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two_p_update <- function(prior, s1f1, s2f2){
p1 <- as.numeric(dimnames(prior)[[1]])
p2 <- as.numeric(dimnames(prior)[[2]])
like1 <- dbinom(s1f1[1], size=s1f1[1] + s1f1[2], prob=p1)
like2 <- dbinom(s2f2[1], size=s2f2[1] + s2f2[2], prob=p2)
likelihood <- outer(like1, like2)
product <- prior * likelihood
product / sum(product)
}
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