########################################################
# This function takes data, and pos (marker positions)
# log-likelihood function is maximized over delta and lambda.
# nlminb is used for maximization.
# It returns max(log-likelihood), mle of delta, mle of lambda, and
# message from nlminb function

mle.null<-function(data, pos) {
  profile <- nlminb(start = c(0.5, 0), mloglik.theta.null, data = data, 
		    pos = pos, lower = c(0.001,  - Inf), upper = c(0.999, Inf))
                               #see below for the definition of mloglik.theta
                               #leta=log(1/lambda)
  
  
  loglik.null <-  - profile$objective	#log-likelihood
  theta <- profile$parameters	#optimized theta value
  messages <- profile$message
  deltahat.null <- theta[1]
  letahat.null <- theta[2]
  lambdahat.null <- 1/exp(letahat.null)
  return(list(loglik.null = loglik.null, deltahat.null = deltahat.null, 
	      lambdahat.null = lambdahat.null, messages = messages))
}

########################################################
# This function computes (-(log-likelihood)) under the null hypo,
# which is exactly same as what mloglik.null does.
# It is just modified to be used as an object function of nlminb.

mloglik.theta.null<- function(theta,data,pos) {
  return (mloglik.null(leta=theta[2],delta=theta[1],data=data,pos=pos))
} 

######## Examples ######################################

pro<-dget("pro.data")
thy<-dget("thy.data")
fjp<-dget("fjp.data")

pro.mle.null<-mle.null(data=pro$data, pos=pro$pos)
thy.mle.null<-mle.null(data=thy$data, pos=thy$pos)
fjp.mle.null<-mle.null(data=fjp$data, pos=fjp$pos)


########################################################