avif: Iterated Smoothing
In nxdao2000/is2: Iterated smoothing for partially observed Markov processes

Description Usage Arguments Re-running avif Iterations Continuing avif Iterations Using avif to estimate initial-value parameters only Details Author(s) References See Also

Iterated smoothing algorithms for estimating the parameters of a partially-observed Markov process.

## S4 method for signature 'pomp'
avif(object, Nis = 1, start, pars, ivps = character(0),
    particles, rw.sd, Np, ic.lag, var.factor, lag,
    cooling.type = c("geometric","hyperbolic"), 
    cooling.fraction, cooling.factor,
    method = c("avif","ris1","is1"),
    tol = 1e-17, max.fail = Inf,
    verbose = getOption("verbose"), transform = FALSE, ...)
## S4 method for signature 'pfilterd2.pomp'
avif(object, Nis = 1, Np, tol, ...)
## S4 method for signature 'avif'
avif(object, Nis, start, pars, ivps,
    particles, rw.sd, Np, ic.lag, lag, var.factor,
    cooling.type, cooling.fraction,
    method, tol, transform, ...)
## S4 method for signature 'avif'
continue(object, Nis = 1, ...)

`object`	An object of class `pomp`.
`Nis`	The number of filtering iterations to perform.
`start`	named numerical vector; the starting guess of the parameters.
`pars`	optional character vector naming the ordinary parameters to be estimated. Every parameter named in `pars` must have a positive random-walk standard deviation specified in `rw.sd`. Leaving `pars` unspecified is equivalent to setting it equal to the names of all parameters with a positive value of `rw.sd` that are not `ivps`.
`ivps`	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 `pars` is empty, i.e., only IVPs are to be estimated, see below “Using avif to estimate initial-value parameters only”.
`particles`	Function of prototype `particles(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`. If `particles` is not supplied by the user, the default behavior is to draw the particles from a multivariate normal distribution with mean `center` and standard deviation `sd`.
`rw.sd`	numeric vector with names; the intensity of the random walk to be applied to parameters. The random walk is only applied to parameters named in `pars` (i.e., not to those named in `ivps`). The algorithm requires that the random walk be nontrivial, so each element in `rw.sd[pars]` must be positive. `rw.sd` is also used to scale the initial-value parameters (via the `particles` function). Therefore, each element of `rw.sd[ivps]` must be positive. The following must be satisfied: `names(rw.sd)` must be a subset of `names(start)`, `rw.sd` must be non-negative (zeros are simply ignored), the name of every positive element of `rw.sd` must be in either `pars` or `ivps`.
`Np`	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.
`ic.lag`	a positive integer; the timepoint for fixed-lag smoothing of initial-value parameters. The `avif` 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.
`var.factor`	a positive number; 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 avif iteration will be `random.walk.sd*var.factor`.
`lag`	a positive integer; the timepoint for fixed-lag smoothing parameters estimation.
`cooling.type, cooling.fraction, cooling.factor`	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 avif iteration, the relative perturbation intensity is `cooling.fraction`-`^(n/50)`. When `cooling.type="hyperbolic"`, on the n-th avif iteration, the relative perturbation intensity is `(s+1)/(s+n)`, where `(s+1)/`-`(s+50)=cooling.fraction`. `cooling.fraction` is the relative magnitude of the parameter perturbations after 50 avif iterations. `cooling.factor` is now deprecated: to achieve the old behavior, use `cooling.type="geometric"` and `cooling.fraction`- `=(cooling.factor)^50`.
`method`	`method` sets the update rule used in the algorithm. `method="avif"` uses the iterated smoothing update rule (Ionides 2015 submitted); `method="ris1"` uses the reduced iterated smoothing update rule (Doucet 2013, Ionides 2015 submitted); `method="is1"` uses the reduced iterated smoothing update rule (Doucet 2013);
`tol`	See the description under `pfilter2`.
`max.fail`	See the description under `pfilter2`.
`verbose`	logical; if TRUE, print progress reports.
`transform`	logical; if `TRUE`, optimization is performed on the transformed scale.
`...`	additional arguments that override the defaults.

To re-run a sequence of avif iterations, one can use the avif method on a avif object. By default, the same parameters used for the original avif run are re-used (except for weighted, 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 avif iterations from where one left off using the continue method. A call to avif to perform Nis=m iterations followed by a call to continue to perform Nis=n iterations will produce precisely the same effect as a single call to avif to perform Nis=m+n iterations. By default, all the algorithmic parameters are the same as used in the original call to avif. Additional arguments will override the defaults.

One can use avif fixed-lag smoothing to estimate only initial value parameters (IVPs). In this case, pars is left empty and the IVPs to be estimated are named in ivps. If theta is the current parameter vector, then at each avif 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 avif 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).

If 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.

Dao Nguyen dxnguyen at olemiss dot edu, Xin Dang xdang at olemiss dot edu, Duc Anh Doan ddoan at olemiss dot edu

D. Nguyen, E. L. Ionides, A second-order iterated smoothing, Computational Statistics, 2017.

A., Doucet, P. E. Jacob, and S. Rubenthaler, Derivative-free estimation of the score vector and observed information matrix with application to state-space models, Preprint arXiv:1304.5768.

A. A. King, D. Nguyen, and E. L. Ionides, Statistical inference for partially observed Markov processes via the R package pomp, Journal of Statistical Software, 2016.

avif-methods, pfilter2. See the “intro_to_avif” vignette for examples.

nxdao2000/is2 documentation built on May 24, 2019, 11:50 a.m.