R/pc-t.R
In inbo/INLA: Full Bayesian Analysis of Latent Gaussian Models using Integrated Nested Laplace Approximations
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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0.012309394450,
0.012292032970,
0.012274694180,
0.012257378070,
0.012240084590,
0.012222813740,
0.012205565470,
0.012188339780,
0.012171136620,
0.012153955970,
0.012136797820,
0.012119662130,
0.012102548870,
0.012085458030,
0.012068389570,
0.012051343480,
0.012034319710,
0.012017318260,
0.012000339090,
0.011983382180,
0.011966447500,
0.011949535020,
0.011932644730,
0.011915776590,
0.011898930580,
0.011882106680,
0.011865304850,
0.011848525080,
0.011831767340,
0.011815031600,
0.011798317840,
0.011781626030,
0.011764956150,
0.011748308170,
0.011731682070,
0.011715077810,
0.011698495550,
0.011681934920,
0.011665396070,
0.011648878970,
0.011632383590,
0.011615909920,
0.011599457920,
0.011583027570,
0.011566618840,
0.011550231720,
0.011533866170,
0.011517522170,
0.011501199690,
0.011484898720,
0.011468619220,
0.011452361180,
0.011436124560,
0.011419909330,
0.011403715490,
0.011387543000,
0.011371391830,
0.011355261970,
0.011339153380,
0.011323066040,
0.011306999940,
0.011290955030,
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0.009176503025,
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0.009150115923,
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0.009123799982,
0.009110668644,
0.009097555032,
0.009084459124,
0.009071380900,
0.009058320337,
0.009045277415,
0.009032252112,
0.009019244407,
0.009006254279,
0.008993281706,
0.008980326666,
0.008967389140,
0.008954469105,
0.008941566541,
0.008928681425,
0.008915813738)
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.
R Package Documentation
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Note that we can't provide technical support on individual packages. You should contact the package authors for that.
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()
{
xx = c(
2.002478752000,
2.002480761000,
2.002482771000,
2.002484783000,
2.002486797000,
2.002488812000,
2.002490829000,
2.002492848000,
2.002494868000,
2.002496890000,
2.002498914000,
2.002500939000,
2.002502966000,
2.002504994000,
2.002507024000,
2.002509056000,
2.002511089000,
2.002513124000,
2.002515161000,
2.002517199000,
2.002519239000,
2.002521281000,
2.002523324000,
2.002525369000,
2.002527415000,
2.002529464000,
2.002531514000,
2.002533565000,
2.002535618000,
2.002537673000,
2.002539730000,
2.002541788000,
2.002543848000,
2.002545909000,
2.002547973000,
2.002550038000,
2.002552104000,
2.002554172000,
2.002556242000,
2.002558314000,
2.002560387000,
2.002562462000,
2.002564539000,
2.002566617000,
2.002568697000,
2.002570779000,
2.002572862000,
2.002574947000,
2.002577034000,
2.002579123000,
2.002581213000,
2.002583305000,
2.002585398000,
2.002587493000,
2.002589590000,
2.002591689000,
2.002593789000,
2.002595891000,
2.002597995000,
2.002600100000,
2.002602208000,
2.002604316000,
2.002606427000,
2.002608539000,
2.002610653000,
2.002612769000,
2.002614886000,
2.002617005000,
2.002619126000,
2.002621249000,
2.002623373000,
2.002625499000,
2.002627627000,
2.002629756000,
2.002631888000,
2.002634020000,
2.002636155000,
2.002638291000,
2.002640430000,
2.002642569000,
2.002644711000,
2.002646854000,
2.002648999000,
2.002651146000,
2.002653295000,
2.002655445000,
2.002657597000,
2.002659751000,
2.002661906000,
2.002664063000,
2.002666222000,
2.002668383000,
2.002670545000,
2.002672710000,
2.002674876000,
2.002677043000,
2.002679213000,
2.002681384000,
2.002683557000,
2.002685732000,
2.002687908000,
2.002690087000,
2.002692267000,
2.002694449000,
2.002696632000,
2.002698818000,
2.002701005000,
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2.002705384000,
2.002707577000,
2.002709771000,
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2.002716365000,
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2.002740678000,
2.002742899000,
2.002745122000,
2.002747347000,
2.002749573000,
2.002751801000,
2.002754031000,
2.002756263000,
2.002758497000,
2.002760733000,
2.002762970000,
2.002765209000,
2.002767450000,
2.002769693000,
2.002771937000,
2.002774184000,
2.002776432000,
2.002778682000,
2.002780934000,
2.002783188000,
2.002785443000,
2.002787700000,
2.002789960000,
2.002792221000,
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2.002796748000,
2.002799015000,
2.002801283000,
2.002803553000,
2.002805825000,
2.002808099000,
2.002810375000,
2.002812652000,
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2.002819496000,
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2.002824068000,
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2.002828647000,
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2.002881844000,
2.002884179000,
2.002886517000,
2.002888856000,
2.002891197000,
2.002893540000,
2.002895885000,
2.002898232000,
2.002900581000,
2.002902931000,
2.002905284000,
2.002907638000,
2.002909995000,
2.002912353000,
2.002914713000,
2.002917075000,
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2.002921805000,
2.002924173000,
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2.002928915000,
2.002931288000,
2.002933664000,
2.002936041000,
2.002938421000,
2.002940802000,
2.002943185000,
2.002945571000,
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2.002950347000,
2.002952738000,
2.002955131000,
2.002957525000,
2.002959922000,
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2.002971936000,
2.002974344000,
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2.003089772000,
2.003092276000,
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2.003097290000,
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2.003102312000,
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2.003158097000,
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2.003170914000,
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2.003188946000,
2.003191530000,
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2.003201889000,
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2.003217489000,
2.003220097000,
2.003222706000,
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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))
}
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