spect_match: Spectrum matching
In pomp: Statistical Inference for Partially Observed Markov Processes

spect_match

R Documentation

Spectrum matching

Description

Estimation of parameters by matching power spectra

Usage

## S4 method for signature 'data.frame'
spect_objfun(
  data,
  est = character(0),
  weights = 1,
  fail.value = NA,
  vars,
  kernel.width,
  nsim,
  seed = NULL,
  transform.data = identity,
  detrend = c("none", "mean", "linear", "quadratic"),
  params,
  rinit,
  rprocess,
  rmeasure,
  partrans,
  ...,
  verbose = getOption("verbose", FALSE)
)

## S4 method for signature 'pomp'
spect_objfun(
  data,
  est = character(0),
  weights = 1,
  fail.value = NA,
  vars,
  kernel.width,
  nsim,
  seed = NULL,
  transform.data = identity,
  detrend = c("none", "mean", "linear", "quadratic"),
  ...,
  verbose = getOption("verbose", FALSE)
)

## S4 method for signature 'spectd_pomp'
spect_objfun(
  data,
  est = character(0),
  weights = 1,
  fail.value = NA,
  vars,
  kernel.width,
  nsim,
  seed = NULL,
  transform.data = identity,
  detrend,
  ...,
  verbose = getOption("verbose", FALSE)
)

## S4 method for signature 'spect_match_objfun'
spect_objfun(
  data,
  est,
  weights,
  fail.value,
  seed = NULL,
  ...,
  verbose = getOption("verbose", FALSE)
)

Arguments

`data`	either a data frame holding the time series data, or an object of class ‘pomp’, i.e., the output of another pomp calculation. Internally, `data` will be coerced to an array with storage-mode `double`.
`est`	character vector; the names of parameters to be estimated.
`weights`	optional numeric or function. The mismatch between model and data is measured by a weighted average of mismatch at each frequency. By default, all frequencies are weighted equally. `weights` can be specified either as a vector (which must have length equal to the number of frequencies) or as a function of frequency. If the latter, `weights(freq)` must return a nonnegative weight for each frequency.
`fail.value`	optional numeric scalar; if non-`NA`, this value is substituted for non-finite values of the objective function. It should be a large number (i.e., bigger than any legitimate values the objective function is likely to take).
`vars`	optional; names of observed variables for which the power spectrum will be computed. By default, the spectrum will be computed for all observables.
`kernel.width`	width parameter for the smoothing kernel used for calculating the estimate of the spectrum.
`nsim`	the number of model simulations to be computed.
`seed`	integer. When fitting, it is often best to fix the seed of the random-number generator (RNG). This is accomplished by setting `seed` to an integer. By default, `seed = NULL`, which does not alter the RNG state.
`transform.data`	function; this transformation will be applied to the observables prior to estimation of the spectrum, and prior to any detrending.
`detrend`	de-trending operation to perform. Options include no detrending, and subtraction of constant, linear, and quadratic trends from the data. Detrending is applied to each data series and to each model simulation independently.
`params`	optional; named numeric vector of parameters. This will be coerced internally to storage mode `double`.
`rinit`	simulator of the initial-state distribution. This can be furnished either as a C snippet, an R function, or the name of a pre-compiled native routine available in a dynamically loaded library. Setting `rinit=NULL` sets the initial-state simulator to its default. For more information, see rinit specification.
`rprocess`	simulator of the latent state process, specified using one of the rprocess plugins. Setting `rprocess=NULL` removes the latent-state simulator. For more information, see rprocess specification for the documentation on these plugins.
`rmeasure`	simulator of the measurement model, specified either as a C snippet, an R function, or the name of a pre-compiled native routine available in a dynamically loaded library. Setting `rmeasure=NULL` removes the measurement model simulator. For more information, see rmeasure specification.
`partrans`	optional parameter transformations, constructed using `parameter_trans`. Many algorithms for parameter estimation search an unconstrained space of parameters. When working with such an algorithm and a model for which the parameters are constrained, it can be useful to transform parameters. One should supply the `partrans` argument via a call to `parameter_trans`. For more information, see parameter_trans. Setting `partrans=NULL` removes the parameter transformations, i.e., sets them to the identity transformation.
`...`	additional arguments are passed to `pomp`.
`verbose`	logical; if `TRUE`, diagnostic messages will be printed to the console.

Details

In spectrum matching, one attempts to minimize the discrepancy between a POMP model's predictions and data, as measured in the frequency domain by the power spectrum.

spect_objfun constructs an objective function that measures the discrepancy. It can be passed to any one of a variety of numerical optimization routines, which will adjust model parameters to minimize the discrepancies between the power spectrum of model simulations and that of the data.

Value

spect_objfun constructs a stateful objective function for spectrum matching. Specifically, spect_objfun returns an object of class ‘spect_match_objfun’, which is a function suitable for use in an optim-like optimizer. This function takes a single numeric-vector argument that is assumed to contain the parameters named in est, in that order. When called, it will return the (optionally weighted) L^2 distance between the data spectrum and simulated spectra. It is a stateful function: Each time it is called, it will remember the values of the parameters and the discrepancy measure.

Note for Windows users

Some Windows users report problems when using C snippets in parallel computations. These appear to arise when the temporary files created during the C snippet compilation process are not handled properly by the operating system. To circumvent this problem, use the cdir and cfile options to cause the C snippets to be written to a file of your choice, thus avoiding the use of temporary files altogether.

Important Note

Since pomp cannot guarantee that the final call an optimizer makes to the function is a call at the optimum, it cannot guarantee that the parameters stored in the function are the optimal ones. Therefore, it is a good idea to evaluate the function on the parameters returned by the optimization routine, which will ensure that these parameters are stored.

Warning! Objective functions based on C snippets

If you use C snippets (see Csnippet), a dynamically loadable library will be built. As a rule, pomp functions load this library as needed and unload it when it is no longer needed. The stateful objective functions are an exception to this rule. For efficiency, calls to the objective function do not execute pompLoad or pompUnload: rather, it is assumed that pompLoad has been called before any call to the objective function. When a stateful objective function using one or more C snippets is created, pompLoad is called internally to build and load the library: therefore, within a single R session, if one creates a stateful objective function, one can freely call that objective function and (more to the point) pass it to an optimizer that calls it freely, without needing to call pompLoad. On the other hand, if one retrieves a stored objective function from a file, or passes one to another R session, one must call pompLoad before using it. Failure to do this will typically result in a segmentation fault (i.e., it will crash the R session).

References

\Reuman

2006

\Reuman

2008

Examples



  ricker() |>
    spect_objfun(
      est=c("r","sigma","N_0"),
      partrans=parameter_trans(log=c("r","sigma","N_0")),
      paramnames=c("r","sigma","N_0"),
      kernel.width=3,
      nsim=100,
      seed=5069977
    ) -> f

  f(log(c(20,0.3,10)))
  f |> spect() |> plot()

  if (require(subplex)) {
    subplex(fn=f,par=log(c(20,0.3,10)),control=list(reltol=1e-5)) -> out
  } else {
    optim(fn=f,par=log(c(20,0.3,10)),control=list(reltol=1e-5)) -> out
  }
  f(out$par)

  f |> summary()

  f |> spect() |> plot()

pomp documentation built on Sept. 13, 2024, 1:08 a.m.