spect_match {pomp}

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 supply new or modify existing model characteristics or components. See pomp for a full list of recognized arguments. When named arguments not recognized by pomp are provided, these are made available to all basic components via the so-called userdata facility. This allows the user to pass information to the basic components outside of the usual routes of covariates (covar) and model parameters (params). See userdata for information on how to use this facility.
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

D.C. Reuman, R.A. Desharnais, R.F. Costantino, O. Ahmad, J.E. Cohen. Power spectra reveal the influence of stochasticity on nonlinear population dynamics. Proceedings of the National Academy of Sciences 103, 18860-18865, 2006

D.C. Reuman, R.F. Costantino, R.A. Desharnais, J.E. Cohen. Color of environmental noise affects the nonlinear dynamics of cycling, stage-structured populations. Ecology Letters 11, 820-830, 2008.

See Also

spect optim subplex nloptr

More on pomp estimation algorithms: abc(), bsmc2(), estimation_algorithms, mif2(), nlf, pmcmc(), pomp-package, probe_match

More on methods based on summary statistics: abc(), basic_probes, nlf, probe(), probe_match, spect()

More on maximization-based estimation methods: mif2(), nlf, probe_match, traj_match

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()

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