R/642.PosteriorProbs_x.R

In proportion: Inference on Single Binomial Proportion and Bayesian Computations

#' Bayesian posterior Probabilities
#' @param x - Number of successes
#' @param n - Number of trials
#' @param a - Prior Parameters
#' @param b - Prior Parameters
#' @param th - Theta value seeking Pr(Theta/X < th)
#' @details  Computes probability of the event \eqn{p < p0} (p0 is specified in [0, 1])
#' based on posterior distribution of Beta-Binomial model with given parameters for prior Beta
#' distribution for all \eqn{x = 0, 1, 2......n } where \code{n} is the number of trials
#' @return A dataframe with
#'  \item{x}{ Number of successes}
#'  \item{PosProb}{ Posterior probability}
#' @family Miscellaneous  functions for Bayesian method
#' @examples
#' x=5; n=5;  a=0.5; b=0.5; th=0.5;
#' probPOSx(x,n,a,b,th)
#' @references
#' [1] 2002 Gelman A, Carlin  JB, Stern HS and Dunson DB
#' Bayesian Data Analysis, Chapman & Hall/CRC
#' [2] 2006  Ghosh M, Delampady M and Samanta T.
#' An introduction to Bayesian analysis: Theory and Methods. Springer, New York
#' @export
#####Bayesian posterior Probabilites Pr(Theta/X < th) Other cases can be obtained from this
probPOSx<-function(x,n,a,b,th)
{
  if (missing(x)) stop("'x' is missing")
  if (missing(n)) stop("'n' is missing")
  if (missing(a)) stop("'a' is missing")
  if (missing(b)) stop("'b' is missing")
  if (missing(th)) stop("'th' is missing")
  if ((class(x) != "integer") & (class(x) != "numeric") || length(x) >1|| x>n || x<0 ) stop("'x' has to be between 0 and n")
  if ((class(n) != "integer") & (class(n) != "numeric") || length(n) >1|| n<0 ) stop("'n' has to be greater or equal to 0")
  if ((class(a) != "integer") & (class(a) != "numeric") || length(a) >1|| a<=0 ) stop("'a' has to be greater than 0")
  if ((class(b) != "integer") & (class(b) != "numeric") || length(b) >1|| b<=0 ) stop("'b' has to be greater than 0")
  if ((class(th) != "integer") & (class(th) != "numeric") || length(th) >1|| th<0 ) stop("'theta' has to be greater than x")

bet=function(p) dbeta(p,shape1=x+a,shape2=n-x+b)
PosProb=integrate(bet,0,th)$value
return(data.frame(x,PosProb))
}