class 'pfilterd.pomp':
mif(object, Nmif = 1, Np, tol, \dots)
## S3 method for class 'mif':
mif(object, Nmif, start, ivps,
particles, rw.sd, Np, ic.lag, var.factor,
cooling.type, cooling.fraction.50,
method, tol, transform, \dots)
## S3 method for class 'mif':
continue(object, Nmif = 1, \dots)
## S3 method for class 'mif':
conv.rec(object, pars, transform = FALSE, \dots)
## S3 method for class 'mifList':
conv.rec(object, \dots)pomp.ivps must have a positive random-walk standard deviation specified in rw.sd.
If there are no regular parameterparticles(Np,center,sd,...) which sets up the starting particle matrix by drawing a sample of size Np from the starting particle distribution centered at center and of width sd.
names(rw.sd) must be a subset of names(start),
The random walk is not dynamically added to the initial-value parameters (named in mif update for initial-value parameters consists of replacing them by their filtering mean at time times[ic.lag], where timerw.sd.
In particular, the width of the distribution of particles at the start of the first mif iteration will bcooling.type specifies the nature of the cooling schedule. When co
method sets the update rule used in the algorithm.
method="mif" uses the iterated filtering update rule (Ionides 2006, 2011);
method="unweighted" updates the parameter to the unweighted average of the filteripfilter.TRUE, optimization is performed on the transformed scale, as defined by the user-supplied parameter transformations (see pomp).mif returns an object of class mif.
The latter inherits from the pfilterd.pomp and pomp classes.mif2.mif, while regular parameters are perturbed at the initial time and after every observation, IVPs are perturbed only at the initial time.mif iterations, one can use the mif method on a mif object.
By default, the same parameters used for the original mif run are re-used (except for tol, max.fail, and verbose, the defaults of which are shown above).
If one does specify additional arguments, these will override the defaults.mif iterations from where one left off using the continue method.
A call to mif to perform Nmif=m iterations followed by a call to continue to perform Nmif=n iterations will produce precisely the same effect as a single call to mif to perform Nmif=m+n iterations.
By default, all the algorithmic parameters are the same as used in the original call to mif.
Additional arguments will override the defaults.mif's fixed-lag smoothing to estimate only initial value parameters (IVPs).
In this case, the IVPs to be estimated are named in ivps and no positive entries in rw.sd correspond to any parameters not named in ivps.
If theta is the current parameter vector, then at each mif iteration, Np particles are drawn from a distribution centered at theta and with width proportional to var.factor*rw.sd, a particle filtering operation is performed, and theta is replaced by the filtering mean at time(object)[ic.lag].
Note the implication that, when mif is used in this way on a time series any longer than ic.lag, unnecessary work is done.
If the time series in object is longer than ic.lag, consider replacing object with window(object,end=ic.lag).particles is not specified, the default behavior is to draw the particles from a multivariate normal distribution.
It is the user's responsibility to ensure that, if the optional particles argument is given, that the particles function satisfies the following conditions: particles has at least the following arguments:
Np, center, sd, and ....
Np may be assumed to be a positive integer;
center and sd will be named vectors of the same length.
Additional arguments may be specified;
these will be filled with the elements of the userdata slot of the underlying pomp object (see pomp).
particles returns a length(center) x Np matrix with rownames matching the names of center and sd.
Each column represents a distinct particle.
The center of the particle distribution returned by particles should be center.
The width of the particle distribution should vary monotonically with sd.
In particular, when sd=0, the particles should return matrices with Np identical columns, each given by the parameters specified in center.
E. L. Ionides, A. Bhadra, Y. Atchad{\'e}, & A. A. King, Iterated filtering, Annals of Statistics, 39:1776--1802, 2011.
E. L. Ionides, D. Nguyen, Y. Atchad{\'e}, S. Stoev, and A. A. King. Inference for dynamic and latent variable models via iterated, perturbed Bayes maps. Proc. Natl. Acad. Sci. U.S.A., 112:719--724, 2015.
A. A. King, E. L. Ionides, M. Pascual, and M. J. Bouma, Inapparent infections and cholera dynamics, Nature, 454:877--880, 2008.
pomp, pfilter, mif2