Returns a list of functions that calculate the transform and its derivatives.
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All the functions
make... functions, require the arguments needed by
Values of the state at the evaluation times
Parameters to be used
A list of additional arguments, in this case
make.genlin requires the specification of further elements in the list. In particular
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.
any values in
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
force.sub defined as in
sub, over-rides the elements of
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?
d2fdx2 Functions and derivatives as would be used to estimate
parameters for the original equations.
pars Parameters to go into
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
a list with objects
beta.fun A function to calculate beta, it should have arguments
betadef and return a matrix giving the value of beta at times
beta.dfdp Should calculate the derivative of
beta.fun with respect to
t returning a matrix. The matrix should be of size
p is the entire parameter vector.
betadef Additional inputs (eg bases) to
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
describe the autoregressive coefficient, and
alphabasis to provide a contant in front of
the functional data object
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
A list of functions that calculate the transform and its derivatives, in a form compatible with the collocation inference functions.
returns the identity transform.
returns the exponential transform.
returns a linear combination transform – see details section below.
returns the FitzHugh-Nagumo equations.
reutrns the Henon map.
returns SEIR equations for estimating the shape of a seasonal forcing component.
functions to perform forcing function diagnostics.
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# 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()
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