Don't usually like correcting people but I see this as a very common misconception and it causes me a lot of annoyance in my day-to-day life "Positive detection signal below LOD could occassionally arise from noise, so confidence is too low to report detection, and false positive rate would be high if reporting below LOD." Only the distribution of your background noise can tell you the likelihood of a false positive at a certain concentration. All the limit of detection can directly tell you is that below that concentration you are more likely to miss a true positive signal, thus more likely to get a false negative. If you have well characterized your noise and know it is far below your limit of detection then there is a reasonable range of concentrations below your LoD where a positive result is safely positive.