Probes and synthetic likelihood: Probe a partially-observed Markov process by computing summary statistics and the synthetic likelihood.

Description

probe applies one or more probes to time series data and model simulations and compares the results. It can be used to diagnose goodness of fit and/or as the basis for probe-matching, a generalized method-of-moments approach to parameter estimation. probe.match calls an optimizer to adjust model parameters to do probe-matching, i.e., to minimize the discrepancy between simulated and actual data. This discrepancy is measured using the synthetic likelihood as defined by Wood (2010). probe.match.objfun constructs an objective function for probe-matching suitable for use in optim-like optimizers.

Usage

## S3 method for class 'pomp':
probe(object, probes, params, nsim, seed = NULL, \dots)
## S3 method for class 'probed.pomp':
probe(object, probes, params, nsim, seed, \dots)
## S3 method for class 'pomp':
probe.match.objfun(object, params, est, probes, nsim,
            seed = NULL, fail.value = NA, transform = FALSE, \dots)
## S3 method for class 'probed.pomp':
probe.match.objfun(object, probes, nsim, seed, \dots)
## S3 method for class 'pomp':
probe.match(object, start, est = character(0),
            probes, nsim, seed = NULL,
            method = c("subplex","Nelder-Mead","SANN","BFGS",
                       "sannbox","nloptr"),
            verbose = getOption("verbose"), 
            fail.value = NA, transform = FALSE, ...)
## S3 method for class 'probed.pomp':
probe.match(object, probes, nsim, seed,
            \dots, verbose = getOption("verbose"))
## S3 method for class 'probe.matched.pomp':
probe.match(object, est, probes,
            nsim, seed, transform, fail.value, \dots,
            verbose = getOption("verbose"))
## S3 method for class 'probed.pomp':
logLik(object, \dots)
## S3 method for class 'probed.pomp':
values(object, \dots)

Arguments

object

An object of class pomp.

probes

A single probe or a list of one or more probes. A probe is simply a scalar- or vector-valued function of one argument that can be applied to the data array of a pomp. A vector-valued probe must always return a vector of the same size.

params

optional named numeric vector of model parameters. By default, params=coef(object).

nsim

The number of model simulations to be computed.

seed

optional; if non-NULL, the random number generator will be initialized with this seed for simulations. See simulate-pomp.

start

named numeric vector; the initial guess of parameters.

est

character vector; the names of parameters to be estimated.

method

Optimization method. Choices refer to algorithms used in optim, subplex, and nloptr.

verbose

logical; print diagnostic messages?

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).

transform

logical; if TRUE, optimization is performed on the transformed scale.

...

Additional arguments. In the case of probe, these are currently ignored. In the case of probe.match, these are passed to the optimizer (one of optim,

Value

probe returns an object of class probed.pomp. probed.pomp is derived from the pomp class and therefore have all the slots of pomp. In addition, a probed.pomp class has the following slots: [object Object],[object Object],[object Object],[object Object],[object Object]
probe.match returns an object of class probe.matched.pomp, which is derived from class probed.pomp. probe.matched.pomp objects therefore have all the slots above plus the following: [object Object],[object Object],[object Object],[object Object]
probe.match.objfun returns a function suitable for use as an objective function in an optim-like optimizer.

Details

A call to probe results in the evaluation of the probe(s) in probes on the data. Additionally, nsim simulated data sets are generated (via a call to simulate) and the probe(s) are applied to each of these. The results of the probe computations on real and simulated data are stored in an object of class probed.pomp.

A call to probe.match results in an attempt to optimize the agreement between model and data, as measured by the specified probes, over the parameters named in est. The results, including coefficients of the fitted model and values of the probes for data and fitted-model simulations, are stored in an object of class probe.matched.pomp.

The objective function minimized by probe.match --- in a form suitable for use with optim-like optimizers --- is created by a call to probe.match.objfun. Specifically, probe.match.objfun will return a function that takes a single numeric-vector argument that is assumed to cotain the parameters named in est, in that order. This function will return the negative synthetic log likelihood for the probes specified.

References

B. E. Kendall, C. J. Briggs, W. M. Murdoch, P. Turchin, S. P. Ellner, E. McCauley, R. M. Nisbet, S. N. Wood Why do populations cycle? A synthesis of statistical and mechanistic modeling approaches, Ecology, 80:1789--1805, 1999.

S. N. Wood Statistical inference for noisy nonlinear ecological dynamic systems, Nature, 466: 1102--1104, 2010.

Examples

Run this code

pompExample(ou2)
good <- probe(
              ou2,
              probes=list(
                y1.mean=probe.mean(var="y1"),
                y2.mean=probe.mean(var="y2"),
                y1.sd=probe.sd(var="y1"),
                y2.sd=probe.sd(var="y2"),
                extra=function(x)max(x["y1",])
                ),
              nsim=500
              )
summary(good)
plot(good)

bad <- probe(
             ou2,
             params=c(alpha.1=0.1,alpha.4=0.2,x1.0=0,x2.0=0,
                      alpha.2=-0.5,alpha.3=0.3,
                      sigma.1=3,sigma.2=-0.5,sigma.3=2,
                      tau=1),
             probes=list(
               y1.mean=probe.mean(var="y1"),
               y2.mean=probe.mean(var="y2"),
               y1.sd=probe.sd(var="y1"),
               y2.sd=probe.sd(var="y2"),
               extra=function(x)range(x["y1",])
               ),
             nsim=500
             )
summary(bad)
plot(bad)

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