pomp (version 0.24-7)

euler: Plug-ins for dynamical models based on stochastic Euler algorithms

Description

Plug-in facilities for implementing discrete-time Markov processes and continuous-time Markov processes using the Euler algorithm. These can be used in the rprocess and dprocess slots of pomp.

Usage

euler.simulate(xstart, times, params, step.fun, delta.t, ...,
               statenames = character(0), paramnames = character(0),
               covarnames = character(0), zeronames = character(0),
               tcovar, covar, PACKAGE)
onestep.simulate(xstart, times, params, step.fun, ...,
                 statenames = character(0), paramnames = character(0),
                 covarnames = character(0), zeronames = character(0),
                 tcovar, covar, PACKAGE)
onestep.density(x, times, params, dens.fun, ...,
                statenames = character(0), paramnames = character(0),
                covarnames = character(0), tcovar, covar, log = FALSE,
                PACKAGE)

Arguments

xstart

Matrix (dimensions nvar x nrep) of states at initial time times[1].

x

Matrix (dimensions nvar x nrep x ntimes) of states at times times.

times

Vector of times (length ntimes) at which states are required or given.

params

Matrix containing parameters of the model. The nrep columns of params correspond to those of xstart.

step.fun

This can be either an R function or the name of a compiled, dynamically loaded native function containing the model simulator. It should be written to take a single Euler step from a single point in state space. If it is a native function, it must

dens.fun

This can be either an R function or a compiled, dynamically loaded native function containing the model transition log probability density function. This function will be called to compute the log likelihood of the actual Euler steps. It must be o

delta.t

Time interval of Euler steps.

statenames, paramnames, covarnames

Names of state variables, parameters, covariates, in the order they will be expected by the routine named in step.fun and dens.fun. This information is only used when the latter are implemented as compiled native functions.

zeronames

Names of additional variables which will be zeroed before each time in times. These are useful, e.g., for storing accumulations of state variables.

covar, tcovar

Matrix of covariates and times at which covariates are measured.

log

logical; if TRUE, log probabilities are given.

...

if step.fun (or dens.fun) is an R function, then additional arguments will be passed to it. If step.fun (or dens.fun) is a native routine, then additional arguments are ignored.

PACKAGE

an optional argument that specifies to which dynamically loaded library we restrict the search for the native routines. If this is '"base"', we search in the R executable itself.

Value

• euler.simulate and onestep.simulate each return a nvar x nrep x ntimes array, where nvar is the number of state variables, nrep is the number of replicate simulations (= number of columns of xstart and params), and ntimes is the length of times. If x is this array, x[,,1] will be identical to xstart; the rownames of x and xstart will also coincide.

  onestep.density returns a nrep x ntimes-1 array. If f is this array, f[i,j] is the likelihood of a transition from x[,i,j] to x[,i,j+1] in exactly one Euler step of duration times[j+1]-times[j].

Details

onestep.simulate assumes that a single call to step.fun will advance the state process from one time to the next. euler.simulate will take multiple Euler steps, each of size at most delta.t (see below for information on how the actual Euler step size is chosen) to get from one time to the next.

onestep.density assumes that no state transitions occure between consecutive times.

If step.fun is written as an R function, it must have at least the arguments x, t, params, delta.t, and .... On a call to this function, x will be a named vector of state variables, t a scalar time, and params a named vector of parameters. The length of the Euler step will be delta.t. If the argument covars is included and a covariate table has been included in the pomp object, then on a call to this function, covars will be filled with the values, at time t, of the covariates. This is accomplished via interpolation of the covariate table. Additional arguments may be given: these will be filled by the correspondingly-named elements in the userdata slot of the pomp object (see pomp).

If step.fun is written in a native language, it must be a function of type "pomp_onestep_sim" as specified in the header "pomp.h" included with the package (see the directory "include" in the installed package directory).

If dens.fun is written as an R function, it must have at least the arguments x1, x2, t1, t2, params, and .... On a call to this function, x1 and x2 will be named vectors of state variables at times t1 and t2, respectively. The named vector params contains the parameters. If the argument covars is included and a covariate table has been included in the pomp object, then on a call to this function, covars will be filled with the values, at time t1, of the covariates. This is accomplished via interpolation of the covariate table. As above, any additional arguments will be filled by the correspondingly-named elements in the userdata slot of the pomp object (see pomp).

If dens.fun is written in a native language, it must be a function of type "pomp_onestep_pdf" as defined in the header "pomp.h" included with the package (see the directory "include" in the installed package directory).

See Also

eulermultinom, pomp

Examples

## an example showing how to use these functions to implement a seasonal SIR model is contained
## in the 'examples' directory
edit(file=system.file("examples/euler_sir.R",package="pomp"))