#This function computes the BF for a set of 2-sample t-tests.
# Based on formulas in Rouder & Morey (2011)
# BF>1 indicates evidence for alternative hypothesis
# when more than one t-value is provided, it computes a meta-BF.
# Calculations verified relative to earlier MatLab code by GF.

# Largely follows code by Richard Morey (one correction to df)
# gfrancis@purdue.edu
# July 15, 2013



BF2N = function(t,N1,N2,lo=-Inf,up=Inf){
result = marglike(t,N1, N2,lo=lo,up=up)/exp(sum(dt(t,(N1+N2-2),log=TRUE)))

return(result)
}



# Helper functions
int1 = function(delta,t,N1, N2){
exp(sum(dt(t,df=(N1+N2-2),ncp=delta*sqrt(N1*N2/(N1+N2)),log=TRUE)) + dcauchy(delta,log=TRUE))
}
v.int1 =Vectorize(int1,"delta")

marglike = function(t,N1, N2,lo=-Inf,up=Inf){
integrate(v.int1,lo,up,N1=N1, N2=N2,t=t)[[1]]
}