# function does Bayes ancestral character estimation
# written by Liam J. Revell 2011

anc.Bayes<-function(tree,x,ngen=10000,control=list()){

	# give the function some defaults (in case none are provided)
	temp<-phyl.vcv(as.matrix(x),vcv(tree),1)
	sig2<-temp$R[1,1]
	a<-temp$alpha
	y<-rep(a,tree$Nnode-1)
	pr.mean<-c(1000,rep(0,tree$Nnode))
	pr.var<-c(pr.mean[1]^2,rep(1000,tree$Nnode))
	prop<-rep(0.01*max(temp$C)*sig2,tree$Nnode+1)

	# populate control list
	con=list(sig2=sig2,a=a,y=y,pr.mean=pr.mean,pr.var=pr.var,prop=prop,sample=100)
	con[(namc<-names(control))]<-control
	con<-con[!sapply(con,is.null)]
	# print control parameters to screen
	message("Control parameters (set by user or default):"); str(con)

	# function returns the log-likelihood
	likelihood<-function(C,x,sig2,a,y){
		logLik<-dmnorm(x=c(x,y),mean=rep(a,nrow(C)),varcov=sig2*C,log=TRUE)
		return(logLik)
	}
	
	# function returns the prior
	log.prior<-function(pr.mean,pr.var,sig2,a,y)
		pp<-dexp(sig2,rate=1/pr.mean[1],log=TRUE)+sum(dnorm(c(a,y),sd=sqrt(pr.var[1+1:tree$Nnode]),log=TRUE))

	# compute C
	C<-vcvPhylo(tree)

	# now set starting values for MCMC
	sig2<-con$sig2; a<-con$a; y<-con$y
	x<-x[tree$tip.label]
	if(is.null(names(y))) names(y)<-length(tree$tip)+2:tree$Nnode
	else y[as.character(length(tree$tip)+2:tree$Nnode)]
	L<-likelihood(C,x,sig2,a,y)
	Pr<-log.prior(con$pr.mean,con$pr.var,sig2,a,y)

	# store
	X<-matrix(NA,ngen/con$sample+1,tree$Nnode+3,dimnames=list(NULL,c("gen","sig2",length(tree$tip)+1:tree$Nnode,"logLik")))
	X[1,]<-c(0,sig2,a,y,L)

	message("Starting MCMC...")

	# start MCMC
	for(i in 1:ngen){
		j<-(i-1)%%(tree$Nnode+1)
		if(j==0){
			# update sig2
			sig2.prime<-sig2+rnorm(n=1,sd=sqrt(con$prop[j+1]))
			if(sig2.prime<0) sig2.prime<--sig2.prime
			L.prime<-likelihood(C,x,sig2.prime,a,y)
			Pr.prime<-log.prior(con$pr.mean,con$pr.var,sig2.prime,a,y)
			post.odds<-min(1,exp(Pr.prime+L.prime-Pr-L))
			if(post.odds>runif(n=1)){ 
				if(i%%con$sample==0) X[i/con$sample+1,]<-c(i,sig2.prime,a,y,L.prime)
				sig2<-sig2.prime
				L<-L.prime
				Pr<-Pr.prime
			} else if(i%%con$sample==0) X[i/con$sample+1,]<-c(i,sig2,a,y,L)
		} else if(j==1){
			# update a
			a.prime<-a+rnorm(n=1,sd=sqrt(con$prop[j+1]))
			L.prime<-likelihood(C,x,sig2,a.prime,y)
			Pr.prime<-log.prior(con$pr.mean,con$pr.var,sig2,a.prime,y)
			post.odds<-min(1,exp(Pr.prime+L.prime-Pr-L))
			if(post.odds>runif(n=1)){ 
				if(i%%con$sample==0) X[i/con$sample+1,]<-c(i,sig2,a.prime,y,L.prime)
				a<-a.prime
				L<-L.prime
				Pr<-Pr.prime
			} else if(i%%con$sample==0) X[i/con$sample+1,]<-c(i,sig2,a,y,L)
		} else {
			k<-j-1 # update node k
			y.prime<-y
			y.prime[k]<-y[k]+rnorm(n=1,sd=sqrt(con$prop[j+1]))
			L.prime<-likelihood(C,x,sig2,a,y.prime)
			Pr.prime<-log.prior(con$pr.mean,con$pr.var,sig2,a,y.prime)
			post.odds<-min(1,exp(Pr.prime+L.prime-Pr-L))
			if(post.odds>runif(n=1)){ 
				if(i%%con$sample==0) X[i/con$sample+1,]<-c(i,sig2,a,y.prime,L.prime)
				y<-y.prime
				L<-L.prime
				Pr<-Pr.prime
			} else if(i%%con$sample==0) X[i/con$sample+1,]<-c(i,sig2,a,y,L)
		}
	}

	# done MCMC
	message("Done MCMC.")
	return(X)
}