eglhmm (version 0.1-3)

postHocGradHess: Obtain gradient and Hessian, post hoc.

Description

Calculates the gradient and Hessian of the log likelihood of an extended generalised hidden Markov model, from the components of a "eglhmm" object, or in certain circumstances, simply extracts these quantities from that object.

Usage

postHocGradHess(object,inclTau=TRUE)

Value

A list with components

• gradient: The gradient of the log likelihood.

• Hessian: The Hessian of the log likelihood.

• numGrad: The numerically calculated gradient of the log likelihood. Present only if object$method is "bf".

• numHess: The numerically calculated Hessian of the log likelihood. Present only if object$method is "bf" and if argument hessian was set equal to TRUE in the call to eglhmm() that produced object.

Arguments

object

An object of class "eglhmm" as returned by eglhmm().

inclTau

Logical scalar; should the vector of “tau” parameters be included in the parameters under consideration?

Author

Rolf Turner

Details

If object is the result of fitting a bivariate model (i.e. if it inherits from "eglhmm.bivariate" then an error is thrown. (No gradient or Hessian is available in this case.)

If object$method is "lm" and if inclTau matches the value used in fitting method, then the appropriate gradient and Hessian have already been calculated and are simply extracted from object. If inclTau does not match the value used in fitting method, then the gradient and Hessian are recalculated (by the undocumented function getHgl()) with the value of inclTau being that specified by the function argument.

If object$method is "em" or "bf", then the gradient and Hessian are calculated (by the undocumented function getHgl()) with the value of inclTau being that specified by the function argument.

If object$method is "bf" then the gradient has been calculated numerically and the Hessian may have been calculated numerically (f the argument hessian of eglhmm() was set equal to TRUE). The corresponding value of the gradient will comprise a component, named "numGrad", of the list returned by this function. The corresponding value of the Hessian, if this was indeed calculated, will comprise a component, named "numHess", of the list returned by this function.

References

R. Nazim Khan, (2002). Statistical modelling and analysis of ion channel data based on hidden Markov models and the EM algorithm. Ph.D. thesis, the University of Western Australia, Crawley, WA 6009.

David Oakes, Direct calculation of the information matrix via the EM algorithm (1999). Journal of the Royal Statistical Society, series B, 61, pp. 479 -- 482.

Theodore C. Lystig and James P. Hughes (2002). Exact computation of the observed information matrix for hidden Markov models. Journal of Computational and Graphical Statistics, 11 (3), pp. 678 -- 689.

Olivier Cappé and Eric Moulines (July 2005). Recursive computation of the score and observed information matrix in hidden Markov models, IEEE Workshop on Statistical Signal Processing, Bordeaux.

See Also

eglhmm()

Examples

fit.em <- eglhmm(y~locn+depth,data=SydColCount,distr="P",
                 cells=c("locn","depth"),K=2,method="em",verb=TRUE)
gh.em  <- postHocGradHess(fit.em) # Calculates using inclTau=TRUE.
if (FALSE) {
    gh.em.noTau <- postHocGradHess(fit.em,inclTau=FALSE)
    fit.lm <- eglhmm(y~locn+depth,data=SydColCount,distr="P",
                     cells=c("locn","depth"),K=2,verb=TRUE)
    gh.lm  <- postHocGradHess(fit.lm) # Just extracts the relevant components.
    gh.lm.noTau  <- postHocGradHess(fit.lm,inclTau=FALSE)
    fit.bf <- eglhmm(y~locn+depth,data=SydColCount,distr="P",
                     cells=c("locn","depth"),K=2,method="bf",verb=TRUE,
                     hessian=TRUE)
    gh.bf  <- postHocGradHess(fit.bf) # Calculates using inclTau=TRUE; also
                                      # extracts numerically computed quantities.
    gh.bf.noTau <- postHocGradHess(fit.bf,inclTau=FALSE) # Calculates; also
                                                         # extracts numerically
                                                         # computed quantities.
}