Nothing
x <- c(20, 24, 27, 28, 28, 28, 29, 30,
30, 30, 30, 32, 33, 34, 35, 38)
mean(x)
sd(x)
posterior <- function(x, mu0, sigma0, sigma = 5) {
n <- length(x)
N <- (n * mean(x) / sigma^2 + mu0 / sigma0^2)
D <- (n / sigma^2 + 1 / sigma0^2)
mu1 <- N / D; sigma1 <- sqrt(1 / D)
precision1 <- D
precision0 <- 1 / sigma0^2
precision.data <- n / sigma^2
return(cbind(mu1, sigma1, precision1, precision0, precision.data))
}
posterior(x, 20, 1)
posterior(x, 20, 4)
posterior(x, 20, 16)
posterior(x, 20, 1000)
# with very difuse prior, all the precision is coming from the data
# so sigma1 is sigma/sqrt(n)
5 / sqrt(length(x))
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