FitMatch: Estimating Hidden States
In CollocInfer: Collocation Inference for Dynamic Systems

FitMatch

R Documentation

Estimating Hidden States

Description

Estimating hidden states to maximize agreement with the process.

Usage

FitMatchOpt(coefs,which,pars,proc,meth='nlminb',control=list())

FitMatchErr(coefs,allcoefs,which,pars,proc,sgn=1)

FitMatchDC(coefs,allcoefs,which,pars,proc,sgn=1)

FitMatchDC2(coefs,allcoefs,which,pars,proc,sgn=1)

FitMatchList(coefs,allcoefs,which,pars,proc,sgn=1)

Arguments

`coefs`	Vector giving the current estimate of the coefficients for the hidden states.
`allcoefs`	Matrix giving the coefficients of all the states including initial values for `coefs`.
`which`	Vector of indices of states to be estimated.
`pars`	Parameters to be used for the processes.
`proc`	`proc` object defining the state process.
`sgn`	Is the minimizing (1) or maximizing (0)?
`meth`	Optimization function currently one of 'nlminb', 'MaxNR', 'optim' or 'trust'.
`control`	Control object for optimization function.

Details

These routines allow the values of coefficients for some states to be optimized relative to the others. That is, the objective defined by proc is minimized over those states specified in which leaving the others constant. This would be typically done, for example, a smooth is taken to estimate some states non-parametrically, but data is not available on all of them.

A number of optimization routines have been implemented in FitMatchOpt, some experimentation is advised.

Value

`FitMatchOpt`	A list containing coefs The optimized coefficients for all states. res The output of the optimization routine.
`FitMatchErr`	The value of the process likelihood at the current estimated states.
`FitMatchDC`	The derivative of `FitMatchErr` with respect to the elements `coefs` for the states being estimated.
`FitMatchDC2`	The second derivative of `FitMatchErr` with respect to the elements `coefs` for the states being estimated.
`FitMatchList`	Returns a list with elements `value`, `gradient` and `hessian` given by the output of `FitMatchErr`, `FitMatchDC` and `FitMatchDC2`.

Examples

###############################
#### Some Data            #####
###############################

data(FhNdata)

# And parameter estimates

data(FhNest)


###############################
####  Basis Object      #######
###############################

knots = seq(0,20,0.2)
norder = 3
nbasis = length(knots) + norder - 2
range = c(0,20)

bbasis = create.bspline.basis(range=range(FhNtimes),nbasis=nbasis,
	norder=norder,breaks=knots)


# Initial values for coefficients will be obtained by smoothing

fd.data = FhNdata[,1]

DEfd = smooth.basis(FhNtimes,fd.data,fdPar(bbasis,1,0.5))   

coefs = cbind(DEfd$fd$coefs,rep(0,nbasis))
colnames(coefs) = FhNvarnames

#############################################################
### If We Only Observe One State, We Can Re-Smooth Others ### 
#############################################################

profile.obj = LS.setup(pars=FhNpars,coefs=coefs,fn=make.fhn(),
                      basisvals=bbasis,lambda=1000,times=FhNtimes)
lik = profile.obj$lik
proc= profile.obj$proc

#  DD = Matrix(diag(1,200),sparse=TRUE)
#  tDD = t(DD)

fres = FitMatchOpt(coefs=coefs,which=2,pars=FhNpars,proc)

plot(fd(fres$coefs,bbasis))

CollocInfer documentation built on April 4, 2025, 2:21 a.m.