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estimate_posterior_nominator <- function(x, prior = c("normal", "flat"), interimmean, interimSE, priormean, ...){
# list input arguments
inp <- list(...)
#res1 <- dnorm(x, mean = interimmean, sd = interimSE) * dnorm(x, mean = priormean, sd = priorsigma)
if (prior == "normal"){res <- exp(- 1 / (2 * interimSE ^ 2) * (x - interimmean) ^ 2) * dnorm(x, mean = priormean, sd = inp$priorsigma)}
if (prior == "flat"){res <- dnorm(x, mean = interimmean, sd = interimSE) * dUniformNormalTails(x, mu = priormean, width = inp$width, height = inp$height)}
return(res)
}
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