mif: The MIF algorithm

Description

The MIF algorithm for estimating the parameters of a partially-observed Markov process.

Usage

mif(object, ...)
## S3 method for class 'pomp':
mif(object, Nmif, start, pars, ivps = character(0),
    particles, rw.sd, alg.pars, weighted = TRUE,
    tol = 1e-17, warn = TRUE, max.fail = 0, verbose = FALSE)
## S3 method for class 'mif':
mif(object, \dots)
## S3 method for class 'mif':
continue(object, Nmif, \dots)

Arguments

object

An object of class pomp.

Nmif

The number of MIF iterations to perform.

start

The initial guess of the parameters. This must be a named vector.

pars

character vector; names of ordinary parameters to be estimated.

ivps

character vector; names of initial-value parameters to be estimated.

particles

Function of prototype particles(Np,center,sd,...) which sets up the initial particle matrix by drawing a sample of size Np from the initial particle distribution centered at center and of width sd. I

rw.sd

numeric vector; the intensity of the random walk to be applied to parameters. The random walk is only applied to parameters named in pars. The algorithm requires that the random walk be nontrivial. Thus, each element in rw.s

alg.pars

A named list of algorithm parameters. This consists of [object Object],[object Object],[object Object],[object Object]

weighted

Should a weighted average be used? If weighted=F, the MIF update is not used; instead, an unweighed average of the filtering means is used for the update.

tol

Particles with log likelihood below tol are considered to be "lost". A filtering failure occurs when, at some time point, all particles are lost.

warn

Should a warning be generated when a filtering failure occurs?

max.fail

Maximum number of filtering failures permitted. If the number of failures exceeds this number, execution will terminate with an error.

verbose

logical; if TRUE, print progress reports.

...

Additional arguments that can be used to override the defaults.

Re-running MIF Iterations

To re-run a sequence of MIF iterations, one can use the mif method on a mif object. The call sequence is mif(object). By default, the same parameters used for the original MIF run are re-used. If one does specify additional arguments, these will override the defaults. An exception is that one cannot override the particles function.

Continuing MIF Iterations

One can continue a series of MIF iterations from where one left off. The call sequence is continue(object, Nmif). This will perform Nmif additional MIF iterations on the mif object object. 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. Additional arguments are passed to mif. This feature can be used to change any of the parameters (except the particles function).

Details

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 should be assumed to be an 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-class).

particles returns a length(center) x Np matrix with rownames. Each column represents a distinct particle. The rownames are used by the algorithms (see mif, pfilter).

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 corresponding to the parameters specified in center.

References

E. L. Ionides, C. Bret{'o}, & A. A. King, Inference for nonlinear dynamical systems, Proc. Natl. Acad. Sci. U.S.A., 103:18438--18443, 2006.