R/prior_norm_C.R

In StepSignalMargiLike: Step-Wise Signal Extraction via Marginal Likelihood

#'@title prior.norm.C
#'
#'@description
#'This function computes the Norm-C prior proposed in Du, Kao and Kou (2015), which is used under conjugate normal assumption. The variance \eqn{\sigma^2} is assumed to be drawn from an inverse Gamma distribution with shape parameter \eqn{\nu0} and scale parameter \eqn{\sigma0^2}, while mean is assumed to be drawn from a normal distribution with mean \eqn{\mu0} and variance \eqn{\sigma^2/\kappa0}.
#'
#'@details
#'See Manual.pdf in "data" folder.
#'
#'@param
#'data.x Observed data in vector form where each element represents a single observation.
#'
#'@return
#'Vector for prior parameters in the order of (\eqn{\mu0, \kappa0, \nu0, \sigma0^2})
#'
#'@references
#'Chao Du, Chu-Lan Michael Kao and S. C. Kou (2015), "Stepwise Signal Extraction via Marginal Likelihood." Forthcoming in Journal of American Statistical Association.
#'
#'@examples
#'library(StepSignalMargiLike)
#'
#'n <- 5
#'data.x <- rnorm(n, 1, 1)
#'data.x <- c(data.x, rnorm(n, 10,1))
#'data.x <- c(data.x, rnorm(n, 2,1))
#'data.x <- c(data.x, rnorm(n, 10,1))
#'data.x <- c(data.x, rnorm(n, 1,1))
#'
#'prior.norm.C(data.x)
#'
#'@export
prior.norm.C <- function(data.x)
{
  index.ChPT <- est.changepoints(data.x=data.x, model="normal", prior=prior.norm.A(data.x))
  num.segs <- length(index.ChPT)+1
  num.data <- length(data.x)
  index.temp <- c(0, index.ChPT, num.data)
  tau2 <-0
  for (i in 1:num.segs)
  {
    data.temp <- data.x[(index.temp[i]+1):index.temp[i+1]]
    seg.var <- 0
    if (length(data.temp)>1)
    {
      seg.var <- var(data.temp)
    }
    if (seg.var<= 0)
    {
      seg.var <- 1
    }
    tau2 <- tau2 + seg.var
  }
  tau2 <- tau2/num.segs
  temp.var <- 0
  if (length(data.x)>1)
  {
    temp.var <- var(data.x)
  }
  if (temp.var<= 0)
  {
    temp.var <- 1
  }
  return(c(mean(data.x),5*tau2/(12*temp.var),3,3*tau2/5))
}