R/pc-t.R

Defines functions `inla.pc.ddof`

## Export: inla.pc.ddof

##! \name{pc.ddof}
##! \alias{pc.ddof}
##! \alias{inla.pc.ddof}
##! \alias{pc.t}
##! \alias{pc.dof}
##! \alias{inla.pc.t}
##! \alias{inla.pc.dof}
##!
##! \title{PC-prior for dof in a standarized Student-t}
##! 
##! \description{A function to evaluate the PC-prior for the degrees of freedom
##!              in a standarized Student-t distribution}
##! \usage{
##!     inla.pc.ddof(dof, lambda, u, alpha, log=FALSE)
##! }
##! \arguments{
##!   \item{dof}{Degrees of freedom}
##!   \item{log}{Logical. Return the density or the log-density}
##!   \item{lambda}{The optional value of \code{lambda},  instead of defining it implicitely
##!                 through \code{u} and \code{alpha}}
##!   \item{u}{The upper value of dof used to elicitate \code{lambda},  \code{Prob(dof < u) = alpha}}
##!   \item{alpha}{The probability \code{alpha} used to elicitate \code{lambda}}
##!}
##! \details{
##!   These functions implements the PC-prior for the dof in a standarized Student-t
##!   distribution (ie. with unit variance and \code{dof} > 2).
##!   Either \code{lambda}, or \code{u} AND \code{alpha} must be given.
##!   Due the internal tabulation, \code{dof} must be larger than 2.0025.
##! }
##! \value{%%
##!     \code{inla.pc.ddof} returns the prior density for given \code{dof}.
##! }
##! \author{Havard Rue \email{hrue@r-inla.org}}
##! \examples{
##! }


`inla.pc.ddof` = function(dof, lambda, u, alpha, log=FALSE)
{
    func.name.in.env = "inla.pc.t.dof.func"
    dof.lim = 9.0
    dof.min = 2.0025

    pc.dof.kld.approx = function (dof)
    {
        t1 = dof * dof
        t4 = t1 * dof
        t7 = t1 * t1
        t10 = t7 * dof
        t13 = t7 * t1
        t16 = t7 * t4
        t19 = t7 * t7
        t43 = t19 * t19
        t61 = 0.7500000000000000e0 / t1 + 0.1500000000000000e1 / t4 + 0.2125000000000000e1 / t7 + 0.2900000000000000e1 / t10
        + 0.5083333333333333e1 / t13 + 0.1035714285714286e2 / t16 + 0.1706250000000000e2 / t19
        + 0.1983333333333333e2 / t19 / dof + 0.4345000000000000e2 / t19 / t1 + 0.1873181818181818e3 / t19 / t4
        + 0.2570416666666667e3 / t19 / t7 - 0.1155192307692308e4 / t19 / t10 - 0.7801071428571429e3 / t19 / t13
        + 0.3207790000000000e5 / t19 / t16 + 0.3109703125000000e5 / t43 - 0.8438102058823529e6 / t43 / dof
        - 0.7932909722222222e6 / t43 / t1 + 0.2921518928947368e8 / t43 / t4 + 0.2776753702500000e8 / t43 / t7

        return (t61)
    }

    pc.dof.create.spline = function()
    {
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	sfun = splinefun(xx, yy, method = "monoH.FC")
        assign(func.name.in.env, sfun, envir = INLA:::inla.get.inlaEnv())
	return (invisible())
    }

    pc.dof.dist = function(dof, deriv = FALSE)
    {
        ## if 'deriv', then evaluate all 'dof' using the same approximation. in this case, dof
        ## are known to be close.
        n = length(dof)
        kld = numeric(n)

        if (!deriv) {
            idx = which(dof >= dof.lim)
            if (length(idx) > 0) {
                kld[idx] = pc.dof.kld.approx(dof[idx])
            }
            idx = which(dof < dof.lim)
            if (length(idx) > 0) {
                kld[idx] = (do.call(func.name.in.env, args = list(x = dof[idx]),
                                    envir = INLA:::inla.get.inlaEnv()))
            }
        } else {
            if (all(dof < dof.lim)) {
                kld = (do.call(func.name.in.env, args = list(x = dof),
                               envir = INLA:::inla.get.inlaEnv()))
            } else {
                kld = pc.dof.kld.approx(dof)
            }
        }
	return (sqrt(2.0 * kld))
    }

    if (!exists(func.name.in.env, envir = INLA:::inla.get.inlaEnv())) {
        pc.dof.create.spline()
    }
    if (missing(lambda)) {
        stopifnot(!(missing(u) && missing(alpha)))
        stopifnot(u > 2.0 && (alpha > 0 && alpha < 1))
        lambda = -log(alpha) / pc.dof.dist(u)
    } else {
        stopifnot(!(missing(lambda)))
        stopifnot(lambda > 0.0)
    }

    stopifnot(all(dof > dof.min))
    d = pc.dof.dist(dof)

    wf = c( 1.0 / 12.0, -2.0 / 3.0, 0.0, 2.0 / 3.0, -1.0 / 12.0 )
    jac = c()
    for(df in dof) {
        step = sqrt(df) * 1e-3
        if (df - 2.0 * step < dof.min) {
            step = (df - dof.min) / 2.0
        }
        dfs = df + (-2):2 * step 
        dd = pc.dof.dist(dfs, deriv=TRUE)
        val = sum(dd * wf) / step
        jac = c(jac, abs(val))
    }
 
    val = dexp(d, rate = lambda, log = TRUE) + log(jac)
    return (if (log) val else exp(val))
}
inbo/INLA documentation built on Dec. 6, 2019, 9:51 a.m.