pbetat=function(p0,prob,ab,data)
{
#
# PBETAT Performs a test that a proportion is equal to a specific value.
#	PBETAT(P0,PROB,AB,DATA) gives a vector of the Bayes factor and
#	the probability of the hypothesis P=P0, where P0 is the proportion
#	value to be tested, PROB is the prior probability of the hypothesis,
#	AB is the vector of parameters of the beta density under the 
#	alternative hypothesis, and DATA is the vector of numbers of 
#	successes and failures.
#------------------------
# Written by Jim Albert
# albert@bgnet.bgsu.edu
# November 2004
#------------------------

a=ab[1]; b=ab[2]
s=data[1]; f=data[2]

lbf=s*log(p0)+f*log(1-p0)+lbeta(a,b)-lbeta(a+s,b+f)

bf=exp(lbf)
post=prob*bf/(prob*bf+1-prob)

return(list(bf=bf,post=post))

}