Iterated filtering algorithms for estimating the parameters of a partially-observed Markov process.
Running 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For most purposes, mif has been superseded by mif2.
# S4 method for pomp
mif(object, Nmif = 1, start, ivps = character(0),
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, …)
# S4 method for pfilterd.pomp
mif(object, Nmif = 1, Np, tol, …)
# S4 method for mif
mif(object, Nmif, start, ivps,
rw.sd, Np, ic.lag, var.factor,
cooling.type, cooling.fraction.50,
method, tol, transform, …)
# S4 method for mif
continue(object, Nmif = 1, …)
# S4 method for mif
conv.rec(object, pars, transform = FALSE, …)
# S4 method for mifList
conv.rec(object, …)An object of class pomp.
The number of filtering iterations to perform.
named numerical vector; the starting guess of the parameters.
optional character vector naming the initial-value parameters (IVPs) to be estimated.
Every parameter named in ivps must have a positive random-walk standard deviation specified in rw.sd.
If there are no regular parameters with positive rw.sd, i.e., only IVPs are to be estimated, see below “"Using mif to estimate initial-value parameters only"”.
numeric vector with names; the intensity of the random walk to be applied to parameters.
names(rw.sd) must be a subset of names(start),
The random walk is not dynamically added to the initial-value parameters (named in ivps).
The algorithm requires that the random walk be nontrivial, so that rw.sd be positive for at least one element.
the number of particles to use in filtering.
This may be specified as a single positive integer, in which case the same number of particles will be used at each timestep.
Alternatively, if one wishes the number of particles to vary across timestep, one may specify Np either as a vector of positive integers (of length length(time(object,t0=TRUE))) or as a function taking a positive integer argument.
In the latter case, Np(k) must be a single positive integer, representing the number of particles to be used at the k-th timestep:
Np(0) is the number of particles to use going from timezero(object) to time(object)[1],
Np(1), from timezero(object) to time(object)[1],
and so on, while when T=length(time(object,t0=TRUE)),
Np(T) is the number of particles to sample at the end of the time-series.
a positive integer;
the timepoint for fixed-lag smoothing of initial-value parameters.
The mif update for initial-value parameters consists of replacing them by their filtering mean at time times[ic.lag], where times=time(object).
It makes no sense to set ic.lag>length(times);
if it is so set, ic.lag is set to length(times) with a warning.
optional positive scalar;
the scaling coefficient relating the width of the starting particle distribution to rw.sd.
In particular, the width of the distribution of particles at the start of the first mif iteration will be random.walk.sd*var.factor.
By default, var.factor=1.
specifications for the cooling schedule, i.e., the manner in which the intensity of the parameter perturbations is reduced with successive filtering iterations.
cooling.type specifies the nature of the cooling schedule.
When cooling.type="geometric", on the n-th mif iteration, the relative perturbation intensity is cooling.fraction.50^(n/50).
When cooling.type="hyperbolic", on the n-th mif iteration, the relative perturbation intensity is (s+1)/(s+n), where (s+1)/(s+50)=cooling.fraction.50.
cooling.fraction.50 is the relative magnitude of the parameter perturbations after 50 mif iterations.
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 filtering means of the parameters at each time;
method="fp" updates the parameter to the filtering mean at the end of the time series.
See the description under pfilter.
logical; if TRUE, print progress reports.
logical;
if TRUE, optimization is performed on the transformed scale, as defined by the user-supplied parameter transformations (see pomp).
additional arguments that override the defaults.
names of parameters.
Upon successful completion, mif returns an object of class mif.
The latter inherits from the pfilterd.pomp and pomp classes.
Initial-value parameters (IVPs) differ from regular parameters in that the majority of the information about these parameters is restricted to the early part of the time series.
That is, increasing the length of the time series provides progressively less additional information about IVPs than it does about regular parameters.
In mif, while regular parameters are perturbed at the initial time and after every observation, IVPs are perturbed only at the initial time.
To re-run a sequence of 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.
One can resume a series of 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.
One can use 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 normal 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).
Methods that can be used to manipulate, display, or extract information from a mif object:
conv.rec(object, pars, transform = FALSE) returns the columns of the convergence-record matrix corresponding to the names in pars.
By default, all columns are returned.
If transform=TRUE, the parameters are transformed from the estimation scale.
Returns the value in the loglik slot.
NB: this is not the same as the likelihood of the model at the MLE!
Concatenates mif objects into a mifList.
Plots a series of diagnostic plots when applied to a mif or mifList object.
E. L. Ionides, C. Breto, & A. A. King, Inference for nonlinear dynamical systems, Proc. Natl. Acad. Sci. U.S.A., 103:18438--18443, 2006.
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.