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#' Normal-Gamma Posterior Updating data.frame
#'
#' @param mu.0 prior mean
#' @param n.0 prior effective sample size
#' @param alpha.0 prior alpha parameter
#' @param beta.0 prior beta parameter
#' @param xbar observed sampled mean
#' @param s observed sample standard deviation
#' @param n sample size
#' @param group text string for group label
#'
#' @return Returns a data.frame with prior, data, and posterior parameters.
#' @export
#' @examples
#' my.ng.post.df <- get.ng.post.df(mu.0 = 0, n.0 = 10, alpha.0 = .25, beta.0 = 1,
#' xbar = .25, s = c(1,2,3), n = 15, group = "Control")
#' my.ng.post.df
get.ng.post.df <- function(mu.0 = 0, n.0 = 10, alpha.0 = .25, beta.0 = 1,
xbar = .25, s = c(1,2,3), n = 15, group = "Control"){
data.frame(mu.0 = mu.0, n.0 = n.0, alpha.0 = alpha.0, beta.0 = beta.0,
xbar = xbar, s = s, n = n, group =group) %>%
mutate(
# Prior NG parameters
mu.0 = mu.0,
n.0 = n.0,
alpha.0 = alpha.0,
beta.0 = beta.0,
# Marginal parameters of t-distribution describing mu.0
tdf.0 = 2 * alpha.0,
sigma.0 = beta.0/(alpha.0 * n.0),
# data
xbar = xbar,
s = s,
n = n,
# Posterior parameters
mu.n = (n.0 * mu.0 + n * xbar)/(n.0 + n),
n.n = n.0 + n,
alpha.n = alpha.0 + n / 2,
beta.n = beta.0 + (n - 1)/2 * s ^ 2 + n.0 * n * (xbar - mu.0) ^ 2/(2 * (n.0 + n)),
# Marginal parameters of t-distribution describing mu.n
tdf.n = 2 * alpha.n,
sigma.n = beta.n/(alpha.n * n.n)
)
}
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