############# Priors and Empirical Bayes estimates #########################

#Use empirical Bayes method to choose Wsoro in prior for method Mr=1
#Or use subjective prior ?

res<-0
if(prior.switch.SORO==0){
    ## Empirical Bayes
	obs.rip.var<-apply(r.s.b,2,var)
    if(prior.switch.SORO.Tony){
        Wsoro<-diag(obs.rip.var) - Vsoro
    }else{
        Wsoro<-var(r.s.b)
    }
    print('SORO: Empirical Bayes prior')
    res<-tryCatch(solve(Wsoro), error=function(e) print("Wsoro is not positive definite"))
}else if(prior.switch.SORO==1){
    ## Subjective prior
    Wsoro.v<-0.02
	Wsoro<-diag(rep(Wsoro.v,Ni))
    print('SORO: Subjective prior')
}else if(prior.switch.SORO==2){
    ## Vague subjective prior
    Wsoro.v<-0.1
	Wsoro<-diag(rep(Wsoro.v,Ni))
    print('SORO: Vague subjective prior')
}
uWsoro<-Wsoro
if(!is.character(res)){
    uWsoro.inv<-solve(Wsoro)
}

##########################################################
#RFSP
#In the provided data, we are rank deficient (NJ=488, No=534), need to handle differently
#Preserve the covariance structure
if(prior.switch.RFSP==0){
    ## Empirical Bayes
	obs.op.var<-c(apply(cop.J.full,2,var),apply(fop.J.full,2,var))
	obs.op.cor<-matrix(0,No,No)
	obs.op.cor[1:Ni,1:Ni]<-cor(cop.J.full)
	obs.op.cor[(Ni+1):No,(Ni+1):No]<-cor(fop.J.full)
    if(prior.switch.RFSP.Tony){
        Rsd<-diag(sqrt(obs.op.var-diag(Vrfsp)))
    }else{
        ##DAS made this empricial Bayes change in light of 1d4d15d
        Rsd<-diag(sqrt(obs.op.var))
    }
    Wsp<-Rsd %*% (obs.op.cor %*% Rsd)
    print('RFSP: Empirical Bayes prior')
}else if(prior.switch.RFSP==1){
    ## Subjective prior
	Wsp.v<-0.02
	Wsp<-diag(rep(Wsp.v,No))
    print('RFSP: Subjective prior')
}else if(prior.switch.RFSP==2){
    ## Vague subjective prior
	Wsp.v<-0.10
	Wsp<-diag(rep(Wsp.v,No))
    print('RFSP: Vague subjective prior')
}

uWsp<-Wsp
uWsp.inv<-solve(Wsp)

##########################################################
##Wca

mca = apply(ccp.J.full, 2, mean)
Wca<-cov(ccp.J.full)  #just in case
res<-0

if(prior.switch.TUF==0){
    ## Empirical Bayes
    if(prior.switch.TUF.Tony){
        obs.ccp.var<-apply(ccp.J.full,2,var)
        Wca<-diag(obs.ccp.var)-Vtuf
    }else{
        Wca<-var(ccp.J.full)
    }
    res<-tryCatch(solve(Wca), error=function(e) print("Wca is not positive definite"))
    print('TUF: Empirical Bayes prior')
}else if(prior.switch.TUF==1){
    ## Subjective prior
	Wca.v<-0.02
	Wca<-diag(rep(Wca.v,Ni))
    print('TUF: Subjective prior')
}else if(prior.switch.TUF==2){
    ## Vague subjective prior
	Wca.v<-0.10
	Wca<-diag(rep(Wca.v,Ni))
    print('TUF: Vague subjective prior')
}
uWca<-Wca
if(!is.character(res)){
    Wca.inv<-solve(Wca)
}

##########################################################
#Without data, we cannot improve on the Wca data
#Wtuf

mtuf<-mca
Wtuf<-Wca