getKDEQuantileError = function(q, p, bw, x)
{
	#This is a function for calculating quantile error given a quantile (q), a lower tail probability (p), KDE bandwidth (bw) and log(MFI) data (x)
	thisP = 0.0
	for(i in 1:length(x))
	{
		thisP = thisP + pnorm(q, x[i], bw, lower.tail = FALSE)/length(x)
	}
	return(abs(p - thisP))
}


getThreshold = function(nonSpecificRawMFIValues, upperQuantile = 0.99)
{
	# This function works out the threshold for positivity
	# (1 - upperQuantile) is the allowable probability of a false positive (0.01 by default)
	# nonSpecificRawMFIValues is a vector of raw MFI values for samples that should give a negative result under this test (used to determine the distribution of MFI noise for negative samples)
	if(min(nonSpecificRawMFIValues) <= 0)
	{
		cat("ERROR: One or more Raw MFI values in nonSpecificRawMFIValues is less than or equal to zero.  MFI values must be positive.  Returning NULL. \n")
		return(NULL)
	}
	else
	{
		nonSpecificRawMFIValues = log(nonSpecificRawMFIValues)
		mfiDensity = density(nonSpecificRawMFIValues)
		nsd = qnorm(upperQuantile)
		mfiQuantile = optim(par = mean(nonSpecificRawMFIValues), fn = getKDEQuantileError, p = (1 - upperQuantile), bw = mfiDensity$bw, x = nonSpecificRawMFIValues, method = "Brent", lower = min(nonSpecificRawMFIValues), upper = max(nonSpecificRawMFIValues) + 2*nsd*mfiDensity$bw, control = list(abstol = 1E-6))
		cat("NOTE: Check that optimConvergenceCode equals 0 for correct results.  If optimConvergenceCode does not equal 0, then consult the covergence codes in function optim() documentation for further information. \n")
		return(list(thresholdForPositivity = exp(mfiQuantile$par), optimConvergenceCode = mfiQuantile$convergence))
	}
}


########################### USAGE EXAMPLE ##########################
# #Raw MFI Data in rawMFI vector
# rawMFI = c(569, 243, 456, 908, 198, 354, 587, 776, 264, 812)
#
# #Now determine the threshold for positivity
# MFI_Threshold = getThreshold(rawMFI)
# MFI_Threshold
####################################################################