mif2 {pomp}  R Documentation 
Iterated filtering: maximum likelihood by iterated, perturbed Bayes maps
Description
An iterated filtering algorithm for estimating the parameters of a partiallyobserved Markov process.
Running mif2
causes the algorithm to perform a specified number of particlefilter iterations.
At each iteration, the particle filter is performed on a perturbed version of the model, in which the parameters to be estimated are subjected to random perturbations at each observation.
This extra variability effectively smooths the likelihood surface and combats particle depletion by introducing diversity into particle population.
As the iterations progress, the magnitude of the perturbations is diminished according to a userspecified cooling schedule.
The algorithm is presented and justified in Ionides et al. (2015).
Usage
## S4 method for signature 'data.frame'
mif2(
data,
Nmif = 1,
rw.sd,
cooling.type = c("geometric", "hyperbolic"),
cooling.fraction.50,
Np,
params,
rinit,
rprocess,
dmeasure,
partrans,
...,
verbose = getOption("verbose", FALSE)
)
## S4 method for signature 'pomp'
mif2(
data,
Nmif = 1,
rw.sd,
cooling.type = c("geometric", "hyperbolic"),
cooling.fraction.50,
Np,
...,
verbose = getOption("verbose", FALSE)
)
## S4 method for signature 'pfilterd_pomp'
mif2(data, Nmif = 1, Np, ..., verbose = getOption("verbose", FALSE))
## S4 method for signature 'mif2d_pomp'
mif2(
data,
Nmif,
rw.sd,
cooling.type,
cooling.fraction.50,
...,
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, 
Nmif 
The number of filtering iterations to perform. 
rw.sd 
specification of the magnitude of the randomwalk perturbations that will be applied to some or all model parameters.
Parameters that are to be estimated should have positive perturbations specified here.
The specification is given using the ifelse(time==time[1],s,0). Likewise, ifelse(time==time[lag],s,0). See below for some examples. The perturbations that are applied are normally distributed with the specified s.d. If parameter transformations have been supplied, then the perturbations are applied on the transformed (estimation) scale. 
cooling.type , cooling.fraction.50 
specifications for the cooling schedule,
i.e., the manner and rate with which the intensity of the parameter perturbations is reduced with successive filtering iterations.

Np 
the number of particles to use.
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 timesteps, one may specify length(time(object,t0=TRUE)) or as a function taking a positive integer argument.
In the latter case, 
params 
optional; named numeric vector of parameters.
This will be coerced internally to storage mode 
rinit 
simulator of the initialstate distribution.
This can be furnished either as a C snippet, an R function, or the name of a precompiled native routine available in a dynamically loaded library.
Setting 
rprocess 
simulator of the latent state process, specified using one of the rprocess plugins.
Setting 
dmeasure 
evaluator of the measurement model density, specified either as a C snippet, an R function, or the name of a precompiled native routine available in a dynamically loaded library.
Setting 
partrans 
optional parameter transformations, constructed using 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 
... 
additional arguments are passed to 
verbose 
logical; if 
Value
Upon successful completion, mif2
returns an object of class
‘mif2d_pomp’.
Number of particles
If Np
is anything other than a constant, the user must take care that the number of particles requested at the end of the time series matches that requested at the beginning.
In particular, if T=length(time(object))
, then one should have Np[1]==Np[T+1]
when Np
is furnished as an integer vector and Np(0)==Np(T)
when Np
is furnished as a function.
Methods
The following methods are available for such an object:
continue
picks up where
mif2
leaves off and performs more filtering iterations.logLik
returns the socalled mif log likelihood which is the log likelihood of the perturbed model, not of the focal model itself. To obtain the latter, it is advisable to run several
pfilter
operations on the result of amif2
computatation.coef
extracts the point estimate
eff_sample_size
extracts the effective sample size of the final filtering iteration
Various other methods can be applied, including all the methods applicable to a pfilterd_pomp
object and all other pomp estimation algorithms and diagnostic methods.
Specifying the perturbations
The rw_sd
function simply returns a list containing its arguments as unevaluated expressions.
These are then evaluated in a context containing the model time
variable.
This allows for easy specification of the structure of the perturbations that are to be applied.
For example,
rw_sd(a=0.05, b=ifelse(time==time[1],0.2,0), c=ivp(0.2), d=ifelse(time==time[13],0.2,0), e=ivp(0.2,lag=13), f=ifelse(time<23,0.02,0))
results in perturbations of parameter a
with s.d. 0.05 at every time step, while parameters b
and c
both get perturbations of s.d. 0.2 only just before the first observation.
Parameters d
and e
, by contrast, get perturbations of s.d. 0.2 only just before the thirteenth observation.
Finally, parameter f
gets a random perturbation of size 0.02 before every observation falling before t=23
.
On the m
th IF2 iteration, prior to timepoint n
, the d
th parameter is given a random increment normally distributed with mean 0
and standard deviation c_{m,n} \sigma_{d,n}
, where c
is the cooling schedule and \sigma
is specified using rw_sd
, as described above.
Let N
be the length of the time series and \alpha=
cooling.fraction.50
.
Then, when cooling.type="geometric"
, we have
c_{m,n}=\alpha^{\frac{n1+(m1)N}{50N}}.
When cooling.type="hyperbolic"
, we have
c_{m,n}=\frac{s+1}{s+n+(m1)N},
where s
satisfies
\frac{s+1}{s+50N}=\alpha.
Thus, in either case, the perturbations at the end of 50 IF2 iterations are a fraction \alpha
smaller than they are at first.
Rerunning IF2 iterations
To rerun a sequence of IF2 iterations, one can use the mif2
method on a ‘mif2d_pomp’ object.
By default, the same parameters used for the original IF2 run are reused (except for verbose
, the default of which is shown above).
If one does specify additional arguments, these will override the defaults.
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.
Author(s)
Aaron A. King, Edward L. Ionides, Dao Nguyen
References
E.L. Ionides, D. Nguyen, Y. AtchadÃ©, S. Stoev, and A.A. King. Inference for dynamic and latent variable models via iterated, perturbed Bayes maps. Proceedings of the National Academy of Sciences 112, 719–724, 2015. doi:10.1073/pnas.1410597112.
See Also
More on fullinformation (i.e., likelihoodbased) methods:
bsmc2()
,
pfilter()
,
pmcmc()
,
wpfilter()
More on sequential Monte Carlo methods:
bsmc2()
,
cond_logLik()
,
eff_sample_size()
,
filter_mean()
,
filter_traj()
,
kalman
,
pfilter()
,
pmcmc()
,
pred_mean()
,
pred_var()
,
saved_states()
,
wpfilter()
More on pomp estimation algorithms:
abc()
,
bsmc2()
,
estimation_algorithms
,
nlf
,
pmcmc()
,
pomppackage
,
probe_match
,
spect_match
More on maximizationbased estimation methods:
nlf
,
probe_match
,
spect_match
,
traj_match