R/NPestT.R

In wiscstatman/rvalues: R-Values for Ranking in High-Dimensional Settings

#PostProbT <- function(x,std_err,df,support,mix.prop) {
#      n <- length(x)
#      T <- length(support)

#      z <- .C("postprobT", as.double(x), as.double(std_err), 
#                  as.double(df),as.double(support), as.double(mix.prop),
#                  as.integer(n), as.integer(T), double(T), 
#                  post = double(n*T), loglik = double(1), PACKAGE = "rvalues")
#      ans <- list()
#      ans$postprobs <- matrix(z$post, nrow=n)
#      ans$loglik <- z$loglik
#      return(ans)
#}              


PostProbT <- function(x, std_err, df, support, mix.prop) {
  ### Amat is nsupport x n matrix
   dff <- (df + 1)/2
   ResidMat <- (outer(x, support, FUN="-")^2)/(std_err^2)
   Amat <- t(exp(-dff*log(1 + ResidMat/df))) 
   
   B <- mix.prop*Amat
   lik <- colSums(B)
   PP <- t(B)/lik
   ans <- list()
   ans$loglik <- sum(log(lik))
   ans$postprobs <- PP

  return(ans)
}



NPestT = function(x,std_err,df,maxiter,tol,nmix)  {
  ### This function takes an initial estimate of the mixing distribution
  ### and the loc.scale matrix and returns a final estimate of the 
  ### mixing distribution using the EM algorithm.
  ### Also, it returns an indicator of convergence.
  ### 0 - did converge.  1 - did not converge.
  
  ### densmat should have dimensions [n,T]
  ### densmat[i,j] - p(X_{j}|\theta_{i})
  
  n <- length(x)
  grid.to <- max(x)
  grid.from <- min(x)
  if(is.null(nmix)) {
      if(n <= 200) {
          nmix <- n
      }
      else{
          ## Number of mixture components grows according to
          ## f(x) = 200 + 5*log(x)*[(x - 200)^(.3)]
  
          nn <- n - 200
          nmix <- 200 + ceiling(5*exp(.3*log(nn))*log(nn))
      }
  }
  log.lik <- rep(0,maxiter + 1)
  counter <- 0
  
  support <- c(1:nmix)*(grid.to/nmix)
  mix.prop <- rep(1/nmix,nmix)
  ss <- 1/(std_err^2)

  tmp <- PostProbT(x,std_err,df,support,mix.prop)
  PP <- tmp$postprobs
  log.lik[1] <- tmp$loglik
  done <- FALSE
 
  aa <- rep(1/2, n)
  for(k in 1:maxiter)  {
      mix.prop <- colMeans(PP)

      ### EM update for the support is based on assuming that (conditional on cluster assignment)
      ### xi ~ N(mu_k, (std_erri^2)/ai), where the latent variables ai ~ Gamma(df/2, df/2) (rate form of gamma)

      bb <- ss*aa
      support <- as.vector(crossprod(PP,x*bb)/crossprod(PP, bb))
      
      tmp <- PostProbT(x,std_err,df,support,mix.prop)
      PP <- tmp$postprobs
      log.lik[k+1] <- tmp$loglik
      
      done <- (abs((log.lik[k+1] - log.lik[k])/log.lik[k]) < tol) 
      counter <- counter + 1
      if(done) {
          break
      }
      
      residMat <- (outer(x, support, FUN="-")^2)*ss
      rsumsPP <- rowSums(PP)
      aa <- ((df-1)*rsumsPP)/(rowSums(PP*residMat)  + df*rsumsPP)
  }
  print(summary(support))
  post.mean <- PP%*%support
  log.lik <- log.lik[1:(counter+1)]
  conv = ifelse(maxiter == counter,1,0)
  return(list(mix.prop=mix.prop,support=support,convergence = conv,log.lik=log.lik,numiter=counter, post.mean=post.mean))
}