xx<-c(0.7012873,0.2661434,0.5750884,0.1432547,0.1929323,0.4916651,0.7922205,0.4219847,0.1840799,0.3095818)

########
# Plotting Beta Likelihood
######
BetaL<-function(a,b,x)
{
n<-length(x)
exp(-n*log(beta(a,b))+(a-1)*sum(log(x))+(b-1)*sum(log(1-x)))
}

a<-seq(0.01,5,length=100)
b<-seq(0.01,8,length=100)
Z<-outer(a,b,BetaL,xx)
persp(a,b,Z,theta=45,phi=45,ticktype="detailed",xlab=expression(alpha),ylab=expression(beta),zlab="Likelihood")

#########################
# Beta MLE using nlm()
#####

beta.mlen<- function(xx,a0,b0) 
{
negLL<-function(p,x)
{
a<-p[1]
b<-p[2]
n<-length(x)
n*log(beta(a,b))-(a-1)*sum(log(x))-(b-1)*sum(log(1-x))
}
nlm(negLL, p = c(a0, b0), hessian = T, x = xx)
}
beta.mlen(xx,0.1,0.1)