make.transfer {CollocInfer}

Transfer Functions

Description

Returns a list of functions that calculate the transform and its derivatives.

Usage

make.id()

make.exp()

make.exptrans()

make.genlin()

make.fhn()

make.Henon()

make.SEIR()

make.NS()

chemo.fun(times,y,p,more=NULL)

Arguments

All the functions created by make... functions, require the arguments needed by chemo.fun

times

Evaluation times

y

Values of the state at the evaluation times

p

Parameters to be used

more

A list of additional arguments, in this case NULL, for pomp.sekelton and pomp.dmeasure, more should be a list containing a pomp object in the element pomp.obj.

Details

make.genlin requires the specification of further elements in the list. In particular the element more should be a list containing

• mat a matrix defining the linear transform before any parameters are added. This may be all zero, but it may also specify fixed elements, if desired.

• sub a k-by-3 matrix indicating which parameters should be entered into which elements of mat. Each row is a triple giving the row and colum of mat to be specified and the element of the parameter vector that should be substituted. sub over-rides any values in mat.

• force if input functions are given, these are given as a list.

• force.mat specifying the influence of the elements of force on the state variables. Defined as in mat.

• force.sub defined as in sub, over-rides the elements of force.mat with parameter values.

make.diagnostics estimates forcing-function diagnostics as in Hooker, 2009 for goodness-of-fit assessment. It requires

• psi Values of a basis expansion for forcing functions at the quadrature points.

• which Which states are to be forced?

• fn, dfdx, d2fdx2 Functions and derivatives as would be used to estimate parameters for the original equations.

• pars Parameters to go into more$fn.

make.SEIR estimates parameters and a seasonal variation in the infection rate in an SEIR model. It requires the specification of the seasonal change rate in more by a list with objects

• beta.fun A function to calculate beta, it should have arguments t, p and betadef and return a matrix giving the value of beta at times t with parameters p.

• beta.dfdp Should calculate the derivative of beta.fun with respect to p, at times t returning a matrix. The matrix should be of size length(t) by length(p) where p is the entire parameter vector.

• betadef Additional inputs (eg bases) to beta.fun and beta.dfdp.

make.NS provides functions for the North Shore example. This is a possibly time-varying forced linear system of one dimension. It requires more to specify betabasis to describe the autoregressive coefficient, and alphabasis to provide a contant in front of the functional data object rainfd.

chemo.fun Is a five-state predator-prey-resources model used as an example. It stands alone as a function and should be used with the findif.ode functions.

Value

A list of functions that calculate the transform and its derivatives, in a form compatible with the collocation inference functions.

make.id

returns the identity transform.

make.exp

returns the exponential transform.

make.genlin

returns a linear combination transform – see details section below.

make.fhn

returns the FitzHugh-Nagumo equations.

make.Henon

reutrns the Henon map.

make.SEIR

returns SEIR equations for estimating the shape of a seasonal forcing component.

make.diagnostics

functions to perform forcing function diagnostics.

See Also

LS.setup, multinorm.setup

Examples

# Observe the FitzHugh-Nagumo equations

proc = make.SSEproc()
proc$more = make.fhn()

lik = make.SSElik()
lik$more = make.id()

# Observe an unknown scalar transform of each component of a Henon map, given
# in the first two elements of the parameter vector:

proc = make.Dproc()
proc$more = make.multinorm()
proc$more$more = c(make.Henon,make.cvar)

lik = make.multinorm()
lik$more = c(make.genlin,make.cvar)
lik$more$more = list(mat = matrix(0,2,2),sub=matrix(c(1,1,1,2,2,2),2,3,byrow=TRUE))

# Model SEIR equations on the log scale and then exponentiate

lik = make.SSElik()
lik$more = make.exp()

proc = make.SSEproc()
proc$more = make.logtrans()
proc$more$more = make.SEIR()