Probe a partiallyobserved 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 “probematching”, a generalized methodofmoments approach to parameter estimation.
probe.match
calls an optimizer to adjust model parameters to do probematching, 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 probematching suitable for use in optim
like optimizers.
Usage
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27  ## S4 method for signature 'pomp'
probe(object, probes, params, nsim, seed = NULL, ...)
## S4 method for signature 'probed.pomp'
probe(object, probes, params, nsim, seed, ...)
## S4 method for signature 'pomp'
probe.match.objfun(object, params, est, probes, nsim,
seed = NULL, fail.value = NA, transform = FALSE, ...)
## S4 method for signature 'probed.pomp'
probe.match.objfun(object, probes, nsim, seed, ...)
## S4 method for signature 'pomp'
probe.match(object, start, est = character(0),
probes, nsim, seed = NULL,
method = c("subplex","NelderMead","SANN","BFGS",
"sannbox","nloptr"),
verbose = getOption("verbose"),
fail.value = NA, transform = FALSE, ...)
## S4 method for signature 'probed.pomp'
probe.match(object, probes, nsim, seed,
..., verbose = getOption("verbose"))
## S4 method for signature 'probe.matched.pomp'
probe.match(object, est, probes,
nsim, seed, transform, fail.value, ...,
verbose = getOption("verbose"))
## S4 method for signature 'probed.pomp'
logLik(object, ...)
## S4 method for signature 'probed.pomp'
values(object, ...)

Arguments
object 
An object of class 
probes 
A single probe or a list of one or more probes.
A probe is simply a scalar or vectorvalued function of one argument that can be applied to the data array of a 
params 
optional named numeric vector of model parameters.
By default, 
nsim 
The number of model simulations to be computed. 
seed 
optional; if non 
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 
verbose 
logical; print diagnostic messages? 
fail.value 
optional numeric scalar;
if non 
transform 
logical;
if 
... 
Additional arguments.
In the case of 
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 fittedmodel 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 numericvector 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.
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:
 probes
list of the probes applied.
 datvals, simvals
values of each of the probes applied to the real and simulated data, respectively.
 quantiles
fraction of simulations with probe values less than the value of the probe of the data.
 pvals

twosided pvalues: fraction of the
simvals
that deviate more extremely from the mean of thesimvals
than doesdatavals
.  synth.loglik

the log synthetic likelihood (Wood 2010). This is the likelihood assuming that the probes are multivariatenormally distributed.
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:
 est, transform, fail.value
values of the corresponding arguments in the call to
probe.match
. value
value of the objective function at the optimum.
 evals

number of function and gradient evaluations by the optimizer. See
optim
.  convergence, msg

Convergence code and message from the optimizer. See
optim
andnloptr
.
probe.match.objfun
returns a function suitable for use as an objective function in an optim
like optimizer.
Methods
 plot

displays diagnostic plots.
 summary

displays summary information.
 values

extracts the realized values of the probes on the data and on the simulations as a data frame in long format. The variable
.id
indicates whether the probes are from the data or simulations.  logLik

returns the synthetic likelihood for the probes. NB: in general, this is not the same as the likelihood.
 as, as.data.frame

when a ‘probed.pomp’ is coerced to a ‘data.frame’, the first row gives the probes applied to the data; the rest of the rows give the probes evaluated on simulated data. The rownames of the result can be used to distinguish these.
In addition, slots of this object can be accessed via the $
operator.
Author(s)
Daniel C. Reuman, Aaron A. King
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.
See Also
pomp, probe functions, spect, and the tutorials on the package website.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32  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)
