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R/calib.R
In BASS: Bayesian Adaptive Spline Surfaces
Defines functions
calibrate.bassBasis
Documented in
calibrate.bassBasis
#' @title Calibrate a bassPCA or bassBasis Model to Data
#'
#' @description Robust modular calibration of a bassPCA or bassBasis emulator using adaptive Metropolis, tempering, and decorrelation steps in an effort to be free of any user-required tuning.
#' @param y vector of calibration data
#' @param mod a emulator of class bassBasis, whose predictions should match y (i.e., predictions from mod should be the same length as y)
#' @param type one of c(1,2). 1 indicates a model that uses independent truncation error variance, no measurement error correlation, and discrepancy on a basis while type 2 indicates a model that uses a full truncation error covariance matrix, a full measurement error correlation matrix, a fixed full discrepancy covariance matrix, and a fixed discrepancy mean. 1 is for situations where computational efficiency is important (because y is dense), while 2 is only for cases where y is a short vector.
#' @param sd.est vector of prior estimates of measurement error standard deviation
#' @param s2.df vector of degrees of freedom for measurement error sd prior estimates
#' @param s2.ind index vector, same length as y, indicating which sd.est goes with which y
#' @param meas.error.cor a fixed correlation matrix for the measurement errors
#' @param bounds a 2xp matrix of bounds for each input parameter, where p is the number of input parameters.
#' @param discrep.mean discrepancy mean (fixed), only used if type=2
#' @param discrep.mat discrepancy covariance (fixed, for type 2) or basis (if not square, for type 1)
#' @param nmcmc number of MCMC iterations.
#' @param temperature.ladder an increasing vector, all greater than 1, for tempering. Geometric spacing is recommended, so that you have (1+delta)^(0:ntemps), where delta is small (typically between 0.05 and 0.2) and ntemps is the number of elements in the vector.
#' @param decor.step.every integer number of MCMC iterations between decorrelation steps.
#' @param verbose logical, whether to print progress.
#'
#' @details Fits a modular Bayesian calibration model, with \deqn{y = Kw(\theta) + Dv + \epsilon, ~~\epsilon \sim N(0,\sigma^2 R)} \deqn{f(x) = a_0 + \sum_{m=1}^M a_m B_m(x)} and \eqn{B_m(x)} is a BASS basis function (tensor product of spline basis functions). We use priors \deqn{a \sim N(0,\sigma^2/\tau (B'B)^{-1})} \deqn{M \sim Poisson(\lambda)} as well as the priors mentioned in the arguments above.
#' @return An object
#' @seealso \link{predict.bassBasis} for prediction and \link{sobolBasis} for sensitivity analysis.
#' @export
#' @import utils
#' @example inst/examplesPCA.R
#'
calibrate.bassBasis<-function(y,
mod,
type,
sd.est,
s2.df,
s2.ind,
meas.error.cor,
bounds,
discrep.mean,
discrep.mat,
nmcmc=10000,
temperature.ladder=1.05^(0:30),
decor.step.every=100,
verbose=T
){
tl<-temperature.ladder
decor<-decor.step.every
func<-function(mod,xx,ii)
predict(mod,xx,mcmc.use=ii,nugget=F,trunc.error=F)
vars<-do.call(cbind,lapply(mod$mod.list,function(a) a$s2))
basis<-mod$dat$basis
if(type==1)
trunc.error.cov<-diag(diag(cov(t(mod$dat$trunc.error))))
if(type==2)
trunc.error.cov<-cov(t(mod$dat$trunc.error))
rmnorm<-function(mu, S){
mu+c(rnorm(length(mu))%*%chol(S))
}
if(any(s2.df==0)){
ldig.kern<-function(x,a,b)
-log(x+1)
} else{
ldig.kern<-function(x,a,b)
-(a+1)*log(x)-b/x
}
unscale.range<-function(x,r){
x*(r[2]-r[1])+r[1]
}
rigammaTemper<-function(n,shape,scale,itemper){
1/rgamma(n,itemper*(shape+1)-1,rate=itemper*scale)
}
myTimestamp<-function(){
x<-Sys.time()
paste('#--',format(x,"%b %d %X"),'--#')
}
cor2cov<-function(R,S) # https://stats.stackexchange.com/questions/62850/obtaining-covariance-matrix-from-correlation-matrix
outer(S,S) * R
p<-ncol(bounds)
a<-s2.df/2
b<-a*sd.est^2
ns2<-length(unique(s2.ind))
n.s2.ind<-rep(0,ns2)
for(j in 1:ns2)
n.s2.ind[j]<-sum(s2.ind==j)
s2.first.ind<-NA
for(j in 1:ns2)
s2.first.ind[j]<-which(s2.ind==j)[1]
ny<-length(y)
ntemps<-length(tl)
class<-'mult'
nd<-1
if(ncol(discrep.mat)<ny){
class<-'func'
nd<-ncol(discrep.mat)
}
theta<-array(dim=c(nmcmc,ntemps,p))
s2<-array(dim=c(nmcmc,ntemps,ns2))
discrep.vars<-array(dim=c(nmcmc,ntemps,nd))
#temp.ind<-matrix(nrow=nmcmc,ncol=ntemps)
itl<-1/tl # inverse temperature ladder
tran<-function(th){
#th2<-pnorm(th)
for(i in 1:ncol(th)){
th[,i]<-unscale.range(th[,i],bounds[,i])
}
th
}
theta[1,,]<-runif(prod(dim(theta[1,,,drop=F])))
s2[1,,]<-1
discrep.vars[1,,]<-0
my.solve<-function(x){
u <- chol(x)
chol2inv(u)
}
swm<-function(Ainv,U,Cinv,V){ # sherman woodbury morrison (A+UCV)^-1
Ainv - Ainv %*% U %*% my.solve(Cinv + V %*% Ainv %*% U) %*% V %*% Ainv
}
swm.ldet<-function(Ainv,U,Cinv,V,Aldet,Cldet){ # sherman woodbury morrison |A+UCV|
determinant(Cinv + V %*% Ainv %*% U, logarithm=T)$mod + Aldet + Cldet
}
curr<-list()
for(t in 1:ntemps)
curr[[t]]<-list()
dat<-list(y=y,basis=basis,s2.ind=s2.ind)
if(class=='mult'){
dat$trunc.error.cov<-trunc.error.cov
dat$meas.error.cor<-meas.error.cor
dat$discrep.cov<-discrep.mat
dat$discrep.mean<-discrep.mean
for(t in 1:ntemps){
curr[[t]]$s2<-s2[1,t,]
}
lik.cov.inv<-function(dat,curr){#trunc.error.cov,Sigma,discrep.mat,discrep.vars,basis,emu.vars){
Sigma<-cor2cov(dat$meas.error.cor,sqrt(curr$s2[dat$s2.ind]))
mat<-chol(dat$trunc.error.cov+Sigma+dat$discrep.cov+dat$basis%*%diag(curr$emu.vars,mod$dat$n.pc)%*%t(dat$basis))
inv<-chol2inv(mat)
ldet<-2*sum(log(diag(mat)))
return(list(inv=inv, ldet=ldet))
}
llik<-function(dat,curr){#y,pred,discrep,cov.inv,ldet){ # use ldet=0 if it doesn't matter
vec <- dat$y-curr$pred-dat$discrep.mean
-.5*(curr$cov$ldet + t(vec)%*%curr$cov$inv%*%(vec))
}
}
if(class=='func'){
dat$trunc.error.var<-diag(trunc.error.cov) # assumed diagonal
dat$D<-discrep.mat
dat$discrep<-dat$D%*%discrep.vars[1,t,]
dat$discrep.tau<-1
dat$nd<-ncol(dat$D)
for(t in 1:ntemps){
curr[[t]]$s2<-s2[1,t,]
#curr[[t]]$vars.sigma<-curr[[t]]$s2[s2.ind]
curr[[t]]$discrep<-dat$D%*%discrep.vars[1,t,]
}
lik.cov.inv<-function(dat,curr){#trunc.error.cov,Sigma,discrep.mat,discrep.vars,basis,emu.vars){ # Sigma, trunc.error.cov are diagonal
vec<-dat$trunc.error.var+curr$s2[dat$s2.ind]
Ainv<-diag(1/vec)
Aldet<-sum(log(vec))
inv<-swm(Ainv,basis,diag(1/curr$emu.vars),t(basis))
ldet<-swm.ldet(Ainv,basis,diag(1/curr$emu.vars),t(basis),Aldet,sum(log(curr$emu.vars)))
return(list(inv=inv, ldet=ldet))
}
llik<-function(dat,curr){#y,pred,discrep,cov.inv,ldet){ # use ldet=0 if it doesn't matter
vec <- dat$y-curr$pred-curr$discrep
-.5*(curr$cov$ldet + t(vec)%*%curr$cov$inv%*%(vec))
}
}
bigMat.curr<-Sigma.curr<-list()
nmcmc.emu<-nrow(vars)
ii<-NA
ii[1]<-sample(nmcmc.emu,1)
pred.curr<-matrix(func(mod,tran(matrix(theta[1,,],ncol=p)),ii[1]),nrow=ntemps)
for(t in 1:ntemps){
curr[[t]]$pred<-pred.curr[t,]
curr[[t]]$emu.vars<-vars[ii[1],]
}
eps<-1e-13
tau<-rep(-4,ntemps) # scaling
tau.ls2<-rep(0,ntemps)
cc<-2.4^2/p
S<-mu<-cov<-S.ls2<-mu.ls2<-cov.ls2<-list()
for(t in 1:ntemps){
S[[t]]<-diag(p)*1e-6
S.ls2[[t]]<-diag(ns2)*1e-6
}
count<-matrix(0,nrow=ntemps,ncol=ntemps)
count.decor<-matrix(0,nrow=p,ncol=ntemps)
count100<-count.s2<-rep(0,ntemps)
for(i in 2:nmcmc){
theta[i,,]<-theta[i-1,,] # current set at previous (update below)
s2[i,,]<-s2[i-1,,]
########################################################
## update s2
ii[i]<-sample(nmcmc.emu,1)
pred.curr<-matrix(func(mod,tran(matrix(theta[i-1,,],ncol=p)),ii[i]),nrow=ntemps)
for(t in 1:ntemps){
curr[[t]]$pred<-pred.curr[t,]
curr[[t]]$emu.vars<-vars[ii[i],]
curr[[t]]$cov<-lik.cov.inv(dat,curr[[t]])
curr[[t]]$llik<-llik(dat,curr[[t]])
}
if(i==300){ # start adapting
for(t in 1:ntemps){
if(ns2>1){
mu.ls2[[t]]<-colMeans(log(s2[1:(i-1),t,]))
cov.ls2[[t]]<-cov(log(s2[1:(i-1),t,]))
} else{
mu.ls2[[t]]<-matrix(mean(log(s2[1:(i-1),t,])))
cov.ls2[[t]]<-matrix(var(log(s2[1:(i-1),t,])))
}
S.ls2[[t]]<- (cov.ls2[[t]]*cc+diag(eps*cc,ns2))*exp(tau.ls2[t])
}
}
if(i>300){ # adaptation updates
for(t in 1:ntemps){
#browser()
mu.ls2[[t]]<-mu.ls2[[t]]+(log(s2[(i-1),t,])-mu.ls2[[t]])/(i-1)
cov.ls2[[t]]<-(i-2)/(i-1)*cov.ls2[[t]] + (i-2)/(i-1)^2*tcrossprod(log(s2[(i-1),t,])-mu.ls2[[t]])
S.ls2[[t]]<-(cov.ls2[[t]]*cc+diag(eps*cc,ns2))*exp(tau.ls2[t])
}
}
#ls2.cand<-matrix(nrow=ntemps,ncol=ns2)
for(t in 1:ntemps){
ls2.cand<-rmnorm(log(curr[[t]]$s2),S.ls2[[t]]) # generate candidate
cand<-curr[[t]]
cand$s2<-exp(ls2.cand)
cand$cov<-lik.cov.inv(dat,cand)
cand$llik<-llik(dat,cand)
alpha<- itl[t]*(
+ cand$llik + sum(ldig.kern(cand$s2,a,b)) + sum(log(cand$s2))
- curr[[t]]$llik - sum(ldig.kern(curr[[t]]$s2,a,b)) - sum(log(curr[[t]]$s2))
) # log lik + log prior + log jacobian
#if(i>5000)
# browser()
if(log(runif(1))<alpha){
curr[[t]]<-cand
s2[i,t,]<-cand$s2
count.s2[t]<-count.s2[t]+1
}
}
#if(i>5000)
# browser()
########################################################
## update discrep.vars with gibbs step
#???~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
if(class=='func'){
for(t in 1:ntemps){
discrep.S<-my.solve(diag(dat$nd)/dat$discrep.tau + t(dat$D) %*% curr[[t]]$cov$inv %*% dat$D)
discrep.m<-t(dat$D) %*% curr[[t]]$cov$inv %*% (dat$y-curr[[t]]$pred)
discrep.vars[i,t,]<-c(rmnorm(discrep.S%*%discrep.m, discrep.S/itl[t]))
curr[[t]]$discrep.vars<-discrep.vars[i,t,]
curr[[t]]$discrep<-dat$D%*%discrep.vars[i,t,]
}
}
########################################################
## adaptive block update for theta within each temperature - covariance of previous samples scaled (by exp(tau)) based on acceptance rate for last 100 samples, since tempering makes large gaps
if(i==300){ # start adapting
for(t in 1:ntemps){
mu[[t]]<-colMeans(theta[1:(i-1),t,])
cov[[t]]<-cov(theta[1:(i-1),t,])
S[[t]]<-(cov[[t]]*cc+diag(eps*cc,p))*exp(tau[t])
}
}
if(i>300){ # adaptation updates
for(t in 1:ntemps){
#browser()
mu[[t]]<-mu[[t]]+(theta[(i-1),t,]-mu[[t]])/(i-1)
cov[[t]]<-(i-2)/(i-1)*cov[[t]] + (i-2)/(i-1)^2*tcrossprod(theta[(i-1),t,]-mu[[t]])
S[[t]]<-(cov[[t]]*cc+diag(eps*cc,p))*exp(tau[t])
}
}
theta.cand<-matrix(nrow=ntemps,ncol=p)
for(t in 1:ntemps)
theta.cand[t,]<-rmnorm(theta[i-1,t,],S[[t]]) # generate candidate for each temperature
pred.cand<-matrix(func(mod,tran(matrix(theta.cand,ncol=p)),ii[i]),nrow=ntemps)
# Dinv.cand is the same as Dinv.curr
for(t in 1:ntemps){ # loop over temperatures, do a block MCMC update
cand<-curr[[t]]
cand$pred<-pred.cand[t,]
cand$theta<-theta.cand[t,]
if(any(cand$theta<0 | cand$theta>1))
alpha<- -9999
else{
cand$llik<-llik(dat,cand)
alpha<- itl[t]*(
+ cand$llik
- curr[[t]]$llik
) # log lik + uniform prior
}
if(log(runif(1))<alpha){
curr[[t]]<-cand
theta[i,t,]<-theta.cand[t,]
count[t,t]<-count[t,t]+1
pred.curr[t,]<-pred.cand[t,]
count100[t]<-count100[t]+1
}
}
########################################################
## acceptance-rate based adaptation of covariance scale
if(i%%100==0){
delta<-min(.1,1/sqrt(i)*5)
for(t in 1:ntemps){
if(count100[t]<23){
tau[t]<-tau[t]-delta
} else if(count100[t]>23){
tau[t]<-tau[t]+delta
}
} # could be vectorized, but probably not expensive
count100<-count100*0
}
########################################################
## decorrelation step for theta, especially to decorrelate the thetas that dont change anything
if(i%%decor==0){ # every so often, do a decorrelation step (use single-site independence sampler)
for(k in 1:p){
theta.cand<-theta[i,,,drop=F] # most up-to-date value
theta.cand[1,,k]<-runif(ntemps) # independence sampler candidate (vectorize over temperatures)
pred.cand<-matrix(func(mod,tran(matrix(theta.cand[1,,],ncol=p)),ii[i]),nrow=ntemps)
for(t in 1:ntemps){
cand<-curr[[t]]
cand$pred<-pred.cand[t,]
cand$theta<-theta.cand[1,t,]
cand$llik<-llik(dat,cand)
alpha<- itl[t]*(
+ cand$llik
- curr[[t]]$llik
) # log lik + uniform prior
if(log(runif(1))<alpha){
curr[[t]]<-cand
theta[i,t,k]<-theta.cand[1,t,k]
count.decor[k,t]<-count.decor[k,t]+1
pred.curr[t,]<-pred.cand[t,]
}
}
}
}
########################################################
## tempering swaps
if(i>1000 & ntemps>1){ # tempering swap
for(dummy in 1:ntemps){ # repeat tempering step a bunch of times
sw<-sort(sample(ntemps,size=2))
alpha<-(itl[sw[2]]-itl[sw[1]])*(
curr[[sw[1]]]$llik + sum(ldig.kern(curr[[sw[1]]]$s2,a,b)) # plus discrep terms
- curr[[sw[2]]]$llik - sum(ldig.kern(curr[[sw[2]]]$s2,a,b))
)
if(log(runif(1))<alpha){
temp<-theta[i,sw[1],]
theta[i,sw[1],]<-theta[i,sw[2],]
theta[i,sw[2],]<-temp
temp<-s2[i,sw[1],]
s2[i,sw[1],]<-s2[i,sw[2],]
s2[i,sw[2],]<-temp
temp<-discrep.vars[i,sw[1],]
discrep.vars[i,sw[1],]<-discrep.vars[i,sw[2],]
discrep.vars[i,sw[2],]<-temp
count[sw[1],sw[2]]<-count[sw[1],sw[2]]+1
temp<-pred.curr[sw[1],] # not sampling posterior predictive each time, for speed
pred.curr[sw[1],]<-pred.curr[sw[2],]
pred.curr[sw[2],]<-temp
temp<-curr[[sw[1]]]
curr[[sw[1]]]<-curr[[sw[2]]]
curr[[sw[2]]]<-temp
}
}
}
if(verbose & i%%100==0){
pr<-c('MCMC iteration',i,myTimestamp(),'count:',diag(count))
cat(pr,'\n')
}
}
##th2<-pnorm(theta)
#for(ii in 1:p){
# theta[,,ii]<-unscale.range(theta[,,ii],bounds[,ii])
#}
return(list(theta=theta,s2=s2,count=count,count.decor=count.decor,tau=tau,ii=ii,curr=curr,dat=dat,discrep.vars=discrep.vars))
}
#
#
#
# ##################################################################################################################################################################
# ##################################################################################################################################################################
# ## modularized calibration
# rmnorm<-function(mu, S){
# mu+c(rnorm(length(mu))%*%chol(S))
# }
# calibrate<-function(mod,y,sd.est,s2.df,bounds,nmcmc,tl=1,verbose=T,decor=100,pred.ncores=1,pred.parType='fork',trunc.error=F){ # assumes inputs to mod are standardized to (0,1), equal variance for all y values (should change to sim covariance)
# p<-ncol(bounds)
# a<-s2.df/2
# b<-a*sd.est^2
#
# # could allow s2.ind vector, like in python code
# # or could allow s2.mult for a functional setup
#
# ny<-length(y)
# ntemps<-length(tl)
#
# theta<-array(dim=c(nmcmc,ntemps,p))
# s2<-matrix(nrow=nmcmc,ncol=ntemps)
# #temp.ind<-matrix(nrow=nmcmc,ncol=ntemps)
#
# itl<-1/tl # inverse temperature ladder
#
# tran<-function(th){
# #th2<-pnorm(th)
# for(i in 1:ncol(th)){
# th[,i]<-unscale.range(th[,i],bounds[,i])
# }
# th
# }
#
# #browser()
# theta[1,,]<-runif(prod(dim(theta[1,,,drop=F])))
# # pred.curr<-matrix(
# # predict(mod,
# # tran(matrix(theta[1,,],ncol=p)),
# # mcmc.use=sample(ns,size=1),
# # trunc.error=trunc.error,
# # nugget = T,
# # n.cores=pred.ncores,
# # parType = pred.parType),
# # nrow=ntemps)
#
# pred.curr<-matrix(mod(tran(matrix(theta[1,,],ncol=p))),nrow=ntemps)
# s2[1,]<-rigammaTemper(ntemps, ny/2+a, b+colSums((t(pred.curr)-y)^2)/2, itl)
#
#
#
# eps<-1e-13
# tau<-rep(-4,ntemps) # scaling
# cc<-2.4^2/p
# S<-mu<-cov<-S.rev<-mu.rev<-cov.rev<-list()
# for(t in 1:ntemps)
# S[[t]]<-diag(p)*1e-6
# count<-matrix(0,nrow=ntemps,ncol=ntemps)
# count.decor<-matrix(0,nrow=p,ncol=ntemps)
# count100<-rep(0,ntemps)
#
#
# for(i in 2:nmcmc){
#
# theta[i,,]<-theta[i-1,,] # current set at previous (update below)
#
# ########################################################
# ## adaptive block update for theta within each temperature - covariance of previous samples scaled (by exp(tau)) based on acceptance rate for last 100 samples, since tempering makes large gaps
#
# if(i==300){ # start adapting
# for(t in 1:ntemps){
# mu[[t]]<-colMeans(theta[1:(i-1),t,])
# cov[[t]]<-cov(theta[1:(i-1),t,])
# S[[t]]<-cov(theta[1:(i-1),t,])*cc+diag(eps*cc,p)
# }
# }
# if(i>300){ # adaptation updates
# for(t in 1:ntemps){
# mu[[t]]<-mu[[t]]+(theta[(i-1),t,]-mu[[t]])/(i-1)
# cov[[t]]<-(i-2)/(i-1)*cov[[t]] + (i-2)/(i-1)^2*tcrossprod(theta[(i-1),t,]-mu[[t]])
# S[[t]]<-(cov[[t]]*cc+diag(eps*cc,p))*exp(tau[t])
# }
# }
#
# # if(i>300 & i<1000){ # start adapting
# # for(t in 1:ntemps){
# # mu[[t]]<-colMeans(theta[1:(i-1),t,])
# # cov[[t]]<-cov(theta[1:(i-1),t,])
# # S[[t]]<-cov[[t]]*cc+diag(eps*cc,p)
# # }
# # }
# # if(i>1000){ # radius-based adaptation
# # for(t in 1:ntemps){
# # #browser()
# # dist<-sqrt(colSums((t(theta[1:(i-2),t,])-theta[i-1,t,])^2))
# # use<-which(dist<=quantile(dist,.15))
# # mu[[t]]<-colMeans(theta[use,t,])
# # cov[[t]]<-cov(theta[use,t,])
# # S[[t]]<-cov[[t]]*cc+diag(eps*cc,p)
# # }
# # }
#
# theta.cand<-matrix(nrow=ntemps,ncol=p)
# for(t in 1:ntemps)
# theta.cand[t,]<-rmnorm(theta[i-1,t,],S[[t]]) # generate candidate for each temperature
#
# # if(i>1000){ # for reversibility when radius-based adapting
# # for(t in 1:ntemps){
# # #browser()
# # dist<-sqrt(colSums((t(theta[1:(i-2),t,])-theta.cand[t,])^2))
# # use<-which(dist<=quantile(dist,.15))
# # mu.rev[[t]]<-colMeans(theta[use,t,])
# # cov.rev[[t]]<-cov(theta[use,t,])
# # S.rev[[t]]<-cov.rev[[t]]*cc+diag(eps*cc,p)
# # }
# # }
#
# # pred.cand<-matrix(
# # predict(mod,
# # tran(matrix(theta.cand,ncol=p)),
# # mcmc.use=sample(ns,size=1),
# # trunc.error=trunc.error,
# # nugget=T,
# # n.cores=pred.ncores,
# # parType = pred.parType),
# # nrow=ntemps) # get BASS prediction at each candidate (major speedup by vectorizing across temperatures)
#
# pred.cand<-matrix(mod(tran(matrix(theta.cand,ncol=p))),nrow=ntemps)
#
# for(t in 1:ntemps){ # loop over temperatures, do a block MCMC update
# if(any(theta.cand[t,]<0 | theta.cand[t,]>1))
# alpha<- -9999
# else{
# alpha<- (-.5/s2[i-1,t]*itl[t]*(sum((y-pred.cand[t,])^2)-sum((y-pred.curr[t,])^2)) # posterior
# #-mnormt::dmnorm(theta.cand[t,],theta[i-1,t,],S[[t]],log = T) + mnormt::dmnorm(theta[i-1,t,],theta.cand[t,],S.rev[[t]],log = T) # proposal when using radius-based adapting
# )
# }
# if(log(runif(1))<alpha){
# theta[i,t,]<-theta.cand[t,]
# count[t,t]<-count[t,t]+1
# pred.curr[t,]<-pred.cand[t,]
# count100[t]<-count100[t]+1
# }
# }
#
# ########################################################
# ## acceptance-rate based adaptation of covariance scale
# if(i%%100==0){
# delta<-min(.1,1/sqrt(i)*5)
# for(t in 1:ntemps){
# if(count100[t]<23){
# tau[t]<-tau[t]-delta
# } else if(count100[t]>23){
# tau[t]<-tau[t]+delta
# }
# } # could be vectorized, but probably not expensive
# count100<-count100*0
# }
#
#
# ########################################################
# ## decorrelation step for theta, especially to decorrelate the thetas that dont change anything
#
# if(i%%decor==0){ # every so often, do a decorrelation step (use single-site independence sampler)
# for(k in 1:p){
# theta.cand<-theta[i,,,drop=F] # most up-to-date value
# theta.cand[1,,k]<-runif(ntemps) # independence sampler candidate (vectorize over temperatures)
# # pred.cand<-matrix(
# # predict(mod,
# # tran(matrix(theta.cand[1,,],ncol=p)),
# # mcmc.use=sample(ns,size=1),
# # trunc.error=trunc.error,
# # nugget=T,
# # n.cores=pred.ncores,
# # parType = pred.parType),
# # nrow=ntemps)
# pred.cand<-matrix(mod(tran(matrix(theta.cand[1,,],ncol=p))),nrow=ntemps)
# for(t in 1:ntemps){
# alpha<- -.5/s2[i-1,t]*itl[t]*(sum((y-pred.cand[t,])^2)-sum((y-pred.curr[t,])^2)) # could do with colsums, but this is cheap
# if(log(runif(1))<alpha){
# theta[i,t,k]<-theta.cand[1,t,k]
# count.decor[k,t]<-count.decor[k,t]+1
# pred.curr[t,]<-pred.cand[t,]
# }
# }
# }
# }
#
# ########################################################
# ## update s2 with gibbs step
#
# s2[i,]<-rigammaTemper(ntemps,ny/2+a, b+colSums((t(pred.curr)-y)^2)/2, itl) # update error variance
#
# #if(i==10000){
# # browser()
# #}
#
# #pred.curr<-predict(mod,theta[i,,],mcmc.use=sample(ns,size=1),trunc.error=F,nugget=T)[1,,]
#
# ########################################################
# ## tempering swaps
#
# if(i>1000 & ntemps>1){ # tempering swap
# for(dummy in 1:ntemps){ # repeat tempering step a bunch of times
# sw<-sort(sample(ntemps,size=2))
#
# alpha<-(itl[sw[2]]-itl[sw[1]])*(
# -ny/2*log(s2[i,sw[1]]) - .5/s2[i,sw[1]]*sum((y-pred.curr[sw[1],])^2) -(a+1)*log(s2[i,sw[1]])-b/s2[i,sw[1]]
# +ny/2*log(s2[i,sw[2]]) + .5/s2[i,sw[2]]*sum((y-pred.curr[sw[2],])^2) +(a+1)*log(s2[i,sw[2]])+b/s2[i,sw[2]]
# )
#
# if(log(runif(1))<alpha){
# temp<-theta[i,sw[1],]
# theta[i,sw[1],]<-theta[i,sw[2],]
# theta[i,sw[2],]<-temp
# temp<-s2[i,sw[1]]
# s2[i,sw[1]]<-s2[i,sw[2]]
# s2[i,sw[2]]<-temp
# count[sw[1],sw[2]]<-count[sw[1],sw[2]]+1
# temp<-pred.curr[sw[1],] # not sampling posterior predictive each time, for speed
# pred.curr[sw[1],]<-pred.curr[sw[2],]
# pred.curr[sw[2],]<-temp
# }
# }
# }
#
# ########################################################
# ## take a new posterior predictive sample from the emulator (helps not get stuck in a mode from a particularly good sample)
# # pred.curr<-matrix(
# # predict(mod,
# # tran(matrix(theta[i,,],ncol=p)),
# # mcmc.use=sample(ns,size=1),
# # trunc.error=trunc.error,
# # nugget=T,
# # n.cores=pred.ncores,
# # parType = pred.parType),
# # nrow=ntemps)
#
# #if(!all(pred.curr == matrix(mod(tran(theta[i,,])),nrow=ntemps)))
# # browser()
#
#
# if(verbose & i%%100==0){
# pr<-c('MCMC iteration',i,myTimestamp(),'count:',diag(count))
# cat(pr,'\n')
# }
# }
#
# #th2<-pnorm(theta)
# for(ii in 1:p){
# theta[,,ii]<-unscale.range(theta[,,ii],bounds[,ii])
# }
# return(list(theta=theta,s2=s2,count=count,count.decor=count.decor,tau=tau))
# }
#
#
#
#
#
# # calibrateIndep<-function(mod,y,a,b,nmcmc,verbose=T){ # assumes inputs to mod are standardized to (0,1), equal variance for all y values (should change to sim covariance)
# # p<-ncol(mod$dat$xx)
# # ny<-length(y)
# # ns<-mod$mod.list[[1]]$nmcmc-mod$mod.list[[1]]$nburn # number of emu mcmc samples
# #
# # theta<-matrix(nrow=nmcmc,ncol=p)
# # s2<-rep(NA,nmcmc)
# #
# # #browser()
# # theta[1,]<-.5
# # pred.curr<-predict(mod,theta[1,,drop=F],mcmc.use=sample(ns,size=1),trunc.error=F)
# # s2[1]<-1/rgamma(1,ny/2+a,b+sum((y-pred.curr)^2))
# #
# # count<-rep(0,p)
# # for(i in 2:nmcmc){
# # s2[i]<-1/rgamma(1,ny/2+a,b+sum((y-pred.curr)^2))
# #
# # theta[i,]<-theta[i-1,]
# #
# # for(j in 1:p){
# # theta.cand<-theta[i,]
# # theta.cand[j]<-runif(1)
# # pred.cand<-predict(mod,t(theta.cand),mcmc.use=sample(ns,size=1),trunc.error=F)
# # alpha<- -.5/s2[i]*(sum((y-pred.cand)^2)-sum((y-pred.curr)^2))
# # if(log(runif(1))<alpha){
# # theta[i,]<-theta.cand
# # count[j]<-count[j]+1
# # }
# # }
# #
# # pred.curr<-predict(mod,theta[i,,drop=F],mcmc.use=sample(ns,size=1),trunc.error=F)
# #
# # if(verbose & i%%100==0){
# # pr<-c('MCMC iteration',i,myTimestamp(),'count:',count)
# # cat(pr,'\n')
# # }
# # }
# #
# # return(list(theta=theta,s2=s2,count=count))
# # }
#
# ldig.kernal<-function(x,a,b)
# (-a-1)*log(x) - b/x
#
# calibrate.probit<-function(mod,y,s2.est,s2.df,bounds,nmcmc,tl=1,verbose=T,decor=100,pred.ncores=1,pred.parType='fork',trunc.error=F){ # assumes inputs to mod are standardized to (0,1), equal variance for all y values (should change to sim covariance)
# # if(class(mod)=='bass'){
# # p<-mod$p
# # ns<-length(mod$s2) # number of emu mcmc samples
# # } else if(class(mod)=='bassBasis'){
# # p<-ncol(mod$dat$xx)
# # ns<-length(mod$mod.list[[1]]$s2) # number of emu mcmc samples
# # }
#
# p<-ncol(bounds)
# a<-s2.df/2
# b<-a*sd.est^2
#
# lpost<-NA
# # could allow s2.ind vector, like in python code
# # or could allow s2.mult for a functional setup
#
# ny<-length(y)
# ntemps<-length(tl)
#
# theta<-array(dim=c(nmcmc,ntemps,p))
# s2<-matrix(nrow=nmcmc,ncol=ntemps)
# #temp.ind<-matrix(nrow=nmcmc,ncol=ntemps)
#
# itl<-1/tl # inverse temperature ladder
#
# tran<-function(th){
# th<-pnorm(th)
# for(i in 1:ncol(th)){
# th[,i]<-unscale.range(th[,i],bounds[,i])
# }
# th
# }
#
# #browser()
# theta[1,,]<-rnorm(prod(dim(theta[1,,,drop=F])))
# # pred.curr<-matrix(
# # predict(mod,
# # tran(matrix(theta[1,,],ncol=p)),
# # mcmc.use=sample(ns,size=1),
# # trunc.error=trunc.error,
# # nugget = T,
# # n.cores=pred.ncores,
# # parType = pred.parType),
# # nrow=ntemps)
# pred.curr<-matrix(mod(tran(matrix(theta[1,,],ncol=p))),nrow=ntemps)
# s2[1,]<-1/rgammaTemper(ntemps, ny/2+a, b+colSums((t(pred.curr)-y)^2)/2, itl)
#
#
#
# eps<-1e-13
# tau<-rep(-0,ntemps) # scaling
# cc<-2.4^2/p
# S<-mu<-cov<-S.rev<-mu.rev<-cov.rev<-list()
# for(t in 1:ntemps)
# S[[t]]<-diag(p)*1e-6
# count<-matrix(0,nrow=ntemps,ncol=ntemps)
# count.decor<-matrix(0,nrow=p,ncol=ntemps)
# count100<-rep(0,ntemps)
#
#
# for(i in 2:nmcmc){
#
# theta[i,,]<-theta[i-1,,] # current set at previous (update below)
#
# ########################################################
# ## adaptive block update for theta within each temperature - covariance of previous samples scaled (by exp(tau)) based on acceptance rate for last 100 samples, since tempering makes large gaps
#
# if(i==300){ # start adapting
# for(t in 1:ntemps){
# mu[[t]]<-colMeans(theta[1:(i-1),t,])
# cov[[t]]<-cov(theta[1:(i-1),t,])
# S[[t]]<-cov(theta[1:(i-1),t,])*cc+diag(eps*cc,p)
# }
# }
# if(i>300){ # adaptation updates
# for(t in 1:ntemps){
# mu[[t]]<-mu[[t]]+(theta[(i-1),t,]-mu[[t]])/(i-1)
# cov[[t]]<-(i-2)/(i-1)*cov[[t]] + (i-2)/(i-1)^2*tcrossprod(theta[(i-1),t,]-mu[[t]])
# S[[t]]<-(cov[[t]]*cc+diag(eps*cc,p))*exp(tau[t])
# }
# }
#
# theta.cand<-matrix(nrow=ntemps,ncol=p)
# for(t in 1:ntemps)
# theta.cand[t,]<-rmnorm(theta[i-1,t,],S[[t]]) # generate candidate for each temperature
#
# # pred.cand<-matrix(
# # predict(mod,
# # tran(matrix(theta.cand,ncol=p)),
# # mcmc.use=sample(ns,size=1),
# # trunc.error=trunc.error,
# # nugget=T,
# # n.cores=pred.ncores,
# # parType = pred.parType),
# # nrow=ntemps) # get BASS prediction at each candidate (major speedup by vectorizing across temperatures)
# pred.cand<-matrix(mod(tran(matrix(theta.cand,ncol=p))),nrow=ntemps)
#
# for(t in 1:ntemps){ # loop over temperatures, do a block MCMC update
# #alpha<- (-.5/s2[i-1,t]*itl[t]*(sum((y-pred.cand[t,])^2)-sum((y-pred.curr[t,])^2)) + itl[t]*(sum(dnorm(theta.cand[t,],log=T)) - sum(dnorm(theta[i-1,t,],log=T))) )
# alpha<-itl[t]*(
# sum(dnorm(y,pred.cand[t,],sqrt(s2[i-1,t]),log=T))
# -sum(dnorm(y,pred.curr[t,],sqrt(s2[i-1,t]),log=T))
# +sum(dnorm(theta.cand[t,],log=T))
# -sum(dnorm(theta[i-1,t,],log=T))
# )
# if(log(runif(1))<alpha){
# theta[i,t,]<-theta.cand[t,]
# count[t,t]<-count[t,t]+1
# pred.curr[t,]<-pred.cand[t,]
# count100[t]<-count100[t]+1
# }
# }
#
# ########################################################
# ## acceptance-rate based adaptation of covariance scale
# if(i%%100==0){
# delta<-min(.1,1/sqrt(i)*5)
# for(t in 1:ntemps){
# if(count100[t]<23){
# tau[t]<-tau[t]-delta
# } else if(count100[t]>23){
# tau[t]<-tau[t]+delta
# }
# } # could be vectorized, but probably not expensive
# count100<-count100*0
# }
#
#
# ########################################################
# ## decorrelation step for theta, especially to decorrelate the thetas that dont change anything
#
# if(i%%decor==0 & i>1000){ # every so often, do a decorrelation step (use single-site independence sampler)
# for(k in 1:p){
# theta.cand<-theta[i,,,drop=F] # most up-to-date value
# theta.cand[1,,k]<-rnorm(ntemps) # independence sampler candidate (vectorize over temperatures)
# #pred.cand<-matrix(
# # predict(mod,
# # tran(matrix(theta.cand[1,,],ncol=p)),
# # mcmc.use=sample(ns,size=1),
# # trunc.error=trunc.error,
# # nugget=T,
# # n.cores=pred.ncores,
# # parType = pred.parType),
# # nrow=ntemps)
# pred.cand<-matrix(mod(tran(matrix(theta.cand[1,,],ncol=p))),nrow=ntemps)
#
# for(t in 1:ntemps){
# #alpha<- -.5/s2[i-1,t]*itl[t]*(sum((y-pred.cand[t,])^2)-sum((y-pred.curr[t,])^2)) + itl[t]*(sum(dnorm(theta.cand[1,t,],log=T)) - sum(dnorm(theta[i,t,],log=T))) # could do with colsums, but this is cheap
# alpha<-itl[t]*(
# sum(dnorm(y,pred.cand[t,],sqrt(s2[i-1,t]),log=T))
# -sum(dnorm(y,pred.curr[t,],sqrt(s2[i-1,t]),log=T))
# +dnorm(theta.cand[1,t,k],log=T)
# -dnorm(theta[i,t,k],log=T)
# )- dnorm(theta.cand[1,t,k],log=T)+ dnorm(theta[i,t,k],log=T)
#
# if(log(runif(1))<alpha){
# #browser()
# theta[i,t,k]<-theta.cand[1,t,k]
# count.decor[k,t]<-count.decor[k,t]+1
# pred.curr[t,]<-pred.cand[t,]
# }
# }
# }
# }
#
# ########################################################
# ## update s2 with gibbs step
#
# #browser()
# s2[i,]<-1/rgammaTemper(ntemps,ny/2+a, b+colSums((t(pred.curr)-y)^2)/2, itl) # update error variance
#
# ########################################################
# ## tempering swaps
#
# if(i>1000 & ntemps>1){ # tempering swap
# #browser()
# for(dummy in 1:ntemps){ # repeat tempering step a bunch of times
# sw<-sort(sample(ntemps,size=2))
#
# # alpha<-(itl[sw[2]]-itl[sw[1]])*(
# # -ny/2*log(s2[i,sw[1]]) - .5/s2[i,sw[1]]*sum((y-pred.curr[sw[1],])^2) -(a+1)*log(s2[i,sw[1]])-b/s2[i,sw[1]]
# # +ny/2*log(s2[i,sw[2]]) + .5/s2[i,sw[2]]*sum((y-pred.curr[sw[2],])^2) +(a+1)*log(s2[i,sw[2]])+b/s2[i,sw[2]]
# # + sum(dnorm(theta[i,sw[1],],log=T)) - sum(dnorm(theta[i,sw[2],],log=T))
# # )
#
# alpha<-(itl[sw[2]]-itl[sw[1]])*(
# sum(dnorm(y,pred.curr[sw[1],],sqrt(s2[i,sw[1]]),log=T))
# -sum(dnorm(y,pred.curr[sw[2],],sqrt(s2[i,sw[2]]),log=T))
# +sum(dnorm(theta[i,sw[1],],log=T))
# -sum(dnorm(theta[i,sw[2],],log=T))
# +ldig.kernal(s2[i,sw[1]],a,b)
# -ldig.kernal(s2[i,sw[2]],a,b)
# )
#
# if(log(runif(1))<alpha){
# if(sw[1]==0 & any(abs(theta[i,sw[2],])>4.5)){
# print('bad')
# }
# #temp<-theta[i,sw[1],]
# #theta[i,sw[1],]<-theta[i,sw[2],]
# #theta[i,sw[2],]<-temp
# theta[i,sw,]<-theta[i,sw[2:1],]
# #temp<-s2[i,sw[1]]
# #s2[i,sw[1]]<-s2[i,sw[2]]
# #s2[i,sw[2]]<-temp
# s2[i,sw]<-s2[i,sw[2:1]]
# count[sw[1],sw[2]]<-count[sw[1],sw[2]]+1
# #temp<-pred.curr[sw[1],] # not sampling posterior predictive each time, for speed
# #pred.curr[sw[1],]<-pred.curr[sw[2],]
# #pred.curr[sw[2],]<-temp
# pred.curr[sw,]<-pred.curr[sw[2:1],]
# }
# }
# }
#
# ########################################################
# ## take a new posterior predictive sample from the emulator (helps not get stuck in a mode from a particularly good sample)
# # pred.curr<-matrix(
# # predict(mod,
# # tran(matrix(theta[i,,],ncol=p)),
# # mcmc.use=sample(ns,size=1),
# # trunc.error=trunc.error,
# # nugget=T,
# # n.cores=pred.ncores,
# # parType = pred.parType),
# # nrow=ntemps)
#
# lpost[i]<-(sum(dnorm(y,pred.curr[1,],sqrt(s2[i,1]),log=T))
# +sum(dnorm(theta[i,1,],log=T))
# +ldig.kernal(s2[i,1],a,b)
# )
#
#
# if(verbose & i%%1000==0){
# pr<-c('MCMC iteration',i,myTimestamp(),'count:',diag(count))
# cat(pr,'\n')
# }
# }
#
# #th2<-pnorm(theta)
# #for(ii in 1:p){
# # theta[,,ii]<-unscale.range(pnorm(theta[,,ii]),bounds[,ii])
# #}
# return(list(theta=theta,s2=s2,count=count,count.decor=count.decor,tau=tau,lpost=lpost))
# }
#
#
#
#
#
#
#
# #calibrate.full<-function(mod,y,s2.est,s2.df,bounds,nmcmc,tl=1,verbose=T,decor=100,pred.ncores=1,pred.parType='fork',trunc.error=F){ # assumes inputs to mod are standardized to (0,1), equal variance for all y values (should change to sim covariance)
#
# #}
#
#
# calibrate.naive.cut<-function(mod,y,s2.est,s2.df,bounds,nmcmc,tl=1,verbose=T,decor=100,pred.ncores=1,pred.parType='fork',trunc.error=F,stoch=F){ # assumes inputs to mod are standardized to (0,1), equal variance for all y values (should change to sim covariance)
#
#
# p<-ncol(bounds)
# a<-s2.df/2
# b<-a*sd.est^2
#
# # could allow s2.ind vector, like in python code
# # or could allow s2.mult for a functional setup
#
# ny<-length(y)
# ntemps<-length(tl)
#
# theta<-array(dim=c(nmcmc,ntemps,p))
# s2<-matrix(nrow=nmcmc,ncol=ntemps)
# #temp.ind<-matrix(nrow=nmcmc,ncol=ntemps)
#
# itl<-1/tl # inverse temperature ladder
#
# tran<-function(th){
# #th2<-pnorm(th)
# for(i in 1:ncol(th)){
# th[,i]<-unscale.range(th[,i],bounds[,i])
# }
# th
# }
#
# #browser()
# theta[1,,]<-runif(prod(dim(theta[1,,,drop=F])))
# # pred.curr<-matrix(
# # predict(mod,
# # tran(matrix(theta[1,,],ncol=p)),
# # mcmc.use=sample(ns,size=1),
# # trunc.error=trunc.error,
# # nugget = T,
# # n.cores=pred.ncores,
# # parType = pred.parType),
# # nrow=ntemps)
#
# pred.curr<-matrix(mod(tran(matrix(theta[1,,],ncol=p))),nrow=ntemps)
# s2[1,]<-rigammaTemper(ntemps, ny/2+a, b+colSums((t(pred.curr)-y)^2)/2, itl)
#
#
#
# eps<-1e-13
# tau<-rep(-4,ntemps) # scaling
# cc<-2.4^2/p
# S<-mu<-cov<-S.rev<-mu.rev<-cov.rev<-list()
# for(t in 1:ntemps)
# S[[t]]<-diag(p)*1e-6
# count<-matrix(0,nrow=ntemps,ncol=ntemps)
# count.decor<-matrix(0,nrow=p,ncol=ntemps)
# count100<-rep(0,ntemps)
#
#
# for(i in 2:nmcmc){
#
# theta[i,,]<-theta[i-1,,] # current set at previous (update below)
#
# ########################################################
# ## adaptive block update for theta within each temperature - covariance of previous samples scaled (by exp(tau)) based on acceptance rate for last 100 samples, since tempering makes large gaps
#
# if(i==300){ # start adapting
# for(t in 1:ntemps){
# mu[[t]]<-colMeans(theta[1:(i-1),t,])
# cov[[t]]<-cov(theta[1:(i-1),t,])
# S[[t]]<-cov(theta[1:(i-1),t,])*cc+diag(eps*cc,p)
# }
# }
# if(i>300){ # adaptation updates
# for(t in 1:ntemps){
# mu[[t]]<-mu[[t]]+(theta[(i-1),t,]-mu[[t]])/(i-1)
# cov[[t]]<-(i-2)/(i-1)*cov[[t]] + (i-2)/(i-1)^2*tcrossprod(theta[(i-1),t,]-mu[[t]])
# S[[t]]<-(cov[[t]]*cc+diag(eps*cc,p))*exp(tau[t])
# }
# }
#
#
#
# theta.cand<-matrix(nrow=ntemps,ncol=p)
# for(t in 1:ntemps)
# theta.cand[t,]<-rmnorm(theta[i-1,t,],S[[t]]) # generate candidate for each temperature
#
#
# # pred.cand<-matrix(
# # predict(mod,
# # tran(matrix(theta.cand,ncol=p)),
# # mcmc.use=sample(ns,size=1),
# # trunc.error=trunc.error,
# # nugget=T,
# # n.cores=pred.ncores,
# # parType = pred.parType),
# # nrow=ntemps) # get BASS prediction at each candidate (major speedup by vectorizing across temperatures)
#
# pred.cand<-matrix(mod(tran(matrix(theta.cand,ncol=p))),nrow=ntemps)
#
# for(t in 1:ntemps){ # loop over temperatures, do a block MCMC update
# if(any(theta.cand[t,]<0 | theta.cand[t,]>1))
# alpha<- -9999
# else{
# alpha<- (-.5/s2[i-1,t]*itl[t]*(sum((y-pred.cand[t,])^2)-sum((y-pred.curr[t,])^2)) # posterior
# #-mnormt::dmnorm(theta.cand[t,],theta[i-1,t,],S[[t]],log = T) + mnormt::dmnorm(theta[i-1,t,],theta.cand[t,],S.rev[[t]],log = T) # proposal when using radius-based adapting
# )
# }
# if(log(runif(1))<alpha){
# theta[i,t,]<-theta.cand[t,]
# count[t,t]<-count[t,t]+1
# pred.curr[t,]<-pred.cand[t,]
# count100[t]<-count100[t]+1
# }
# }
#
# ########################################################
# ## acceptance-rate based adaptation of covariance scale
# if(i%%100==0){
# delta<-min(.1,1/sqrt(i)*5)
# for(t in 1:ntemps){
# if(count100[t]<23){
# tau[t]<-tau[t]-delta
# } else if(count100[t]>23){
# tau[t]<-tau[t]+delta
# }
# } # could be vectorized, but probably not expensive
# count100<-count100*0
# }
#
#
# ########################################################
# ## decorrelation step for theta, especially to decorrelate the thetas that dont change anything
#
# if(i%%decor==0){ # every so often, do a decorrelation step (use single-site independence sampler)
# for(k in 1:p){
# theta.cand<-theta[i,,,drop=F] # most up-to-date value
# theta.cand[1,,k]<-runif(ntemps) # independence sampler candidate (vectorize over temperatures)
# # pred.cand<-matrix(
# # predict(mod,
# # tran(matrix(theta.cand[1,,],ncol=p)),
# # mcmc.use=sample(ns,size=1),
# # trunc.error=trunc.error,
# # nugget=T,
# # n.cores=pred.ncores,
# # parType = pred.parType),
# # nrow=ntemps)
# pred.cand<-matrix(mod(tran(matrix(theta.cand[1,,],ncol=p))),nrow=ntemps)
# for(t in 1:ntemps){
# alpha<- -.5/s2[i-1,t]*itl[t]*(sum((y-pred.cand[t,])^2)-sum((y-pred.curr[t,])^2)) # could do with colsums, but this is cheap
# if(log(runif(1))<alpha){
# theta[i,t,k]<-theta.cand[1,t,k]
# count.decor[k,t]<-count.decor[k,t]+1
# pred.curr[t,]<-pred.cand[t,]
# }
# }
# }
# }
#
# ########################################################
# ## update s2 with gibbs step
#
# s2[i,]<-rigammaTemper(ntemps,ny/2+a, b+colSums((t(pred.curr)-y)^2)/2, itl) # update error variance
#
# #pred.curr<-predict(mod,theta[i,,],mcmc.use=sample(ns,size=1),trunc.error=F,nugget=T)[1,,]
#
# ########################################################
# ## tempering swaps
#
# if(i>1000 & ntemps>1){ # tempering swap
# for(dummy in 1:ntemps){ # repeat tempering step a bunch of times
# sw<-sort(sample(ntemps,size=2))
#
# alpha<-(itl[sw[2]]-itl[sw[1]])*(
# -ny/2*log(s2[i,sw[1]]) - .5/s2[i,sw[1]]*sum((y-pred.curr[sw[1],])^2) -(a+1)*log(s2[i,sw[1]])-b/s2[i,sw[1]]
# +ny/2*log(s2[i,sw[2]]) + .5/s2[i,sw[2]]*sum((y-pred.curr[sw[2],])^2) +(a+1)*log(s2[i,sw[2]])+b/s2[i,sw[2]]
# )
#
# if(log(runif(1))<alpha){
# temp<-theta[i,sw[1],]
# theta[i,sw[1],]<-theta[i,sw[2],]
# theta[i,sw[2],]<-temp
# temp<-s2[i,sw[1]]
# s2[i,sw[1]]<-s2[i,sw[2]]
# s2[i,sw[2]]<-temp
# count[sw[1],sw[2]]<-count[sw[1],sw[2]]+1
# temp<-pred.curr[sw[1],] # not sampling posterior predictive each time, for speed
# pred.curr[sw[1],]<-pred.curr[sw[2],]
# pred.curr[sw[2],]<-temp
# }
# }
# }
#
# ########################################################
# ## take a new posterior predictive sample from the emulator (helps not get stuck in a mode from a particularly good sample)
# # pred.curr<-matrix(
# # predict(mod,
# # tran(matrix(theta[i,,],ncol=p)),
# # mcmc.use=sample(ns,size=1),
# # trunc.error=trunc.error,
# # nugget=T,
# # n.cores=pred.ncores,
# # parType = pred.parType),
# # nrow=ntemps)
#
# #if(!all(pred.curr == matrix(mod(tran(theta[i,,])),nrow=ntemps)))
# # browser()
#
#
# if(verbose & i%%100==0){
# pr<-c('MCMC iteration',i,myTimestamp(),'count:',diag(count))
# cat(pr,'\n')
# }
# }
#
# #th2<-pnorm(theta)
# for(ii in 1:p){
# theta[,,ii]<-unscale.range(theta[,,ii],bounds[,ii])
# }
# return(list(theta=theta,s2=s2,count=count,count.decor=count.decor,tau=tau))
#
#
# }
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Defines functions calibrate.bassBasis
Documented in calibrate.bassBasis
#' @title Calibrate a bassPCA or bassBasis Model to Data
#'
#' @description Robust modular calibration of a bassPCA or bassBasis emulator using adaptive Metropolis, tempering, and decorrelation steps in an effort to be free of any user-required tuning.
#' @param y vector of calibration data
#' @param mod a emulator of class bassBasis, whose predictions should match y (i.e., predictions from mod should be the same length as y)
#' @param type one of c(1,2). 1 indicates a model that uses independent truncation error variance, no measurement error correlation, and discrepancy on a basis while type 2 indicates a model that uses a full truncation error covariance matrix, a full measurement error correlation matrix, a fixed full discrepancy covariance matrix, and a fixed discrepancy mean. 1 is for situations where computational efficiency is important (because y is dense), while 2 is only for cases where y is a short vector.
#' @param sd.est vector of prior estimates of measurement error standard deviation
#' @param s2.df vector of degrees of freedom for measurement error sd prior estimates
#' @param s2.ind index vector, same length as y, indicating which sd.est goes with which y
#' @param meas.error.cor a fixed correlation matrix for the measurement errors
#' @param bounds a 2xp matrix of bounds for each input parameter, where p is the number of input parameters.
#' @param discrep.mean discrepancy mean (fixed), only used if type=2
#' @param discrep.mat discrepancy covariance (fixed, for type 2) or basis (if not square, for type 1)
#' @param nmcmc number of MCMC iterations.
#' @param temperature.ladder an increasing vector, all greater than 1, for tempering. Geometric spacing is recommended, so that you have (1+delta)^(0:ntemps), where delta is small (typically between 0.05 and 0.2) and ntemps is the number of elements in the vector.
#' @param decor.step.every integer number of MCMC iterations between decorrelation steps.
#' @param verbose logical, whether to print progress.
#'
#' @details Fits a modular Bayesian calibration model, with \deqn{y = Kw(\theta) + Dv + \epsilon, ~~\epsilon \sim N(0,\sigma^2 R)} \deqn{f(x) = a_0 + \sum_{m=1}^M a_m B_m(x)} and \eqn{B_m(x)} is a BASS basis function (tensor product of spline basis functions). We use priors \deqn{a \sim N(0,\sigma^2/\tau (B'B)^{-1})} \deqn{M \sim Poisson(\lambda)} as well as the priors mentioned in the arguments above.
#' @return An object
#' @seealso \link{predict.bassBasis} for prediction and \link{sobolBasis} for sensitivity analysis.
#' @export
#' @import utils
#' @example inst/examplesPCA.R
#'
calibrate.bassBasis<-function(y,
mod,
type,
sd.est,
s2.df,
s2.ind,
meas.error.cor,
bounds,
discrep.mean,
discrep.mat,
nmcmc=10000,
temperature.ladder=1.05^(0:30),
decor.step.every=100,
verbose=T
){
tl<-temperature.ladder
decor<-decor.step.every
func<-function(mod,xx,ii)
predict(mod,xx,mcmc.use=ii,nugget=F,trunc.error=F)
vars<-do.call(cbind,lapply(mod$mod.list,function(a) a$s2))
basis<-mod$dat$basis
if(type==1)
trunc.error.cov<-diag(diag(cov(t(mod$dat$trunc.error))))
if(type==2)
trunc.error.cov<-cov(t(mod$dat$trunc.error))
rmnorm<-function(mu, S){
mu+c(rnorm(length(mu))%*%chol(S))
}
if(any(s2.df==0)){
ldig.kern<-function(x,a,b)
-log(x+1)
} else{
ldig.kern<-function(x,a,b)
-(a+1)*log(x)-b/x
}
unscale.range<-function(x,r){
x*(r[2]-r[1])+r[1]
}
rigammaTemper<-function(n,shape,scale,itemper){
1/rgamma(n,itemper*(shape+1)-1,rate=itemper*scale)
}
myTimestamp<-function(){
x<-Sys.time()
paste('#--',format(x,"%b %d %X"),'--#')
}
cor2cov<-function(R,S) # https://stats.stackexchange.com/questions/62850/obtaining-covariance-matrix-from-correlation-matrix
outer(S,S) * R
p<-ncol(bounds)
a<-s2.df/2
b<-a*sd.est^2
ns2<-length(unique(s2.ind))
n.s2.ind<-rep(0,ns2)
for(j in 1:ns2)
n.s2.ind[j]<-sum(s2.ind==j)
s2.first.ind<-NA
for(j in 1:ns2)
s2.first.ind[j]<-which(s2.ind==j)[1]
ny<-length(y)
ntemps<-length(tl)
class<-'mult'
nd<-1
if(ncol(discrep.mat)<ny){
class<-'func'
nd<-ncol(discrep.mat)
}
theta<-array(dim=c(nmcmc,ntemps,p))
s2<-array(dim=c(nmcmc,ntemps,ns2))
discrep.vars<-array(dim=c(nmcmc,ntemps,nd))
#temp.ind<-matrix(nrow=nmcmc,ncol=ntemps)
itl<-1/tl # inverse temperature ladder
tran<-function(th){
#th2<-pnorm(th)
for(i in 1:ncol(th)){
th[,i]<-unscale.range(th[,i],bounds[,i])
}
th
}
theta[1,,]<-runif(prod(dim(theta[1,,,drop=F])))
s2[1,,]<-1
discrep.vars[1,,]<-0
my.solve<-function(x){
u <- chol(x)
chol2inv(u)
}
swm<-function(Ainv,U,Cinv,V){ # sherman woodbury morrison (A+UCV)^-1
Ainv - Ainv %*% U %*% my.solve(Cinv + V %*% Ainv %*% U) %*% V %*% Ainv
}
swm.ldet<-function(Ainv,U,Cinv,V,Aldet,Cldet){ # sherman woodbury morrison |A+UCV|
determinant(Cinv + V %*% Ainv %*% U, logarithm=T)$mod + Aldet + Cldet
}
curr<-list()
for(t in 1:ntemps)
curr[[t]]<-list()
dat<-list(y=y,basis=basis,s2.ind=s2.ind)
if(class=='mult'){
dat$trunc.error.cov<-trunc.error.cov
dat$meas.error.cor<-meas.error.cor
dat$discrep.cov<-discrep.mat
dat$discrep.mean<-discrep.mean
for(t in 1:ntemps){
curr[[t]]$s2<-s2[1,t,]
}
lik.cov.inv<-function(dat,curr){#trunc.error.cov,Sigma,discrep.mat,discrep.vars,basis,emu.vars){
Sigma<-cor2cov(dat$meas.error.cor,sqrt(curr$s2[dat$s2.ind]))
mat<-chol(dat$trunc.error.cov+Sigma+dat$discrep.cov+dat$basis%*%diag(curr$emu.vars,mod$dat$n.pc)%*%t(dat$basis))
inv<-chol2inv(mat)
ldet<-2*sum(log(diag(mat)))
return(list(inv=inv, ldet=ldet))
}
llik<-function(dat,curr){#y,pred,discrep,cov.inv,ldet){ # use ldet=0 if it doesn't matter
vec <- dat$y-curr$pred-dat$discrep.mean
-.5*(curr$cov$ldet + t(vec)%*%curr$cov$inv%*%(vec))
}
}
if(class=='func'){
dat$trunc.error.var<-diag(trunc.error.cov) # assumed diagonal
dat$D<-discrep.mat
dat$discrep<-dat$D%*%discrep.vars[1,t,]
dat$discrep.tau<-1
dat$nd<-ncol(dat$D)
for(t in 1:ntemps){
curr[[t]]$s2<-s2[1,t,]
#curr[[t]]$vars.sigma<-curr[[t]]$s2[s2.ind]
curr[[t]]$discrep<-dat$D%*%discrep.vars[1,t,]
}
lik.cov.inv<-function(dat,curr){#trunc.error.cov,Sigma,discrep.mat,discrep.vars,basis,emu.vars){ # Sigma, trunc.error.cov are diagonal
vec<-dat$trunc.error.var+curr$s2[dat$s2.ind]
Ainv<-diag(1/vec)
Aldet<-sum(log(vec))
inv<-swm(Ainv,basis,diag(1/curr$emu.vars),t(basis))
ldet<-swm.ldet(Ainv,basis,diag(1/curr$emu.vars),t(basis),Aldet,sum(log(curr$emu.vars)))
return(list(inv=inv, ldet=ldet))
}
llik<-function(dat,curr){#y,pred,discrep,cov.inv,ldet){ # use ldet=0 if it doesn't matter
vec <- dat$y-curr$pred-curr$discrep
-.5*(curr$cov$ldet + t(vec)%*%curr$cov$inv%*%(vec))
}
}
bigMat.curr<-Sigma.curr<-list()
nmcmc.emu<-nrow(vars)
ii<-NA
ii[1]<-sample(nmcmc.emu,1)
pred.curr<-matrix(func(mod,tran(matrix(theta[1,,],ncol=p)),ii[1]),nrow=ntemps)
for(t in 1:ntemps){
curr[[t]]$pred<-pred.curr[t,]
curr[[t]]$emu.vars<-vars[ii[1],]
}
eps<-1e-13
tau<-rep(-4,ntemps) # scaling
tau.ls2<-rep(0,ntemps)
cc<-2.4^2/p
S<-mu<-cov<-S.ls2<-mu.ls2<-cov.ls2<-list()
for(t in 1:ntemps){
S[[t]]<-diag(p)*1e-6
S.ls2[[t]]<-diag(ns2)*1e-6
}
count<-matrix(0,nrow=ntemps,ncol=ntemps)
count.decor<-matrix(0,nrow=p,ncol=ntemps)
count100<-count.s2<-rep(0,ntemps)
for(i in 2:nmcmc){
theta[i,,]<-theta[i-1,,] # current set at previous (update below)
s2[i,,]<-s2[i-1,,]
########################################################
## update s2
ii[i]<-sample(nmcmc.emu,1)
pred.curr<-matrix(func(mod,tran(matrix(theta[i-1,,],ncol=p)),ii[i]),nrow=ntemps)
for(t in 1:ntemps){
curr[[t]]$pred<-pred.curr[t,]
curr[[t]]$emu.vars<-vars[ii[i],]
curr[[t]]$cov<-lik.cov.inv(dat,curr[[t]])
curr[[t]]$llik<-llik(dat,curr[[t]])
}
if(i==300){ # start adapting
for(t in 1:ntemps){
if(ns2>1){
mu.ls2[[t]]<-colMeans(log(s2[1:(i-1),t,]))
cov.ls2[[t]]<-cov(log(s2[1:(i-1),t,]))
} else{
mu.ls2[[t]]<-matrix(mean(log(s2[1:(i-1),t,])))
cov.ls2[[t]]<-matrix(var(log(s2[1:(i-1),t,])))
}
S.ls2[[t]]<- (cov.ls2[[t]]*cc+diag(eps*cc,ns2))*exp(tau.ls2[t])
}
}
if(i>300){ # adaptation updates
for(t in 1:ntemps){
#browser()
mu.ls2[[t]]<-mu.ls2[[t]]+(log(s2[(i-1),t,])-mu.ls2[[t]])/(i-1)
cov.ls2[[t]]<-(i-2)/(i-1)*cov.ls2[[t]] + (i-2)/(i-1)^2*tcrossprod(log(s2[(i-1),t,])-mu.ls2[[t]])
S.ls2[[t]]<-(cov.ls2[[t]]*cc+diag(eps*cc,ns2))*exp(tau.ls2[t])
}
}
#ls2.cand<-matrix(nrow=ntemps,ncol=ns2)
for(t in 1:ntemps){
ls2.cand<-rmnorm(log(curr[[t]]$s2),S.ls2[[t]]) # generate candidate
cand<-curr[[t]]
cand$s2<-exp(ls2.cand)
cand$cov<-lik.cov.inv(dat,cand)
cand$llik<-llik(dat,cand)
alpha<- itl[t]*(
+ cand$llik + sum(ldig.kern(cand$s2,a,b)) + sum(log(cand$s2))
- curr[[t]]$llik - sum(ldig.kern(curr[[t]]$s2,a,b)) - sum(log(curr[[t]]$s2))
) # log lik + log prior + log jacobian
#if(i>5000)
# browser()
if(log(runif(1))<alpha){
curr[[t]]<-cand
s2[i,t,]<-cand$s2
count.s2[t]<-count.s2[t]+1
}
}
#if(i>5000)
# browser()
########################################################
## update discrep.vars with gibbs step
#???~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
if(class=='func'){
for(t in 1:ntemps){
discrep.S<-my.solve(diag(dat$nd)/dat$discrep.tau + t(dat$D) %*% curr[[t]]$cov$inv %*% dat$D)
discrep.m<-t(dat$D) %*% curr[[t]]$cov$inv %*% (dat$y-curr[[t]]$pred)
discrep.vars[i,t,]<-c(rmnorm(discrep.S%*%discrep.m, discrep.S/itl[t]))
curr[[t]]$discrep.vars<-discrep.vars[i,t,]
curr[[t]]$discrep<-dat$D%*%discrep.vars[i,t,]
}
}
########################################################
## adaptive block update for theta within each temperature - covariance of previous samples scaled (by exp(tau)) based on acceptance rate for last 100 samples, since tempering makes large gaps
if(i==300){ # start adapting
for(t in 1:ntemps){
mu[[t]]<-colMeans(theta[1:(i-1),t,])
cov[[t]]<-cov(theta[1:(i-1),t,])
S[[t]]<-(cov[[t]]*cc+diag(eps*cc,p))*exp(tau[t])
}
}
if(i>300){ # adaptation updates
for(t in 1:ntemps){
#browser()
mu[[t]]<-mu[[t]]+(theta[(i-1),t,]-mu[[t]])/(i-1)
cov[[t]]<-(i-2)/(i-1)*cov[[t]] + (i-2)/(i-1)^2*tcrossprod(theta[(i-1),t,]-mu[[t]])
S[[t]]<-(cov[[t]]*cc+diag(eps*cc,p))*exp(tau[t])
}
}
theta.cand<-matrix(nrow=ntemps,ncol=p)
for(t in 1:ntemps)
theta.cand[t,]<-rmnorm(theta[i-1,t,],S[[t]]) # generate candidate for each temperature
pred.cand<-matrix(func(mod,tran(matrix(theta.cand,ncol=p)),ii[i]),nrow=ntemps)
# Dinv.cand is the same as Dinv.curr
for(t in 1:ntemps){ # loop over temperatures, do a block MCMC update
cand<-curr[[t]]
cand$pred<-pred.cand[t,]
cand$theta<-theta.cand[t,]
if(any(cand$theta<0 | cand$theta>1))
alpha<- -9999
else{
cand$llik<-llik(dat,cand)
alpha<- itl[t]*(
+ cand$llik
- curr[[t]]$llik
) # log lik + uniform prior
}
if(log(runif(1))<alpha){
curr[[t]]<-cand
theta[i,t,]<-theta.cand[t,]
count[t,t]<-count[t,t]+1
pred.curr[t,]<-pred.cand[t,]
count100[t]<-count100[t]+1
}
}
########################################################
## acceptance-rate based adaptation of covariance scale
if(i%%100==0){
delta<-min(.1,1/sqrt(i)*5)
for(t in 1:ntemps){
if(count100[t]<23){
tau[t]<-tau[t]-delta
} else if(count100[t]>23){
tau[t]<-tau[t]+delta
}
} # could be vectorized, but probably not expensive
count100<-count100*0
}
########################################################
## decorrelation step for theta, especially to decorrelate the thetas that dont change anything
if(i%%decor==0){ # every so often, do a decorrelation step (use single-site independence sampler)
for(k in 1:p){
theta.cand<-theta[i,,,drop=F] # most up-to-date value
theta.cand[1,,k]<-runif(ntemps) # independence sampler candidate (vectorize over temperatures)
pred.cand<-matrix(func(mod,tran(matrix(theta.cand[1,,],ncol=p)),ii[i]),nrow=ntemps)
for(t in 1:ntemps){
cand<-curr[[t]]
cand$pred<-pred.cand[t,]
cand$theta<-theta.cand[1,t,]
cand$llik<-llik(dat,cand)
alpha<- itl[t]*(
+ cand$llik
- curr[[t]]$llik
) # log lik + uniform prior
if(log(runif(1))<alpha){
curr[[t]]<-cand
theta[i,t,k]<-theta.cand[1,t,k]
count.decor[k,t]<-count.decor[k,t]+1
pred.curr[t,]<-pred.cand[t,]
}
}
}
}
########################################################
## tempering swaps
if(i>1000 & ntemps>1){ # tempering swap
for(dummy in 1:ntemps){ # repeat tempering step a bunch of times
sw<-sort(sample(ntemps,size=2))
alpha<-(itl[sw[2]]-itl[sw[1]])*(
curr[[sw[1]]]$llik + sum(ldig.kern(curr[[sw[1]]]$s2,a,b)) # plus discrep terms
- curr[[sw[2]]]$llik - sum(ldig.kern(curr[[sw[2]]]$s2,a,b))
)
if(log(runif(1))<alpha){
temp<-theta[i,sw[1],]
theta[i,sw[1],]<-theta[i,sw[2],]
theta[i,sw[2],]<-temp
temp<-s2[i,sw[1],]
s2[i,sw[1],]<-s2[i,sw[2],]
s2[i,sw[2],]<-temp
temp<-discrep.vars[i,sw[1],]
discrep.vars[i,sw[1],]<-discrep.vars[i,sw[2],]
discrep.vars[i,sw[2],]<-temp
count[sw[1],sw[2]]<-count[sw[1],sw[2]]+1
temp<-pred.curr[sw[1],] # not sampling posterior predictive each time, for speed
pred.curr[sw[1],]<-pred.curr[sw[2],]
pred.curr[sw[2],]<-temp
temp<-curr[[sw[1]]]
curr[[sw[1]]]<-curr[[sw[2]]]
curr[[sw[2]]]<-temp
}
}
}
if(verbose & i%%100==0){
pr<-c('MCMC iteration',i,myTimestamp(),'count:',diag(count))
cat(pr,'\n')
}
}
##th2<-pnorm(theta)
#for(ii in 1:p){
# theta[,,ii]<-unscale.range(theta[,,ii],bounds[,ii])
#}
return(list(theta=theta,s2=s2,count=count,count.decor=count.decor,tau=tau,ii=ii,curr=curr,dat=dat,discrep.vars=discrep.vars))
}
#
#
#
# ##################################################################################################################################################################
# ##################################################################################################################################################################
# ## modularized calibration
# rmnorm<-function(mu, S){
# mu+c(rnorm(length(mu))%*%chol(S))
# }
# calibrate<-function(mod,y,sd.est,s2.df,bounds,nmcmc,tl=1,verbose=T,decor=100,pred.ncores=1,pred.parType='fork',trunc.error=F){ # assumes inputs to mod are standardized to (0,1), equal variance for all y values (should change to sim covariance)
# p<-ncol(bounds)
# a<-s2.df/2
# b<-a*sd.est^2
#
# # could allow s2.ind vector, like in python code
# # or could allow s2.mult for a functional setup
#
# ny<-length(y)
# ntemps<-length(tl)
#
# theta<-array(dim=c(nmcmc,ntemps,p))
# s2<-matrix(nrow=nmcmc,ncol=ntemps)
# #temp.ind<-matrix(nrow=nmcmc,ncol=ntemps)
#
# itl<-1/tl # inverse temperature ladder
#
# tran<-function(th){
# #th2<-pnorm(th)
# for(i in 1:ncol(th)){
# th[,i]<-unscale.range(th[,i],bounds[,i])
# }
# th
# }
#
# #browser()
# theta[1,,]<-runif(prod(dim(theta[1,,,drop=F])))
# # pred.curr<-matrix(
# # predict(mod,
# # tran(matrix(theta[1,,],ncol=p)),
# # mcmc.use=sample(ns,size=1),
# # trunc.error=trunc.error,
# # nugget = T,
# # n.cores=pred.ncores,
# # parType = pred.parType),
# # nrow=ntemps)
#
# pred.curr<-matrix(mod(tran(matrix(theta[1,,],ncol=p))),nrow=ntemps)
# s2[1,]<-rigammaTemper(ntemps, ny/2+a, b+colSums((t(pred.curr)-y)^2)/2, itl)
#
#
#
# eps<-1e-13
# tau<-rep(-4,ntemps) # scaling
# cc<-2.4^2/p
# S<-mu<-cov<-S.rev<-mu.rev<-cov.rev<-list()
# for(t in 1:ntemps)
# S[[t]]<-diag(p)*1e-6
# count<-matrix(0,nrow=ntemps,ncol=ntemps)
# count.decor<-matrix(0,nrow=p,ncol=ntemps)
# count100<-rep(0,ntemps)
#
#
# for(i in 2:nmcmc){
#
# theta[i,,]<-theta[i-1,,] # current set at previous (update below)
#
# ########################################################
# ## adaptive block update for theta within each temperature - covariance of previous samples scaled (by exp(tau)) based on acceptance rate for last 100 samples, since tempering makes large gaps
#
# if(i==300){ # start adapting
# for(t in 1:ntemps){
# mu[[t]]<-colMeans(theta[1:(i-1),t,])
# cov[[t]]<-cov(theta[1:(i-1),t,])
# S[[t]]<-cov(theta[1:(i-1),t,])*cc+diag(eps*cc,p)
# }
# }
# if(i>300){ # adaptation updates
# for(t in 1:ntemps){
# mu[[t]]<-mu[[t]]+(theta[(i-1),t,]-mu[[t]])/(i-1)
# cov[[t]]<-(i-2)/(i-1)*cov[[t]] + (i-2)/(i-1)^2*tcrossprod(theta[(i-1),t,]-mu[[t]])
# S[[t]]<-(cov[[t]]*cc+diag(eps*cc,p))*exp(tau[t])
# }
# }
#
# # if(i>300 & i<1000){ # start adapting
# # for(t in 1:ntemps){
# # mu[[t]]<-colMeans(theta[1:(i-1),t,])
# # cov[[t]]<-cov(theta[1:(i-1),t,])
# # S[[t]]<-cov[[t]]*cc+diag(eps*cc,p)
# # }
# # }
# # if(i>1000){ # radius-based adaptation
# # for(t in 1:ntemps){
# # #browser()
# # dist<-sqrt(colSums((t(theta[1:(i-2),t,])-theta[i-1,t,])^2))
# # use<-which(dist<=quantile(dist,.15))
# # mu[[t]]<-colMeans(theta[use,t,])
# # cov[[t]]<-cov(theta[use,t,])
# # S[[t]]<-cov[[t]]*cc+diag(eps*cc,p)
# # }
# # }
#
# theta.cand<-matrix(nrow=ntemps,ncol=p)
# for(t in 1:ntemps)
# theta.cand[t,]<-rmnorm(theta[i-1,t,],S[[t]]) # generate candidate for each temperature
#
# # if(i>1000){ # for reversibility when radius-based adapting
# # for(t in 1:ntemps){
# # #browser()
# # dist<-sqrt(colSums((t(theta[1:(i-2),t,])-theta.cand[t,])^2))
# # use<-which(dist<=quantile(dist,.15))
# # mu.rev[[t]]<-colMeans(theta[use,t,])
# # cov.rev[[t]]<-cov(theta[use,t,])
# # S.rev[[t]]<-cov.rev[[t]]*cc+diag(eps*cc,p)
# # }
# # }
#
# # pred.cand<-matrix(
# # predict(mod,
# # tran(matrix(theta.cand,ncol=p)),
# # mcmc.use=sample(ns,size=1),
# # trunc.error=trunc.error,
# # nugget=T,
# # n.cores=pred.ncores,
# # parType = pred.parType),
# # nrow=ntemps) # get BASS prediction at each candidate (major speedup by vectorizing across temperatures)
#
# pred.cand<-matrix(mod(tran(matrix(theta.cand,ncol=p))),nrow=ntemps)
#
# for(t in 1:ntemps){ # loop over temperatures, do a block MCMC update
# if(any(theta.cand[t,]<0 | theta.cand[t,]>1))
# alpha<- -9999
# else{
# alpha<- (-.5/s2[i-1,t]*itl[t]*(sum((y-pred.cand[t,])^2)-sum((y-pred.curr[t,])^2)) # posterior
# #-mnormt::dmnorm(theta.cand[t,],theta[i-1,t,],S[[t]],log = T) + mnormt::dmnorm(theta[i-1,t,],theta.cand[t,],S.rev[[t]],log = T) # proposal when using radius-based adapting
# )
# }
# if(log(runif(1))<alpha){
# theta[i,t,]<-theta.cand[t,]
# count[t,t]<-count[t,t]+1
# pred.curr[t,]<-pred.cand[t,]
# count100[t]<-count100[t]+1
# }
# }
#
# ########################################################
# ## acceptance-rate based adaptation of covariance scale
# if(i%%100==0){
# delta<-min(.1,1/sqrt(i)*5)
# for(t in 1:ntemps){
# if(count100[t]<23){
# tau[t]<-tau[t]-delta
# } else if(count100[t]>23){
# tau[t]<-tau[t]+delta
# }
# } # could be vectorized, but probably not expensive
# count100<-count100*0
# }
#
#
# ########################################################
# ## decorrelation step for theta, especially to decorrelate the thetas that dont change anything
#
# if(i%%decor==0){ # every so often, do a decorrelation step (use single-site independence sampler)
# for(k in 1:p){
# theta.cand<-theta[i,,,drop=F] # most up-to-date value
# theta.cand[1,,k]<-runif(ntemps) # independence sampler candidate (vectorize over temperatures)
# # pred.cand<-matrix(
# # predict(mod,
# # tran(matrix(theta.cand[1,,],ncol=p)),
# # mcmc.use=sample(ns,size=1),
# # trunc.error=trunc.error,
# # nugget=T,
# # n.cores=pred.ncores,
# # parType = pred.parType),
# # nrow=ntemps)
# pred.cand<-matrix(mod(tran(matrix(theta.cand[1,,],ncol=p))),nrow=ntemps)
# for(t in 1:ntemps){
# alpha<- -.5/s2[i-1,t]*itl[t]*(sum((y-pred.cand[t,])^2)-sum((y-pred.curr[t,])^2)) # could do with colsums, but this is cheap
# if(log(runif(1))<alpha){
# theta[i,t,k]<-theta.cand[1,t,k]
# count.decor[k,t]<-count.decor[k,t]+1
# pred.curr[t,]<-pred.cand[t,]
# }
# }
# }
# }
#
# ########################################################
# ## update s2 with gibbs step
#
# s2[i,]<-rigammaTemper(ntemps,ny/2+a, b+colSums((t(pred.curr)-y)^2)/2, itl) # update error variance
#
# #if(i==10000){
# # browser()
# #}
#
# #pred.curr<-predict(mod,theta[i,,],mcmc.use=sample(ns,size=1),trunc.error=F,nugget=T)[1,,]
#
# ########################################################
# ## tempering swaps
#
# if(i>1000 & ntemps>1){ # tempering swap
# for(dummy in 1:ntemps){ # repeat tempering step a bunch of times
# sw<-sort(sample(ntemps,size=2))
#
# alpha<-(itl[sw[2]]-itl[sw[1]])*(
# -ny/2*log(s2[i,sw[1]]) - .5/s2[i,sw[1]]*sum((y-pred.curr[sw[1],])^2) -(a+1)*log(s2[i,sw[1]])-b/s2[i,sw[1]]
# +ny/2*log(s2[i,sw[2]]) + .5/s2[i,sw[2]]*sum((y-pred.curr[sw[2],])^2) +(a+1)*log(s2[i,sw[2]])+b/s2[i,sw[2]]
# )
#
# if(log(runif(1))<alpha){
# temp<-theta[i,sw[1],]
# theta[i,sw[1],]<-theta[i,sw[2],]
# theta[i,sw[2],]<-temp
# temp<-s2[i,sw[1]]
# s2[i,sw[1]]<-s2[i,sw[2]]
# s2[i,sw[2]]<-temp
# count[sw[1],sw[2]]<-count[sw[1],sw[2]]+1
# temp<-pred.curr[sw[1],] # not sampling posterior predictive each time, for speed
# pred.curr[sw[1],]<-pred.curr[sw[2],]
# pred.curr[sw[2],]<-temp
# }
# }
# }
#
# ########################################################
# ## take a new posterior predictive sample from the emulator (helps not get stuck in a mode from a particularly good sample)
# # pred.curr<-matrix(
# # predict(mod,
# # tran(matrix(theta[i,,],ncol=p)),
# # mcmc.use=sample(ns,size=1),
# # trunc.error=trunc.error,
# # nugget=T,
# # n.cores=pred.ncores,
# # parType = pred.parType),
# # nrow=ntemps)
#
# #if(!all(pred.curr == matrix(mod(tran(theta[i,,])),nrow=ntemps)))
# # browser()
#
#
# if(verbose & i%%100==0){
# pr<-c('MCMC iteration',i,myTimestamp(),'count:',diag(count))
# cat(pr,'\n')
# }
# }
#
# #th2<-pnorm(theta)
# for(ii in 1:p){
# theta[,,ii]<-unscale.range(theta[,,ii],bounds[,ii])
# }
# return(list(theta=theta,s2=s2,count=count,count.decor=count.decor,tau=tau))
# }
#
#
#
#
#
# # calibrateIndep<-function(mod,y,a,b,nmcmc,verbose=T){ # assumes inputs to mod are standardized to (0,1), equal variance for all y values (should change to sim covariance)
# # p<-ncol(mod$dat$xx)
# # ny<-length(y)
# # ns<-mod$mod.list[[1]]$nmcmc-mod$mod.list[[1]]$nburn # number of emu mcmc samples
# #
# # theta<-matrix(nrow=nmcmc,ncol=p)
# # s2<-rep(NA,nmcmc)
# #
# # #browser()
# # theta[1,]<-.5
# # pred.curr<-predict(mod,theta[1,,drop=F],mcmc.use=sample(ns,size=1),trunc.error=F)
# # s2[1]<-1/rgamma(1,ny/2+a,b+sum((y-pred.curr)^2))
# #
# # count<-rep(0,p)
# # for(i in 2:nmcmc){
# # s2[i]<-1/rgamma(1,ny/2+a,b+sum((y-pred.curr)^2))
# #
# # theta[i,]<-theta[i-1,]
# #
# # for(j in 1:p){
# # theta.cand<-theta[i,]
# # theta.cand[j]<-runif(1)
# # pred.cand<-predict(mod,t(theta.cand),mcmc.use=sample(ns,size=1),trunc.error=F)
# # alpha<- -.5/s2[i]*(sum((y-pred.cand)^2)-sum((y-pred.curr)^2))
# # if(log(runif(1))<alpha){
# # theta[i,]<-theta.cand
# # count[j]<-count[j]+1
# # }
# # }
# #
# # pred.curr<-predict(mod,theta[i,,drop=F],mcmc.use=sample(ns,size=1),trunc.error=F)
# #
# # if(verbose & i%%100==0){
# # pr<-c('MCMC iteration',i,myTimestamp(),'count:',count)
# # cat(pr,'\n')
# # }
# # }
# #
# # return(list(theta=theta,s2=s2,count=count))
# # }
#
# ldig.kernal<-function(x,a,b)
# (-a-1)*log(x) - b/x
#
# calibrate.probit<-function(mod,y,s2.est,s2.df,bounds,nmcmc,tl=1,verbose=T,decor=100,pred.ncores=1,pred.parType='fork',trunc.error=F){ # assumes inputs to mod are standardized to (0,1), equal variance for all y values (should change to sim covariance)
# # if(class(mod)=='bass'){
# # p<-mod$p
# # ns<-length(mod$s2) # number of emu mcmc samples
# # } else if(class(mod)=='bassBasis'){
# # p<-ncol(mod$dat$xx)
# # ns<-length(mod$mod.list[[1]]$s2) # number of emu mcmc samples
# # }
#
# p<-ncol(bounds)
# a<-s2.df/2
# b<-a*sd.est^2
#
# lpost<-NA
# # could allow s2.ind vector, like in python code
# # or could allow s2.mult for a functional setup
#
# ny<-length(y)
# ntemps<-length(tl)
#
# theta<-array(dim=c(nmcmc,ntemps,p))
# s2<-matrix(nrow=nmcmc,ncol=ntemps)
# #temp.ind<-matrix(nrow=nmcmc,ncol=ntemps)
#
# itl<-1/tl # inverse temperature ladder
#
# tran<-function(th){
# th<-pnorm(th)
# for(i in 1:ncol(th)){
# th[,i]<-unscale.range(th[,i],bounds[,i])
# }
# th
# }
#
# #browser()
# theta[1,,]<-rnorm(prod(dim(theta[1,,,drop=F])))
# # pred.curr<-matrix(
# # predict(mod,
# # tran(matrix(theta[1,,],ncol=p)),
# # mcmc.use=sample(ns,size=1),
# # trunc.error=trunc.error,
# # nugget = T,
# # n.cores=pred.ncores,
# # parType = pred.parType),
# # nrow=ntemps)
# pred.curr<-matrix(mod(tran(matrix(theta[1,,],ncol=p))),nrow=ntemps)
# s2[1,]<-1/rgammaTemper(ntemps, ny/2+a, b+colSums((t(pred.curr)-y)^2)/2, itl)
#
#
#
# eps<-1e-13
# tau<-rep(-0,ntemps) # scaling
# cc<-2.4^2/p
# S<-mu<-cov<-S.rev<-mu.rev<-cov.rev<-list()
# for(t in 1:ntemps)
# S[[t]]<-diag(p)*1e-6
# count<-matrix(0,nrow=ntemps,ncol=ntemps)
# count.decor<-matrix(0,nrow=p,ncol=ntemps)
# count100<-rep(0,ntemps)
#
#
# for(i in 2:nmcmc){
#
# theta[i,,]<-theta[i-1,,] # current set at previous (update below)
#
# ########################################################
# ## adaptive block update for theta within each temperature - covariance of previous samples scaled (by exp(tau)) based on acceptance rate for last 100 samples, since tempering makes large gaps
#
# if(i==300){ # start adapting
# for(t in 1:ntemps){
# mu[[t]]<-colMeans(theta[1:(i-1),t,])
# cov[[t]]<-cov(theta[1:(i-1),t,])
# S[[t]]<-cov(theta[1:(i-1),t,])*cc+diag(eps*cc,p)
# }
# }
# if(i>300){ # adaptation updates
# for(t in 1:ntemps){
# mu[[t]]<-mu[[t]]+(theta[(i-1),t,]-mu[[t]])/(i-1)
# cov[[t]]<-(i-2)/(i-1)*cov[[t]] + (i-2)/(i-1)^2*tcrossprod(theta[(i-1),t,]-mu[[t]])
# S[[t]]<-(cov[[t]]*cc+diag(eps*cc,p))*exp(tau[t])
# }
# }
#
# theta.cand<-matrix(nrow=ntemps,ncol=p)
# for(t in 1:ntemps)
# theta.cand[t,]<-rmnorm(theta[i-1,t,],S[[t]]) # generate candidate for each temperature
#
# # pred.cand<-matrix(
# # predict(mod,
# # tran(matrix(theta.cand,ncol=p)),
# # mcmc.use=sample(ns,size=1),
# # trunc.error=trunc.error,
# # nugget=T,
# # n.cores=pred.ncores,
# # parType = pred.parType),
# # nrow=ntemps) # get BASS prediction at each candidate (major speedup by vectorizing across temperatures)
# pred.cand<-matrix(mod(tran(matrix(theta.cand,ncol=p))),nrow=ntemps)
#
# for(t in 1:ntemps){ # loop over temperatures, do a block MCMC update
# #alpha<- (-.5/s2[i-1,t]*itl[t]*(sum((y-pred.cand[t,])^2)-sum((y-pred.curr[t,])^2)) + itl[t]*(sum(dnorm(theta.cand[t,],log=T)) - sum(dnorm(theta[i-1,t,],log=T))) )
# alpha<-itl[t]*(
# sum(dnorm(y,pred.cand[t,],sqrt(s2[i-1,t]),log=T))
# -sum(dnorm(y,pred.curr[t,],sqrt(s2[i-1,t]),log=T))
# +sum(dnorm(theta.cand[t,],log=T))
# -sum(dnorm(theta[i-1,t,],log=T))
# )
# if(log(runif(1))<alpha){
# theta[i,t,]<-theta.cand[t,]
# count[t,t]<-count[t,t]+1
# pred.curr[t,]<-pred.cand[t,]
# count100[t]<-count100[t]+1
# }
# }
#
# ########################################################
# ## acceptance-rate based adaptation of covariance scale
# if(i%%100==0){
# delta<-min(.1,1/sqrt(i)*5)
# for(t in 1:ntemps){
# if(count100[t]<23){
# tau[t]<-tau[t]-delta
# } else if(count100[t]>23){
# tau[t]<-tau[t]+delta
# }
# } # could be vectorized, but probably not expensive
# count100<-count100*0
# }
#
#
# ########################################################
# ## decorrelation step for theta, especially to decorrelate the thetas that dont change anything
#
# if(i%%decor==0 & i>1000){ # every so often, do a decorrelation step (use single-site independence sampler)
# for(k in 1:p){
# theta.cand<-theta[i,,,drop=F] # most up-to-date value
# theta.cand[1,,k]<-rnorm(ntemps) # independence sampler candidate (vectorize over temperatures)
# #pred.cand<-matrix(
# # predict(mod,
# # tran(matrix(theta.cand[1,,],ncol=p)),
# # mcmc.use=sample(ns,size=1),
# # trunc.error=trunc.error,
# # nugget=T,
# # n.cores=pred.ncores,
# # parType = pred.parType),
# # nrow=ntemps)
# pred.cand<-matrix(mod(tran(matrix(theta.cand[1,,],ncol=p))),nrow=ntemps)
#
# for(t in 1:ntemps){
# #alpha<- -.5/s2[i-1,t]*itl[t]*(sum((y-pred.cand[t,])^2)-sum((y-pred.curr[t,])^2)) + itl[t]*(sum(dnorm(theta.cand[1,t,],log=T)) - sum(dnorm(theta[i,t,],log=T))) # could do with colsums, but this is cheap
# alpha<-itl[t]*(
# sum(dnorm(y,pred.cand[t,],sqrt(s2[i-1,t]),log=T))
# -sum(dnorm(y,pred.curr[t,],sqrt(s2[i-1,t]),log=T))
# +dnorm(theta.cand[1,t,k],log=T)
# -dnorm(theta[i,t,k],log=T)
# )- dnorm(theta.cand[1,t,k],log=T)+ dnorm(theta[i,t,k],log=T)
#
# if(log(runif(1))<alpha){
# #browser()
# theta[i,t,k]<-theta.cand[1,t,k]
# count.decor[k,t]<-count.decor[k,t]+1
# pred.curr[t,]<-pred.cand[t,]
# }
# }
# }
# }
#
# ########################################################
# ## update s2 with gibbs step
#
# #browser()
# s2[i,]<-1/rgammaTemper(ntemps,ny/2+a, b+colSums((t(pred.curr)-y)^2)/2, itl) # update error variance
#
# ########################################################
# ## tempering swaps
#
# if(i>1000 & ntemps>1){ # tempering swap
# #browser()
# for(dummy in 1:ntemps){ # repeat tempering step a bunch of times
# sw<-sort(sample(ntemps,size=2))
#
# # alpha<-(itl[sw[2]]-itl[sw[1]])*(
# # -ny/2*log(s2[i,sw[1]]) - .5/s2[i,sw[1]]*sum((y-pred.curr[sw[1],])^2) -(a+1)*log(s2[i,sw[1]])-b/s2[i,sw[1]]
# # +ny/2*log(s2[i,sw[2]]) + .5/s2[i,sw[2]]*sum((y-pred.curr[sw[2],])^2) +(a+1)*log(s2[i,sw[2]])+b/s2[i,sw[2]]
# # + sum(dnorm(theta[i,sw[1],],log=T)) - sum(dnorm(theta[i,sw[2],],log=T))
# # )
#
# alpha<-(itl[sw[2]]-itl[sw[1]])*(
# sum(dnorm(y,pred.curr[sw[1],],sqrt(s2[i,sw[1]]),log=T))
# -sum(dnorm(y,pred.curr[sw[2],],sqrt(s2[i,sw[2]]),log=T))
# +sum(dnorm(theta[i,sw[1],],log=T))
# -sum(dnorm(theta[i,sw[2],],log=T))
# +ldig.kernal(s2[i,sw[1]],a,b)
# -ldig.kernal(s2[i,sw[2]],a,b)
# )
#
# if(log(runif(1))<alpha){
# if(sw[1]==0 & any(abs(theta[i,sw[2],])>4.5)){
# print('bad')
# }
# #temp<-theta[i,sw[1],]
# #theta[i,sw[1],]<-theta[i,sw[2],]
# #theta[i,sw[2],]<-temp
# theta[i,sw,]<-theta[i,sw[2:1],]
# #temp<-s2[i,sw[1]]
# #s2[i,sw[1]]<-s2[i,sw[2]]
# #s2[i,sw[2]]<-temp
# s2[i,sw]<-s2[i,sw[2:1]]
# count[sw[1],sw[2]]<-count[sw[1],sw[2]]+1
# #temp<-pred.curr[sw[1],] # not sampling posterior predictive each time, for speed
# #pred.curr[sw[1],]<-pred.curr[sw[2],]
# #pred.curr[sw[2],]<-temp
# pred.curr[sw,]<-pred.curr[sw[2:1],]
# }
# }
# }
#
# ########################################################
# ## take a new posterior predictive sample from the emulator (helps not get stuck in a mode from a particularly good sample)
# # pred.curr<-matrix(
# # predict(mod,
# # tran(matrix(theta[i,,],ncol=p)),
# # mcmc.use=sample(ns,size=1),
# # trunc.error=trunc.error,
# # nugget=T,
# # n.cores=pred.ncores,
# # parType = pred.parType),
# # nrow=ntemps)
#
# lpost[i]<-(sum(dnorm(y,pred.curr[1,],sqrt(s2[i,1]),log=T))
# +sum(dnorm(theta[i,1,],log=T))
# +ldig.kernal(s2[i,1],a,b)
# )
#
#
# if(verbose & i%%1000==0){
# pr<-c('MCMC iteration',i,myTimestamp(),'count:',diag(count))
# cat(pr,'\n')
# }
# }
#
# #th2<-pnorm(theta)
# #for(ii in 1:p){
# # theta[,,ii]<-unscale.range(pnorm(theta[,,ii]),bounds[,ii])
# #}
# return(list(theta=theta,s2=s2,count=count,count.decor=count.decor,tau=tau,lpost=lpost))
# }
#
#
#
#
#
#
#
# #calibrate.full<-function(mod,y,s2.est,s2.df,bounds,nmcmc,tl=1,verbose=T,decor=100,pred.ncores=1,pred.parType='fork',trunc.error=F){ # assumes inputs to mod are standardized to (0,1), equal variance for all y values (should change to sim covariance)
#
# #}
#
#
# calibrate.naive.cut<-function(mod,y,s2.est,s2.df,bounds,nmcmc,tl=1,verbose=T,decor=100,pred.ncores=1,pred.parType='fork',trunc.error=F,stoch=F){ # assumes inputs to mod are standardized to (0,1), equal variance for all y values (should change to sim covariance)
#
#
# p<-ncol(bounds)
# a<-s2.df/2
# b<-a*sd.est^2
#
# # could allow s2.ind vector, like in python code
# # or could allow s2.mult for a functional setup
#
# ny<-length(y)
# ntemps<-length(tl)
#
# theta<-array(dim=c(nmcmc,ntemps,p))
# s2<-matrix(nrow=nmcmc,ncol=ntemps)
# #temp.ind<-matrix(nrow=nmcmc,ncol=ntemps)
#
# itl<-1/tl # inverse temperature ladder
#
# tran<-function(th){
# #th2<-pnorm(th)
# for(i in 1:ncol(th)){
# th[,i]<-unscale.range(th[,i],bounds[,i])
# }
# th
# }
#
# #browser()
# theta[1,,]<-runif(prod(dim(theta[1,,,drop=F])))
# # pred.curr<-matrix(
# # predict(mod,
# # tran(matrix(theta[1,,],ncol=p)),
# # mcmc.use=sample(ns,size=1),
# # trunc.error=trunc.error,
# # nugget = T,
# # n.cores=pred.ncores,
# # parType = pred.parType),
# # nrow=ntemps)
#
# pred.curr<-matrix(mod(tran(matrix(theta[1,,],ncol=p))),nrow=ntemps)
# s2[1,]<-rigammaTemper(ntemps, ny/2+a, b+colSums((t(pred.curr)-y)^2)/2, itl)
#
#
#
# eps<-1e-13
# tau<-rep(-4,ntemps) # scaling
# cc<-2.4^2/p
# S<-mu<-cov<-S.rev<-mu.rev<-cov.rev<-list()
# for(t in 1:ntemps)
# S[[t]]<-diag(p)*1e-6
# count<-matrix(0,nrow=ntemps,ncol=ntemps)
# count.decor<-matrix(0,nrow=p,ncol=ntemps)
# count100<-rep(0,ntemps)
#
#
# for(i in 2:nmcmc){
#
# theta[i,,]<-theta[i-1,,] # current set at previous (update below)
#
# ########################################################
# ## adaptive block update for theta within each temperature - covariance of previous samples scaled (by exp(tau)) based on acceptance rate for last 100 samples, since tempering makes large gaps
#
# if(i==300){ # start adapting
# for(t in 1:ntemps){
# mu[[t]]<-colMeans(theta[1:(i-1),t,])
# cov[[t]]<-cov(theta[1:(i-1),t,])
# S[[t]]<-cov(theta[1:(i-1),t,])*cc+diag(eps*cc,p)
# }
# }
# if(i>300){ # adaptation updates
# for(t in 1:ntemps){
# mu[[t]]<-mu[[t]]+(theta[(i-1),t,]-mu[[t]])/(i-1)
# cov[[t]]<-(i-2)/(i-1)*cov[[t]] + (i-2)/(i-1)^2*tcrossprod(theta[(i-1),t,]-mu[[t]])
# S[[t]]<-(cov[[t]]*cc+diag(eps*cc,p))*exp(tau[t])
# }
# }
#
#
#
# theta.cand<-matrix(nrow=ntemps,ncol=p)
# for(t in 1:ntemps)
# theta.cand[t,]<-rmnorm(theta[i-1,t,],S[[t]]) # generate candidate for each temperature
#
#
# # pred.cand<-matrix(
# # predict(mod,
# # tran(matrix(theta.cand,ncol=p)),
# # mcmc.use=sample(ns,size=1),
# # trunc.error=trunc.error,
# # nugget=T,
# # n.cores=pred.ncores,
# # parType = pred.parType),
# # nrow=ntemps) # get BASS prediction at each candidate (major speedup by vectorizing across temperatures)
#
# pred.cand<-matrix(mod(tran(matrix(theta.cand,ncol=p))),nrow=ntemps)
#
# for(t in 1:ntemps){ # loop over temperatures, do a block MCMC update
# if(any(theta.cand[t,]<0 | theta.cand[t,]>1))
# alpha<- -9999
# else{
# alpha<- (-.5/s2[i-1,t]*itl[t]*(sum((y-pred.cand[t,])^2)-sum((y-pred.curr[t,])^2)) # posterior
# #-mnormt::dmnorm(theta.cand[t,],theta[i-1,t,],S[[t]],log = T) + mnormt::dmnorm(theta[i-1,t,],theta.cand[t,],S.rev[[t]],log = T) # proposal when using radius-based adapting
# )
# }
# if(log(runif(1))<alpha){
# theta[i,t,]<-theta.cand[t,]
# count[t,t]<-count[t,t]+1
# pred.curr[t,]<-pred.cand[t,]
# count100[t]<-count100[t]+1
# }
# }
#
# ########################################################
# ## acceptance-rate based adaptation of covariance scale
# if(i%%100==0){
# delta<-min(.1,1/sqrt(i)*5)
# for(t in 1:ntemps){
# if(count100[t]<23){
# tau[t]<-tau[t]-delta
# } else if(count100[t]>23){
# tau[t]<-tau[t]+delta
# }
# } # could be vectorized, but probably not expensive
# count100<-count100*0
# }
#
#
# ########################################################
# ## decorrelation step for theta, especially to decorrelate the thetas that dont change anything
#
# if(i%%decor==0){ # every so often, do a decorrelation step (use single-site independence sampler)
# for(k in 1:p){
# theta.cand<-theta[i,,,drop=F] # most up-to-date value
# theta.cand[1,,k]<-runif(ntemps) # independence sampler candidate (vectorize over temperatures)
# # pred.cand<-matrix(
# # predict(mod,
# # tran(matrix(theta.cand[1,,],ncol=p)),
# # mcmc.use=sample(ns,size=1),
# # trunc.error=trunc.error,
# # nugget=T,
# # n.cores=pred.ncores,
# # parType = pred.parType),
# # nrow=ntemps)
# pred.cand<-matrix(mod(tran(matrix(theta.cand[1,,],ncol=p))),nrow=ntemps)
# for(t in 1:ntemps){
# alpha<- -.5/s2[i-1,t]*itl[t]*(sum((y-pred.cand[t,])^2)-sum((y-pred.curr[t,])^2)) # could do with colsums, but this is cheap
# if(log(runif(1))<alpha){
# theta[i,t,k]<-theta.cand[1,t,k]
# count.decor[k,t]<-count.decor[k,t]+1
# pred.curr[t,]<-pred.cand[t,]
# }
# }
# }
# }
#
# ########################################################
# ## update s2 with gibbs step
#
# s2[i,]<-rigammaTemper(ntemps,ny/2+a, b+colSums((t(pred.curr)-y)^2)/2, itl) # update error variance
#
# #pred.curr<-predict(mod,theta[i,,],mcmc.use=sample(ns,size=1),trunc.error=F,nugget=T)[1,,]
#
# ########################################################
# ## tempering swaps
#
# if(i>1000 & ntemps>1){ # tempering swap
# for(dummy in 1:ntemps){ # repeat tempering step a bunch of times
# sw<-sort(sample(ntemps,size=2))
#
# alpha<-(itl[sw[2]]-itl[sw[1]])*(
# -ny/2*log(s2[i,sw[1]]) - .5/s2[i,sw[1]]*sum((y-pred.curr[sw[1],])^2) -(a+1)*log(s2[i,sw[1]])-b/s2[i,sw[1]]
# +ny/2*log(s2[i,sw[2]]) + .5/s2[i,sw[2]]*sum((y-pred.curr[sw[2],])^2) +(a+1)*log(s2[i,sw[2]])+b/s2[i,sw[2]]
# )
#
# if(log(runif(1))<alpha){
# temp<-theta[i,sw[1],]
# theta[i,sw[1],]<-theta[i,sw[2],]
# theta[i,sw[2],]<-temp
# temp<-s2[i,sw[1]]
# s2[i,sw[1]]<-s2[i,sw[2]]
# s2[i,sw[2]]<-temp
# count[sw[1],sw[2]]<-count[sw[1],sw[2]]+1
# temp<-pred.curr[sw[1],] # not sampling posterior predictive each time, for speed
# pred.curr[sw[1],]<-pred.curr[sw[2],]
# pred.curr[sw[2],]<-temp
# }
# }
# }
#
# ########################################################
# ## take a new posterior predictive sample from the emulator (helps not get stuck in a mode from a particularly good sample)
# # pred.curr<-matrix(
# # predict(mod,
# # tran(matrix(theta[i,,],ncol=p)),
# # mcmc.use=sample(ns,size=1),
# # trunc.error=trunc.error,
# # nugget=T,
# # n.cores=pred.ncores,
# # parType = pred.parType),
# # nrow=ntemps)
#
# #if(!all(pred.curr == matrix(mod(tran(theta[i,,])),nrow=ntemps)))
# # browser()
#
#
# if(verbose & i%%100==0){
# pr<-c('MCMC iteration',i,myTimestamp(),'count:',diag(count))
# cat(pr,'\n')
# }
# }
#
# #th2<-pnorm(theta)
# for(ii in 1:p){
# theta[,,ii]<-unscale.range(theta[,,ii],bounds[,ii])
# }
# return(list(theta=theta,s2=s2,count=count,count.decor=count.decor,tau=tau))
#
#
# }
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