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R/150a_gev_p1.R
In fitdistcp: Distribution Fitting with Calibrating Priors for Commonly Used Distributions
Defines functions
tgev_p1_cp
pgev_p1_cp
dgev_p1_cp
rgev_p1_cp
qgev_p1_cp
Documented in
dgev_p1_cp
pgev_p1_cp
qgev_p1_cp
rgev_p1_cp
tgev_p1_cp
#' Generalized Extreme Value Distribution with a Predictor, Predictions Based on a Calibrating Prior
#'
#' @inherit man description author references seealso return
#' @inheritParams man
#'
#' @inheritSection man Optional Return Values
#' @inheritSection man Optional Return Values (EVT models only)
#' @inheritSection man Optional Return Values (some EVT models only)
# #' @inheritSection man Details (homogeneous models)
#' @inheritSection man Details (non-homogeneous models)
# #' @inheritSection man Details (analytic integration)
#' @inheritSection man Details (DMGS integration)
#' @inheritSection man Details (RUST)
#'
#' @section Details of the Model:
#' The GEV distribution with a predictor has distribution function
#' \deqn{F(x;a,b,\sigma,\xi)=\exp{(-t(x;\mu(a,b),\sigma,\xi))}}
#' where
#' \deqn{t(x;\mu(a,b),\sigma,\xi) =
#' \begin{cases}
#' {\left[1+\xi\left(\frac{x-\mu(a,b)}{\sigma}\right)\right]}^{-1/\xi} & \text{if $\xi \ne 0$}\\
#' \exp{\left(-\frac{x-\mu(a,b)}{\sigma}\right)} & \text{if $\xi=0$}
#' \end{cases}}
#' where
#' \eqn{x} is the random variable,
#' \eqn{\mu=a+bt} is the location parameter,
#' modelled as a function of parameters \eqn{a,b} and predictor \eqn{t},
#' and \eqn{\sigma>0,\xi} are the scale and shape parameters.
#'
#' The calibrating prior we use is given by
#' \deqn{\pi(a,b,\sigma,\xi) \propto \frac{1}{\sigma}}
#' as given in Jewson et al. (2025).
#'
#' The code will stop with an error if the
#' input data gives a maximum likelihood
#' value for the shape parameter that lies outside the range \code{(minxi,maxxi)},
#' since outside this range there may be numerical problems.
#' Such values seldom occur
#' in real observed data for maxima.
#'
#' @example man/examples/example_150_gev_p1.R
#'
#' @name gev_p1_cp
NULL
#' @rdname gev_p1_cp
#' @inheritParams man
#' @export
#'
qgev_p1_cp=function(x,t,t0=NA,n0=NA,p=seq(0.1,0.9,0.1),ics=c(0,0,0,0),
d1=0.01,d2=0.01,fd3=0.01,d4=0.01,fdalpha=0.01,
minxi=-0.45,maxxi=0.45,
means=FALSE,waicscores=FALSE,extramodels=FALSE,
pdf=FALSE,dmgs=TRUE,rust=FALSE,nrust=100000,predictordata=TRUE,
centering=TRUE,debug=FALSE,aderivs=TRUE){
stopifnot( is.finite(x),!is.na(x),is.finite(p),!is.na(p),p>0,p<1,
length(ics)==4)
#
# 1 intro
#
alpha=1-p
nx=length(x)
nalpha=length(alpha)
t0=maket0(t0,n0,t)
if(debug)message(" t0=",t0)
if(pdf){
dalpha=pmin(fdalpha*alpha,fdalpha*(1-alpha))
alpham=alpha-dalpha
alphap=alpha+dalpha
}
#
# 2 centering
#
if(centering){
meant=mean(t)
t=t-meant
t0=t0-meant
}
#
# 3 ml param estimate
#
if(debug)message(" ml param estimate")
ics=gev_p1_setics(x,t,ics)
opt1=optim(ics,gev_p1_loglik,x=x,t=t,control=list(fnscale=-1)) #this one uses the evd routine for dgev
v1hat=opt1$par[1]
v2hat=opt1$par[2]
v3hat=opt1$par[3]
v4hat=opt1$par[4]
ml_params=c(v1hat,v2hat,v3hat,v4hat)
# gev_p1_checkmle(ml_params,minxi,maxxi)
if(debug)message(" ml_params=",ml_params)
if(abs(v4hat)>=1){revert2ml=TRUE}else{revert2ml=FALSE}
#
# 4 predictordata
#
prd=gev_p1_predictordata(predictordata,x,t,t0,ml_params)
predictedparameter=prd$predictedparameter
adjustedx=prd$adjustedx
#
# 5 aic
#
if(debug)message(" aic")
ml_value=opt1$val
maic=make_maic(ml_value,nparams=4)
#
# 6 calc ml quantiles and density
#
if(debug)message(" ml_quantiles")
ml_quantiles=qgev_p1((1-alpha),t0,ymn=v1hat,slope=v2hat,sigma=v3hat,xi=v4hat)
if(v4hat<0){
ml_max=(v1hat+v2hat*t0)-v3hat/v4hat
} else {
ml_max=Inf
}
fhat=dgev_p1(ml_quantiles,t0,ymn=v1hat,slope=v2hat,sigma=v3hat,xi=v4hat,log=FALSE)
if(debug)message(" ml_quantiles=",ml_quantiles)
if(debug)message(" fhat=",fhat)
#
# dmgs
#
standard_errors="dmgs not selected"
rh_flat_quantiles="dmgs not selected"
flat_quantiles="dmgs not selected"
rh_ml_quantiles="dmgs not selected"
cp_quantiles="dmgs not selected"
jp_quantiles="dmgs not selected"
ru_quantiles="dmgs not selected"
rh_flat_pdf="dmgs not selected"
ml_pdf="dmgs not selected"
cp_pdf="dmgs not selected"
waic1="dmgs not selected"
waic2="dmgs not selected"
ml_mean="dmgs not selected"
cp_mean="dmgs not selected"
rh_flat_mean="dmgs not selected"
flat_mean="dmgs not selected"
rh_ml_mean="dmgs not selected"
jp_mean="dmgs not selected"
cp_method="dmgs not selected"
if((dmgs)&&(!revert2ml)){
#
# 7 alpha pdf stuff
# -for now, I only make the pdf. I could add cdf too I suppose. Somehow.
if(pdf){
ml_quantilesm=qgev_p1((1-alpham),t0,ymn=v1hat,slope=v2hat,sigma=v3hat,xi=v4hat)
ml_quantilesp=qgev_p1((1-alphap),t0,ymn=v1hat,slope=v2hat,sigma=v3hat,xi=v4hat)
fhatm=dgev_p1(ml_quantilesm,t0,ymn=v1hat,slope=v2hat,sigma=v3hat,xi=v4hat,log=FALSE)
fhatp=dgev_p1(ml_quantilesp,t0,ymn=v1hat,slope=v2hat,sigma=v3hat,xi=v4hat,log=FALSE)
}
#
# 8 ldd
#
if(aderivs) ldd=gev_p1_ldda(x,t,v1hat,v2hat,v3hat,v4hat)
if(!aderivs)ldd=gev_p1_ldd(x,t,v1hat,d1,v2hat,d2,v3hat,fd3,v4hat,d4)
if(debug)message(" ldd=",ldd)
if(debug)message(" det(ldd)=",det(ldd))
lddi=solve(ldd)
standard_errors=make_se(nx,lddi)
if(extramodels|means){
if(aderivs) ldd_k4=gev_p1k3_ldda(x,t,v1hat,v2hat,v3hat,v4hat)
if(!aderivs)ldd_k4=gev_p1k3_ldd(x,t,v1hat,d1,v2hat,d2,v3hat,fd3,v4hat)
lddi_k4=solve(ldd_k4)
}
#
# 9 information matrix and related (for Jeffreys prior)
# -because of difficulty of calculating expected information, I just use observed information
if(debug)message(" call gev.infomat")
if(extramodels|means){
gg=-ldd
ggi=solve(gg)
detg=det(gg)
ggd=gev_p1_ggd(x,t,v1hat,d1,v2hat,d2,v3hat,fd3,v4hat,d4) #uses ldd! so not expected at all, just observed
}
#
# 10 calculate lddd (two versions)
#
if(debug)message(" lddd")
if(aderivs) lddd=gev_p1_lddda(x,t,v1hat,v2hat,v3hat,v4hat)
if(!aderivs)lddd=gev_p1_lddd(x,t,v1hat,d1,v2hat,d2,v3hat,fd3,v4hat,d4)
if(extramodels|means){
if(aderivs) lddd_k4=gev_p1k3_lddda(x,t,v1hat,v2hat,v3hat,v4hat)
if(!aderivs)lddd_k4=gev_p1k3_lddd(x,t,v1hat,d1,v2hat,d2,v3hat,fd3,v4hat)
}
#
# 11 mu1 (two versions)
#
if(debug)message(" calculate mu1")
if(aderivs) mu1=gev_p1_mu1fa(alpha,t0,v1hat,v2hat,v3hat,v4hat)
if(!aderivs)mu1=gev_p1_mu1f(alpha,t0,v1hat,d1,v2hat,d2,v3hat,fd3,v4hat,d4)
if(extramodels|means)mu1_k4=gev_p1k3_mu1f(alpha,t0,v1hat,d1,v2hat,d2,v3hat,fd3,v4hat)
if(pdf){
if(aderivs){
mu1m=gev_p1_mu1fa(alpham,t0,v1hat,v2hat,v3hat,v4hat)
mu1p=gev_p1_mu1fa(alphap,t0,v1hat,v2hat,v3hat,v4hat)
} else{
mu1m=gev_p1_mu1f(alpham,t0,v1hat,d1,v2hat,d2,v3hat,fd3,v4hat,d4)
mu1p=gev_p1_mu1f(alphap,t0,v1hat,d1,v2hat,d2,v3hat,fd3,v4hat,d4)
}
}
#
# 12 mu2 (two versions)
#
if(debug)message(" calculate mu2")
if(aderivs) mu2=gev_p1_mu2fa(alpha,t0,v1hat,v2hat,v3hat,v4hat)
if(!aderivs)mu2=gev_p1_mu2f(alpha,t0,v1hat,d1,v2hat,d2,v3hat,fd3,v4hat,d4)
if(extramodels|means)mu2_k4=gev_p1k3_mu2f(alpha,t0,v1hat,d1,v2hat,d2,v3hat,fd3,v4hat)
if(pdf){
if(aderivs){
mu2m=gev_p1_mu2fa(alpham,t0,v1hat,v2hat,v3hat,v4hat)
mu2p=gev_p1_mu2fa(alphap,t0,v1hat,v2hat,v3hat,v4hat)
} else {
mu2m=gev_p1_mu2f(alpham,t0,v1hat,d1,v2hat,d2,v3hat,fd3,v4hat,d4)
mu2p=gev_p1_mu2f(alphap,t0,v1hat,d1,v2hat,d2,v3hat,fd3,v4hat,d4)
}
}
#
# 13 model 2: flat prior
#
if(extramodels|means){
lambdad_flat=matrix(0,4)
dq=dmgs(lddi,lddd,mu1,lambdad_flat,mu2,dim=4)
flat_quantiles=ml_quantiles+dq/(nx*fhat)
} else {
flat_quantiles="extramodels not selected"
}
#
# 14 model 3: rh_ML (needs to use 3d version of Bayesian code, and fixedshape ldd,lddd,mu1,mu2)
#
if(extramodels|means){
lambdad_rh_mle=c(0,0,-1/v3hat)
dq=dmgs(lddi_k4,lddd_k4,mu1_k4,lambdad_rh_mle,mu2_k4,dim=3)
rh_ml_quantiles=ml_quantiles+dq/(nx*fhat)
} else {
rh_ml_quantiles="extramodels not selected"
}
#
# 15 model 4: rh_Flat with flat prior on shape (needs to use 4d version of Bayesian code)
#
lambdad_rh_flat=c(0,0,-1/v3hat,0)
dq=dmgs(lddi,lddd,mu1,lambdad_rh_flat,mu2,dim=4)
rh_flat_quantiles=ml_quantiles+dq/(nx*fhat)
if(pdf){
dqm=dmgs(lddi,lddd,mu1m,lambdad_rh_flat,mu2m,dim=4)
dqp=dmgs(lddi,lddd,mu1p,lambdad_rh_flat,mu2p,dim=4)
quantilesm=ml_quantilesm+dqm/(nx*fhatm)
quantilesp=ml_quantilesp+dqp/(nx*fhatp)
ml_pdf=fhat
rh_flat_pdf=-(alphap-alpham)/(quantilesp-quantilesm)
} else{
ml_pdf=fhat
rh_flat_pdf="pdf not selected"
}
#
# 16 model 5:
#
if(extramodels|means){
lambdad_jp=jpf4p(ggd,detg,ggi) #this is jp
dq=dmgs(lddi,lddd,mu1,lambdad_jp,mu2,dim=4)
jp_quantiles=ml_quantiles+dq/(nx*fhat)
} else {
jp_quantiles="extramodels not selected"
}
#
# 17 means
#
means=gev_p1_means(means,t0,ml_params,lddi,lddi_k4,lddd,lddd_k4,
lambdad_flat,lambdad_rh_mle,lambdad_rh_flat,lambdad_jp,nx,dim=4)
ml_mean =means$ml_mean
flat_mean =means$flat_mean
rh_ml_mean =means$rh_ml_mean
rh_flat_mean =means$rh_flat_mean
jp_mean =means$jp_mean
#
# 18 waicscores
#
waic=gev_p1_waic(waicscores,x,t,v1hat,d1,v2hat,d2,v3hat,fd3,v4hat,d4,
lddi,lddd,lambdad_rh_flat,aderivs)
waic1=waic$waic1
waic2=waic$waic2
#
# 20 rust
#
ru_quantiles="rust not selected"
if(rust){
rustsim=rgev_p1_cp(nrust,x,t=t,t0=t0,rust=TRUE,mlcp=FALSE)
ru_quantiles=makeq(rustsim$ru_deviates,p)
}
} else {
flat_quantiles=ml_quantiles
rh_ml_quantiles=ml_quantiles
rh_flat_quantiles=ml_quantiles
ru_quantiles=ml_quantiles
jp_quantiles=ml_quantiles
rh_flat_pdf=ml_pdf
flat_mean=ml_mean
rh_ml_mean=ml_mean
rh_flat_mean=ml_mean
jp_mean=ml_mean
} #end of if(dmgs)
#
# 21 decentering
#
if(centering){
ml_params[1]=ml_params[1]-ml_params[2]*meant
if(predictordata)predictedparameter=predictedparameter-ml_params[2]*meant
}
list( ml_params=ml_params,
ml_value=ml_value,
predictedparameter=predictedparameter,
adjustedx=adjustedx,
# expinfmat=expinfmat,
# expinfmati=expinfmati,
standard_errors=standard_errors,
revert2ml=revert2ml,
ml_quantiles=ml_quantiles,
ml_max=ml_max,
flat_quantiles=flat_quantiles,
rh_ml_quantiles=rh_ml_quantiles,
cp_quantiles=rh_flat_quantiles,
ru_quantiles=ru_quantiles,
jp_quantiles=jp_quantiles,
ml_pdf=ml_pdf,
cp_pdf=rh_flat_pdf,
maic=maic,
waic1=waic1,
waic2=waic2,
ml_mean=ml_mean,
flat_mean=flat_mean,
rh_ml_mean=rh_ml_mean,
cp_mean=rh_flat_mean,
jp_mean=jp_mean,
cp_method=crhpflat_dmgs_cpmethod())
}
#' @rdname gev_p1_cp
#' @inheritParams man
#' @export
rgev_p1_cp=function(n,x,t,t0=NA,n0=NA,ics=c(0,0,0,0),
d1=0.01,d2=0.01,fd3=0.01,d4=0.01,
minxi=-0.45,maxxi=0.45,
extramodels=FALSE,rust=FALSE,mlcp=TRUE,debug=FALSE,aderivs=TRUE){
# stopifnot(is.finite(n),!is.na(n),is.finite(x),!is.na(x),is.finite(t),!is.na(t),
# length(ics)==4)
stopifnot(is.finite(x),!is.na(x),is.finite(t),!is.na(t),
length(ics)==4)
t0=maket0(t0=t0,n0=n0,t=t)
#
# centering
#
meant=mean(t)
t=t-meant
t0=t0-meant
ml_params="mlcp not selected"
ml_deviates="mlcp not selected"
flat_deviates="mlcp not selected"
rh_ml_deviates="mlcp not selected"
jp_deviates="mlcp not selected"
ru_deviates="rust not selected"
cp_deviates="rust not selected"
if(mlcp){
q=qgev_p1_cp(x,t=t,t0=t0,n0=NA,p=runif(n),ics=ics,d1=d1,d2=d2,fd3=fd3,d4=d4,
extramodels=extramodels,aderivs=aderivs)
ml_params=q$ml_params
ml_deviates=q$ml_quantiles
flat_deviates=q$flat_quantiles
rh_ml_deviates=q$rh_ml_quantiles
ru_deviates=q$ru_quantiles
cp_deviates=q$cp_quantiles
jp_deviates=q$jp_quantiles
}
if(rust){
th=tgev_p1_cp(n,x,t)$theta_samples
ru_deviates=numeric(0)
for (i in 1:n){
mu=th[i,1]+t0*th[i,2]
ru_deviates[i]=rgev(1,mu=mu,sigma=th[i,3],xi=th[i,4])
}
}
#
# decentering
#
if(mlcp)ml_params[1]=ml_params[1]-ml_params[2]*meant
op=list(ml_params=ml_params,
ml_deviates=ml_deviates,
flat_deviates=flat_deviates,
rh_ml_deviates=rh_ml_deviates,
cp_deviates=cp_deviates,
ru_deviates=ru_deviates,
jp_deviates=jp_deviates,
cp_method=crhpflat_dmgs_cpmethod())
return(op)
}
#' @rdname gev_p1_cp
#' @inheritParams man
#' @export
dgev_p1_cp=function(x,t,t0=NA,n0=NA,y=x,ics=c(0,0,0,0),
d1=0.01,d2=0.01,fd3=0.01,d4=0.01,
minxi=-0.45,maxxi=0.45,extramodels=FALSE,
rust=FALSE,nrust=1000,centering=TRUE,debug=FALSE,aderivs=TRUE){
stopifnot(is.finite(x),!is.na(x),is.finite(y),!is.na(y),
is.finite(t),!is.na(t),length(ics)==4)
t0=maket0(t0,n0,t)
#
# centering
#
if(centering){
meant=mean(t)
t=t-meant
t0=t0-meant
}
ics=gev_p1_setics(x,t,ics)
opt1=optim(ics,gev_p1_loglik,x=x,t=t,control=list(fnscale=-1)) #this one uses the evd routine for dgev
v1hat=opt1$par[1]
v2hat=opt1$par[2]
v3hat=opt1$par[3]
v4hat=opt1$par[4]
if(v4hat<=(-1)){revert2ml=TRUE}else{revert2ml=FALSE}
ml_params=c(v1hat,v2hat,v3hat,v4hat)
# gev_p1_checkmle(ml_params,minxi,maxxi)
dd=dgev_p1sub(x=x,t=t,y=y,t0=t0,ics=ics,d1,d2,fd3,d4,
minxi,maxxi,extramodels=extramodels,aderivs=aderivs)
ru_pdf="rust not selected"
ml_params=dd$ml_params
if(rust&&(!revert2ml)){
th=tgev_p1_cp(nrust,x,t)$theta_samples
ru_pdf=numeric(length(y))
for (ir in 1:nrust){
mu=th[ir,1]+t0*th[ir,2]
ru_pdf=ru_pdf+dgev(y,mu=mu,sigma=th[ir,3],xi=th[ir,4])
}
ru_pdf=ru_pdf/nrust
} else {
ru_pdf=dd$ml_pdf
}
#
# decentering
#
if(centering)ml_params[1]=ml_params[1]-ml_params[2]*meant
op=list(
ml_params=ml_params,
ml_pdf=dd$ml_pdf,
revert2ml=revert2ml,
ru_pdf=ru_pdf,
cp_method=nopdfcdfmsg())
return(op)
}
#' @rdname gev_p1_cp
#' @inheritParams man
#' @export
pgev_p1_cp=function(x,t,t0=NA,n0=NA,y=x,ics=c(0,0,0,0),
d1=0.01,d2=0.01,fd3=0.01,d4=0.01,
minxi=-0.45,maxxi=0.45,extramodels=FALSE,
rust=FALSE,nrust=1000,centering=TRUE,debug=FALSE,aderivs=TRUE){
stopifnot(is.finite(x),!is.na(x),is.finite(y),!is.na(y),
is.finite(t),!is.na(t),length(ics)==4)
t0=maket0(t0,n0,t)
#
# centering
#
if(centering){
meant=mean(t)
t=t-meant
t0=t0-meant
}
ics=gev_p1_setics(x,t,ics)
opt1=optim(ics,gev_p1_loglik,x=x,t=t,control=list(fnscale=-1)) #this one uses the evd routine for dgev
v1hat=opt1$par[1]
v2hat=opt1$par[2]
v3hat=opt1$par[3]
v4hat=opt1$par[4]
if(v4hat<=(-1)){revert2ml=TRUE}else{revert2ml=FALSE}
ml_params=c(v1hat,v2hat,v3hat,v4hat)
# gev_p1_checkmle(ml_params,minxi,maxxi)
dd=dgev_p1sub(x=x,t=t,y=y,t0=t0,ics=ics,d1,d2,fd3,d4,
minxi,maxxi,extramodels=extramodels,aderivs=aderivs)
ru_cdf="rust not selected"
ml_params=dd$ml_params
if(rust&&(!revert2ml)){
th=tgev_p1_cp(nrust,x,t)$theta_samples
ru_cdf=numeric(length(y))
for (ir in 1:nrust){
mu=th[ir,1]+t0*th[ir,2]
ru_cdf=ru_cdf+pgev(y,mu=mu,sigma=th[ir,3],xi=th[ir,4])
}
ru_cdf=ru_cdf/nrust
} else {
ru_pdf=dd$ml_pdf
}
#
# decentering
#
if(centering)ml_params[1]=ml_params[1]-ml_params[2]*meant
op=list(
ml_params=ml_params,
ml_cdf=dd$ml_cdf,
revert2ml=revert2ml,
ru_cdf=ru_cdf,
cp_method=nopdfcdfmsg())
return(op)
}
#' @rdname gev_p1_cp
#' @inheritParams man
#' @export
tgev_p1_cp=function(n,x,t,ics=c(0,0,0,0),
d1=0.01,d2=0.01,fd3=0.01,d4=0.01,
extramodels=FALSE,debug=FALSE){
# stopifnot(is.finite(n),!is.na(n),is.finite(x),!is.na(x),is.finite(t),!is.na(t),
# length(ics)==4)
stopifnot(is.finite(x),!is.na(x),is.finite(t),!is.na(t),
length(ics)==4)
#
# centering
#
meant=mean(t)
t=t-meant
ics=gev_p1_setics(x,t,ics)
# th=ru(gev_p1_logf,x=x,t=t,n=n,d=4,init=c(0,0,1,0))
th=ru(gev_p1_logf,x=x,t=t,n=n,d=4,init=ics)
theta_samples=th$sim_vals
#
# decentering
#
theta_samples[,1]=theta_samples[,1]-theta_samples[,2]*meant
list(theta_samples=theta_samples)
}
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Defines functions tgev_p1_cp pgev_p1_cp dgev_p1_cp rgev_p1_cp qgev_p1_cp
Documented in dgev_p1_cp pgev_p1_cp qgev_p1_cp rgev_p1_cp tgev_p1_cp
#' Generalized Extreme Value Distribution with a Predictor, Predictions Based on a Calibrating Prior
#'
#' @inherit man description author references seealso return
#' @inheritParams man
#'
#' @inheritSection man Optional Return Values
#' @inheritSection man Optional Return Values (EVT models only)
#' @inheritSection man Optional Return Values (some EVT models only)
# #' @inheritSection man Details (homogeneous models)
#' @inheritSection man Details (non-homogeneous models)
# #' @inheritSection man Details (analytic integration)
#' @inheritSection man Details (DMGS integration)
#' @inheritSection man Details (RUST)
#'
#' @section Details of the Model:
#' The GEV distribution with a predictor has distribution function
#' \deqn{F(x;a,b,\sigma,\xi)=\exp{(-t(x;\mu(a,b),\sigma,\xi))}}
#' where
#' \deqn{t(x;\mu(a,b),\sigma,\xi) =
#' \begin{cases}
#' {\left[1+\xi\left(\frac{x-\mu(a,b)}{\sigma}\right)\right]}^{-1/\xi} & \text{if $\xi \ne 0$}\\
#' \exp{\left(-\frac{x-\mu(a,b)}{\sigma}\right)} & \text{if $\xi=0$}
#' \end{cases}}
#' where
#' \eqn{x} is the random variable,
#' \eqn{\mu=a+bt} is the location parameter,
#' modelled as a function of parameters \eqn{a,b} and predictor \eqn{t},
#' and \eqn{\sigma>0,\xi} are the scale and shape parameters.
#'
#' The calibrating prior we use is given by
#' \deqn{\pi(a,b,\sigma,\xi) \propto \frac{1}{\sigma}}
#' as given in Jewson et al. (2025).
#'
#' The code will stop with an error if the
#' input data gives a maximum likelihood
#' value for the shape parameter that lies outside the range \code{(minxi,maxxi)},
#' since outside this range there may be numerical problems.
#' Such values seldom occur
#' in real observed data for maxima.
#'
#' @example man/examples/example_150_gev_p1.R
#'
#' @name gev_p1_cp
NULL
#' @rdname gev_p1_cp
#' @inheritParams man
#' @export
#'
qgev_p1_cp=function(x,t,t0=NA,n0=NA,p=seq(0.1,0.9,0.1),ics=c(0,0,0,0),
d1=0.01,d2=0.01,fd3=0.01,d4=0.01,fdalpha=0.01,
minxi=-0.45,maxxi=0.45,
means=FALSE,waicscores=FALSE,extramodels=FALSE,
pdf=FALSE,dmgs=TRUE,rust=FALSE,nrust=100000,predictordata=TRUE,
centering=TRUE,debug=FALSE,aderivs=TRUE){
stopifnot( is.finite(x),!is.na(x),is.finite(p),!is.na(p),p>0,p<1,
length(ics)==4)
#
# 1 intro
#
alpha=1-p
nx=length(x)
nalpha=length(alpha)
t0=maket0(t0,n0,t)
if(debug)message(" t0=",t0)
if(pdf){
dalpha=pmin(fdalpha*alpha,fdalpha*(1-alpha))
alpham=alpha-dalpha
alphap=alpha+dalpha
}
#
# 2 centering
#
if(centering){
meant=mean(t)
t=t-meant
t0=t0-meant
}
#
# 3 ml param estimate
#
if(debug)message(" ml param estimate")
ics=gev_p1_setics(x,t,ics)
opt1=optim(ics,gev_p1_loglik,x=x,t=t,control=list(fnscale=-1)) #this one uses the evd routine for dgev
v1hat=opt1$par[1]
v2hat=opt1$par[2]
v3hat=opt1$par[3]
v4hat=opt1$par[4]
ml_params=c(v1hat,v2hat,v3hat,v4hat)
# gev_p1_checkmle(ml_params,minxi,maxxi)
if(debug)message(" ml_params=",ml_params)
if(abs(v4hat)>=1){revert2ml=TRUE}else{revert2ml=FALSE}
#
# 4 predictordata
#
prd=gev_p1_predictordata(predictordata,x,t,t0,ml_params)
predictedparameter=prd$predictedparameter
adjustedx=prd$adjustedx
#
# 5 aic
#
if(debug)message(" aic")
ml_value=opt1$val
maic=make_maic(ml_value,nparams=4)
#
# 6 calc ml quantiles and density
#
if(debug)message(" ml_quantiles")
ml_quantiles=qgev_p1((1-alpha),t0,ymn=v1hat,slope=v2hat,sigma=v3hat,xi=v4hat)
if(v4hat<0){
ml_max=(v1hat+v2hat*t0)-v3hat/v4hat
} else {
ml_max=Inf
}
fhat=dgev_p1(ml_quantiles,t0,ymn=v1hat,slope=v2hat,sigma=v3hat,xi=v4hat,log=FALSE)
if(debug)message(" ml_quantiles=",ml_quantiles)
if(debug)message(" fhat=",fhat)
#
# dmgs
#
standard_errors="dmgs not selected"
rh_flat_quantiles="dmgs not selected"
flat_quantiles="dmgs not selected"
rh_ml_quantiles="dmgs not selected"
cp_quantiles="dmgs not selected"
jp_quantiles="dmgs not selected"
ru_quantiles="dmgs not selected"
rh_flat_pdf="dmgs not selected"
ml_pdf="dmgs not selected"
cp_pdf="dmgs not selected"
waic1="dmgs not selected"
waic2="dmgs not selected"
ml_mean="dmgs not selected"
cp_mean="dmgs not selected"
rh_flat_mean="dmgs not selected"
flat_mean="dmgs not selected"
rh_ml_mean="dmgs not selected"
jp_mean="dmgs not selected"
cp_method="dmgs not selected"
if((dmgs)&&(!revert2ml)){
#
# 7 alpha pdf stuff
# -for now, I only make the pdf. I could add cdf too I suppose. Somehow.
if(pdf){
ml_quantilesm=qgev_p1((1-alpham),t0,ymn=v1hat,slope=v2hat,sigma=v3hat,xi=v4hat)
ml_quantilesp=qgev_p1((1-alphap),t0,ymn=v1hat,slope=v2hat,sigma=v3hat,xi=v4hat)
fhatm=dgev_p1(ml_quantilesm,t0,ymn=v1hat,slope=v2hat,sigma=v3hat,xi=v4hat,log=FALSE)
fhatp=dgev_p1(ml_quantilesp,t0,ymn=v1hat,slope=v2hat,sigma=v3hat,xi=v4hat,log=FALSE)
}
#
# 8 ldd
#
if(aderivs) ldd=gev_p1_ldda(x,t,v1hat,v2hat,v3hat,v4hat)
if(!aderivs)ldd=gev_p1_ldd(x,t,v1hat,d1,v2hat,d2,v3hat,fd3,v4hat,d4)
if(debug)message(" ldd=",ldd)
if(debug)message(" det(ldd)=",det(ldd))
lddi=solve(ldd)
standard_errors=make_se(nx,lddi)
if(extramodels|means){
if(aderivs) ldd_k4=gev_p1k3_ldda(x,t,v1hat,v2hat,v3hat,v4hat)
if(!aderivs)ldd_k4=gev_p1k3_ldd(x,t,v1hat,d1,v2hat,d2,v3hat,fd3,v4hat)
lddi_k4=solve(ldd_k4)
}
#
# 9 information matrix and related (for Jeffreys prior)
# -because of difficulty of calculating expected information, I just use observed information
if(debug)message(" call gev.infomat")
if(extramodels|means){
gg=-ldd
ggi=solve(gg)
detg=det(gg)
ggd=gev_p1_ggd(x,t,v1hat,d1,v2hat,d2,v3hat,fd3,v4hat,d4) #uses ldd! so not expected at all, just observed
}
#
# 10 calculate lddd (two versions)
#
if(debug)message(" lddd")
if(aderivs) lddd=gev_p1_lddda(x,t,v1hat,v2hat,v3hat,v4hat)
if(!aderivs)lddd=gev_p1_lddd(x,t,v1hat,d1,v2hat,d2,v3hat,fd3,v4hat,d4)
if(extramodels|means){
if(aderivs) lddd_k4=gev_p1k3_lddda(x,t,v1hat,v2hat,v3hat,v4hat)
if(!aderivs)lddd_k4=gev_p1k3_lddd(x,t,v1hat,d1,v2hat,d2,v3hat,fd3,v4hat)
}
#
# 11 mu1 (two versions)
#
if(debug)message(" calculate mu1")
if(aderivs) mu1=gev_p1_mu1fa(alpha,t0,v1hat,v2hat,v3hat,v4hat)
if(!aderivs)mu1=gev_p1_mu1f(alpha,t0,v1hat,d1,v2hat,d2,v3hat,fd3,v4hat,d4)
if(extramodels|means)mu1_k4=gev_p1k3_mu1f(alpha,t0,v1hat,d1,v2hat,d2,v3hat,fd3,v4hat)
if(pdf){
if(aderivs){
mu1m=gev_p1_mu1fa(alpham,t0,v1hat,v2hat,v3hat,v4hat)
mu1p=gev_p1_mu1fa(alphap,t0,v1hat,v2hat,v3hat,v4hat)
} else{
mu1m=gev_p1_mu1f(alpham,t0,v1hat,d1,v2hat,d2,v3hat,fd3,v4hat,d4)
mu1p=gev_p1_mu1f(alphap,t0,v1hat,d1,v2hat,d2,v3hat,fd3,v4hat,d4)
}
}
#
# 12 mu2 (two versions)
#
if(debug)message(" calculate mu2")
if(aderivs) mu2=gev_p1_mu2fa(alpha,t0,v1hat,v2hat,v3hat,v4hat)
if(!aderivs)mu2=gev_p1_mu2f(alpha,t0,v1hat,d1,v2hat,d2,v3hat,fd3,v4hat,d4)
if(extramodels|means)mu2_k4=gev_p1k3_mu2f(alpha,t0,v1hat,d1,v2hat,d2,v3hat,fd3,v4hat)
if(pdf){
if(aderivs){
mu2m=gev_p1_mu2fa(alpham,t0,v1hat,v2hat,v3hat,v4hat)
mu2p=gev_p1_mu2fa(alphap,t0,v1hat,v2hat,v3hat,v4hat)
} else {
mu2m=gev_p1_mu2f(alpham,t0,v1hat,d1,v2hat,d2,v3hat,fd3,v4hat,d4)
mu2p=gev_p1_mu2f(alphap,t0,v1hat,d1,v2hat,d2,v3hat,fd3,v4hat,d4)
}
}
#
# 13 model 2: flat prior
#
if(extramodels|means){
lambdad_flat=matrix(0,4)
dq=dmgs(lddi,lddd,mu1,lambdad_flat,mu2,dim=4)
flat_quantiles=ml_quantiles+dq/(nx*fhat)
} else {
flat_quantiles="extramodels not selected"
}
#
# 14 model 3: rh_ML (needs to use 3d version of Bayesian code, and fixedshape ldd,lddd,mu1,mu2)
#
if(extramodels|means){
lambdad_rh_mle=c(0,0,-1/v3hat)
dq=dmgs(lddi_k4,lddd_k4,mu1_k4,lambdad_rh_mle,mu2_k4,dim=3)
rh_ml_quantiles=ml_quantiles+dq/(nx*fhat)
} else {
rh_ml_quantiles="extramodels not selected"
}
#
# 15 model 4: rh_Flat with flat prior on shape (needs to use 4d version of Bayesian code)
#
lambdad_rh_flat=c(0,0,-1/v3hat,0)
dq=dmgs(lddi,lddd,mu1,lambdad_rh_flat,mu2,dim=4)
rh_flat_quantiles=ml_quantiles+dq/(nx*fhat)
if(pdf){
dqm=dmgs(lddi,lddd,mu1m,lambdad_rh_flat,mu2m,dim=4)
dqp=dmgs(lddi,lddd,mu1p,lambdad_rh_flat,mu2p,dim=4)
quantilesm=ml_quantilesm+dqm/(nx*fhatm)
quantilesp=ml_quantilesp+dqp/(nx*fhatp)
ml_pdf=fhat
rh_flat_pdf=-(alphap-alpham)/(quantilesp-quantilesm)
} else{
ml_pdf=fhat
rh_flat_pdf="pdf not selected"
}
#
# 16 model 5:
#
if(extramodels|means){
lambdad_jp=jpf4p(ggd,detg,ggi) #this is jp
dq=dmgs(lddi,lddd,mu1,lambdad_jp,mu2,dim=4)
jp_quantiles=ml_quantiles+dq/(nx*fhat)
} else {
jp_quantiles="extramodels not selected"
}
#
# 17 means
#
means=gev_p1_means(means,t0,ml_params,lddi,lddi_k4,lddd,lddd_k4,
lambdad_flat,lambdad_rh_mle,lambdad_rh_flat,lambdad_jp,nx,dim=4)
ml_mean =means$ml_mean
flat_mean =means$flat_mean
rh_ml_mean =means$rh_ml_mean
rh_flat_mean =means$rh_flat_mean
jp_mean =means$jp_mean
#
# 18 waicscores
#
waic=gev_p1_waic(waicscores,x,t,v1hat,d1,v2hat,d2,v3hat,fd3,v4hat,d4,
lddi,lddd,lambdad_rh_flat,aderivs)
waic1=waic$waic1
waic2=waic$waic2
#
# 20 rust
#
ru_quantiles="rust not selected"
if(rust){
rustsim=rgev_p1_cp(nrust,x,t=t,t0=t0,rust=TRUE,mlcp=FALSE)
ru_quantiles=makeq(rustsim$ru_deviates,p)
}
} else {
flat_quantiles=ml_quantiles
rh_ml_quantiles=ml_quantiles
rh_flat_quantiles=ml_quantiles
ru_quantiles=ml_quantiles
jp_quantiles=ml_quantiles
rh_flat_pdf=ml_pdf
flat_mean=ml_mean
rh_ml_mean=ml_mean
rh_flat_mean=ml_mean
jp_mean=ml_mean
} #end of if(dmgs)
#
# 21 decentering
#
if(centering){
ml_params[1]=ml_params[1]-ml_params[2]*meant
if(predictordata)predictedparameter=predictedparameter-ml_params[2]*meant
}
list( ml_params=ml_params,
ml_value=ml_value,
predictedparameter=predictedparameter,
adjustedx=adjustedx,
# expinfmat=expinfmat,
# expinfmati=expinfmati,
standard_errors=standard_errors,
revert2ml=revert2ml,
ml_quantiles=ml_quantiles,
ml_max=ml_max,
flat_quantiles=flat_quantiles,
rh_ml_quantiles=rh_ml_quantiles,
cp_quantiles=rh_flat_quantiles,
ru_quantiles=ru_quantiles,
jp_quantiles=jp_quantiles,
ml_pdf=ml_pdf,
cp_pdf=rh_flat_pdf,
maic=maic,
waic1=waic1,
waic2=waic2,
ml_mean=ml_mean,
flat_mean=flat_mean,
rh_ml_mean=rh_ml_mean,
cp_mean=rh_flat_mean,
jp_mean=jp_mean,
cp_method=crhpflat_dmgs_cpmethod())
}
#' @rdname gev_p1_cp
#' @inheritParams man
#' @export
rgev_p1_cp=function(n,x,t,t0=NA,n0=NA,ics=c(0,0,0,0),
d1=0.01,d2=0.01,fd3=0.01,d4=0.01,
minxi=-0.45,maxxi=0.45,
extramodels=FALSE,rust=FALSE,mlcp=TRUE,debug=FALSE,aderivs=TRUE){
# stopifnot(is.finite(n),!is.na(n),is.finite(x),!is.na(x),is.finite(t),!is.na(t),
# length(ics)==4)
stopifnot(is.finite(x),!is.na(x),is.finite(t),!is.na(t),
length(ics)==4)
t0=maket0(t0=t0,n0=n0,t=t)
#
# centering
#
meant=mean(t)
t=t-meant
t0=t0-meant
ml_params="mlcp not selected"
ml_deviates="mlcp not selected"
flat_deviates="mlcp not selected"
rh_ml_deviates="mlcp not selected"
jp_deviates="mlcp not selected"
ru_deviates="rust not selected"
cp_deviates="rust not selected"
if(mlcp){
q=qgev_p1_cp(x,t=t,t0=t0,n0=NA,p=runif(n),ics=ics,d1=d1,d2=d2,fd3=fd3,d4=d4,
extramodels=extramodels,aderivs=aderivs)
ml_params=q$ml_params
ml_deviates=q$ml_quantiles
flat_deviates=q$flat_quantiles
rh_ml_deviates=q$rh_ml_quantiles
ru_deviates=q$ru_quantiles
cp_deviates=q$cp_quantiles
jp_deviates=q$jp_quantiles
}
if(rust){
th=tgev_p1_cp(n,x,t)$theta_samples
ru_deviates=numeric(0)
for (i in 1:n){
mu=th[i,1]+t0*th[i,2]
ru_deviates[i]=rgev(1,mu=mu,sigma=th[i,3],xi=th[i,4])
}
}
#
# decentering
#
if(mlcp)ml_params[1]=ml_params[1]-ml_params[2]*meant
op=list(ml_params=ml_params,
ml_deviates=ml_deviates,
flat_deviates=flat_deviates,
rh_ml_deviates=rh_ml_deviates,
cp_deviates=cp_deviates,
ru_deviates=ru_deviates,
jp_deviates=jp_deviates,
cp_method=crhpflat_dmgs_cpmethod())
return(op)
}
#' @rdname gev_p1_cp
#' @inheritParams man
#' @export
dgev_p1_cp=function(x,t,t0=NA,n0=NA,y=x,ics=c(0,0,0,0),
d1=0.01,d2=0.01,fd3=0.01,d4=0.01,
minxi=-0.45,maxxi=0.45,extramodels=FALSE,
rust=FALSE,nrust=1000,centering=TRUE,debug=FALSE,aderivs=TRUE){
stopifnot(is.finite(x),!is.na(x),is.finite(y),!is.na(y),
is.finite(t),!is.na(t),length(ics)==4)
t0=maket0(t0,n0,t)
#
# centering
#
if(centering){
meant=mean(t)
t=t-meant
t0=t0-meant
}
ics=gev_p1_setics(x,t,ics)
opt1=optim(ics,gev_p1_loglik,x=x,t=t,control=list(fnscale=-1)) #this one uses the evd routine for dgev
v1hat=opt1$par[1]
v2hat=opt1$par[2]
v3hat=opt1$par[3]
v4hat=opt1$par[4]
if(v4hat<=(-1)){revert2ml=TRUE}else{revert2ml=FALSE}
ml_params=c(v1hat,v2hat,v3hat,v4hat)
# gev_p1_checkmle(ml_params,minxi,maxxi)
dd=dgev_p1sub(x=x,t=t,y=y,t0=t0,ics=ics,d1,d2,fd3,d4,
minxi,maxxi,extramodels=extramodels,aderivs=aderivs)
ru_pdf="rust not selected"
ml_params=dd$ml_params
if(rust&&(!revert2ml)){
th=tgev_p1_cp(nrust,x,t)$theta_samples
ru_pdf=numeric(length(y))
for (ir in 1:nrust){
mu=th[ir,1]+t0*th[ir,2]
ru_pdf=ru_pdf+dgev(y,mu=mu,sigma=th[ir,3],xi=th[ir,4])
}
ru_pdf=ru_pdf/nrust
} else {
ru_pdf=dd$ml_pdf
}
#
# decentering
#
if(centering)ml_params[1]=ml_params[1]-ml_params[2]*meant
op=list(
ml_params=ml_params,
ml_pdf=dd$ml_pdf,
revert2ml=revert2ml,
ru_pdf=ru_pdf,
cp_method=nopdfcdfmsg())
return(op)
}
#' @rdname gev_p1_cp
#' @inheritParams man
#' @export
pgev_p1_cp=function(x,t,t0=NA,n0=NA,y=x,ics=c(0,0,0,0),
d1=0.01,d2=0.01,fd3=0.01,d4=0.01,
minxi=-0.45,maxxi=0.45,extramodels=FALSE,
rust=FALSE,nrust=1000,centering=TRUE,debug=FALSE,aderivs=TRUE){
stopifnot(is.finite(x),!is.na(x),is.finite(y),!is.na(y),
is.finite(t),!is.na(t),length(ics)==4)
t0=maket0(t0,n0,t)
#
# centering
#
if(centering){
meant=mean(t)
t=t-meant
t0=t0-meant
}
ics=gev_p1_setics(x,t,ics)
opt1=optim(ics,gev_p1_loglik,x=x,t=t,control=list(fnscale=-1)) #this one uses the evd routine for dgev
v1hat=opt1$par[1]
v2hat=opt1$par[2]
v3hat=opt1$par[3]
v4hat=opt1$par[4]
if(v4hat<=(-1)){revert2ml=TRUE}else{revert2ml=FALSE}
ml_params=c(v1hat,v2hat,v3hat,v4hat)
# gev_p1_checkmle(ml_params,minxi,maxxi)
dd=dgev_p1sub(x=x,t=t,y=y,t0=t0,ics=ics,d1,d2,fd3,d4,
minxi,maxxi,extramodels=extramodels,aderivs=aderivs)
ru_cdf="rust not selected"
ml_params=dd$ml_params
if(rust&&(!revert2ml)){
th=tgev_p1_cp(nrust,x,t)$theta_samples
ru_cdf=numeric(length(y))
for (ir in 1:nrust){
mu=th[ir,1]+t0*th[ir,2]
ru_cdf=ru_cdf+pgev(y,mu=mu,sigma=th[ir,3],xi=th[ir,4])
}
ru_cdf=ru_cdf/nrust
} else {
ru_pdf=dd$ml_pdf
}
#
# decentering
#
if(centering)ml_params[1]=ml_params[1]-ml_params[2]*meant
op=list(
ml_params=ml_params,
ml_cdf=dd$ml_cdf,
revert2ml=revert2ml,
ru_cdf=ru_cdf,
cp_method=nopdfcdfmsg())
return(op)
}
#' @rdname gev_p1_cp
#' @inheritParams man
#' @export
tgev_p1_cp=function(n,x,t,ics=c(0,0,0,0),
d1=0.01,d2=0.01,fd3=0.01,d4=0.01,
extramodels=FALSE,debug=FALSE){
# stopifnot(is.finite(n),!is.na(n),is.finite(x),!is.na(x),is.finite(t),!is.na(t),
# length(ics)==4)
stopifnot(is.finite(x),!is.na(x),is.finite(t),!is.na(t),
length(ics)==4)
#
# centering
#
meant=mean(t)
t=t-meant
ics=gev_p1_setics(x,t,ics)
# th=ru(gev_p1_logf,x=x,t=t,n=n,d=4,init=c(0,0,1,0))
th=ru(gev_p1_logf,x=x,t=t,n=n,d=4,init=ics)
theta_samples=th$sim_vals
#
# decentering
#
theta_samples[,1]=theta_samples[,1]-theta_samples[,2]*meant
list(theta_samples=theta_samples)
}
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