Theory of signal detection
- 1. C THEORY OF SIGNAL DETECTION Facilitated: Dr Ekemiri Kingsley(OD,MPH) LECTURER & OPTOMETRIST The University of the West Indies
- 2. Learning outcome • Neural activation needed for detection • Background neural noise • Neural excitation when the stimulus is present or absent • Detectability • Effect of different criteria
- 3. Introduction • When ever a subject tries to detect a stimulus, the threshold can vary depending on a number of factors such as motivation, attention and fatigue etc. • The response can also depend on the amount of background noise in the neural system at that point in time. • Theory of signal detection: tries to account for the influence of background neural noise and the varying subjective criteria on the measure threshold.
- 4. • S.D.T. is a procedure for measuring sensitivity to stimulation, independent of the subject’s response bias. • When ever the visual system is activated the brain receives electrical signal this is referred to neural activation. • For every weak stimuli the neural activation is small but for strong stimuli it is large activation
- 5. • Explanation: let us assume that in order for the subject to detect the stimulus( see it) the neural activation must exceed some fixed threshold criteria for the brain • Whenever the neural activation exceeds this threshold the subject will respond “I see it” Threshold Criteria Neural Activation Can’t see these I can see it When ever retinal receptors receives an image, they send a signal to the brain that is proportional to the stimulus strength. When ever the neural signal are strong enough , the person will perceive that he/she perceive the object
- 6. Detection Experiment • We want to measure a subject’s ability to detect very weak stimuli. • How do we know when the subject is objectively incorrect?
- 7. BACK GROUND NEURAL NOISE • Even when the stimulus is not present, neurons are still firing randomly, but the level of electrical activity will be low. • None the less it is always present and it is called background neural noise • The strength of the neural noise is varies
- 8. • But we can assume that the range of value will have a normal distribution around some mean values. • With a bell shaped curve which represent the normal distribution.
- 9. • Background neural noise usually produce a weak signal that is well below the threshold criteria for detection. • However there are rare instances when the neural noise might be strong enough to exceed the threshold criteria- in that case the person would mistakenly think he/she is seeing a stimuli. • Be he/she is only receiving a neural activation caused by neural noise • .
- 10. • Neuronal noise is a general term that designates random influences on the transmembrane voltage of single neurons and by extension the firing activity of neural networks. • This noise can influence the transmission and integration of signals from other neurons as as alter the firing activity of neurons in isolation
- 11. Neural excitation in the presence of stimulus • We will assume that for one particular intensity setting, the stimulus alone always causes a fixed of neural activation when ever presented. • For example lets assume that the stimulus alone causes a neural signal with a strength of 100 arbitrary unit. • Since noise is always present, the total neural activation received when the stimulus is on will be due to the combined effects of the stimulus + neural noise.
- 13. Neural Excitation……. • The stimulus always have the same value but the neural noise is varies randomly. • Therefore the sum of Stimulus + Neural noise will also vary. • Since the variation is completely due to the changes in noise.
- 14. Neural Excitation…… • The probability distribution curve for Stimulus + Noise signal will be the same shape as the noise probability distribution curve (bell curve). • But will be shifted to the right. This is because excitation due to stimulus is added to the noise.
- 15. Neural Excitation…… • Note that the two curves shows two different stimulus conditions- when the stimulus is turned on and off. • Both distribution are shown on the same curve for comparison. • At any time , the neural signal will come from either one of these distribution.
- 16. Neural Excitation…… • Note, where the threshold criteria is drawn and consider the stimulus + noise curve only. • Most of the time when the stimulus is turned on, the neural activation from the stimulus + noise curve will be above the criterion line and the brain will respond “ I see it” • The probability of seeing the stimulus is proportional to the area under the curve to the right of the criterion line
- 17. Neural Excitation…… • Also note that even when the stimulus is present, the noise is so low that the combined neural signal from the stimulus plus the noise falls below the criterion line. • When ever the neural activation is this low the brain responds “ I see nothing” • This is indicated by the area under the noise – only curve by the left of the criteria line
- 18. Neural Activation in absence of stimulus • When no stimulus is present the probability distribution for receiving a certain level of neural activation(due to noise only) is shown by the left bell shape curve. • Most of the time the neural activation caused by noise alone is below the threshold criterion and the subject will correctly say he/she see nothing. • Also note that occasionly the noise alone is sufficient to exceed the threshold criterion and the patient will incorrectly think he/she is sees something.
- 19. Detectability • A subject must decide whether he/she sees a stimulus based upon the neural excitation he/she receives. • He/she will not know which distribution the neural excitation came from- whether the excitation came from the noise only or from stimulus + noise. • As long as it exceeds the threshold the response is the same- “I see it”
- 20. Detectability…… • On every trial experiment the person tries to decide if he/she is looking at the noise-only distribution or a signal + noise distribution • When stimulus intensity is small the right curve will be shifted to the right of the noisy curve slightly and this may cause an overlap between the two distributions. It will be difficult to pick the stimulus out of the noise and the subject will make many error
- 21. Detectability…… • If the intensity is large, the signal + noise distribution will be pushed further to the right and it will be easier to distinguish between the distributions
- 22. Effect of Different Criteria Example d is small(small stimulus intensity), so if the noise (N) and signal+ noise(N+S) DISTRIBUTION were drawn on the same plot they would have considerable overlap. It is remember however that during any particular experiment, the subject will see a neural signal produced by either the N or N+S Distribution but not both. How would different criteria affects according to the theory of signal detection?
- 23. • Considering a hypothetical experiment: • A subject sits in a perfectly dark room facing a panel and after hearing a tone he/she will report whether he/she saw the faint light or not. • But in order to keep the subject honest, you as the experimenter will mix in some null trials- that is sometimes when the tone sounds, the light will not be turned on. • Other time the light will be present
- 24. • Every time he /she hears the tone the subject must say “I see it” or “I did not see it”. • That is for every presentation there are two possible response, each of which could be right or wrong Four possible outcomes in the a detection experiment Subject Response Stimulus No Stimulus Says “ I see it” Hit(True Positive) False Alarm(False Positive) Says “I did not see it” Miss(False Negative) Correct rejection(True Negative)
- 26. Lax Criteria- Noise Only • This is the lowest level of criteria presented to a subject- LAX. • In this situation a subject will say” I see it” for low levels of neural excitation. • With regards to visual field test(VFT) such a person could be called a “trigger happy”
- 27. • Such people responds “ I see it” if no stimulus were present during a particular trial- that means in this case, the brain was receives neural activation from the noise alone. • Most of the time excitation produce by the Noise alone is above the criterion. • They will say “I see it”- but actually just noise. • This response is a false alarm or false positive
- 28. • Sometimes excitation from N may be below the criterion and he/she responds seeing nothing- which is correct(because it was nothing but a Nosie without stimulus. • This called correct rejection or true negative. • If the stimulus was turned on during the presentation, now it presents with neural excitation caused by Signal + Noise (N+S). • If N+S is above criteria, he/she will say “I see it” which is correct- this called a HIT • Hit or True Positive.
- 29. • Also there are situation when the N+S produces a very weak neural excitation. • The subject may respond “I did not see it”. • This is called a Miss or False negative- since he/she fails to see the stimulus when present
- 30. • From previous explanation, we can see that when the criteria is set low you will get many hits (True positive)and also many false alarm(False Positive). • It is possible to influence a subject’s criteria using rewards or penalties. • For example, suppose you tell the subject “Every time you see the dim light, I will give you a 100$” • This will encourage the subject to set his/her criteria low and he/she may be quick to say “ I see it”- this will cause a false Alarm • But still on the other he/she will also correctly say “ I see it” accurately - Hits
- 31. Strict Criteria • If the criteria is strict, the subject will say I see it only if neural excitation is relatively high. In this type of criteria the probability of getting a false alarm may be reduced because most N distribution is below the criteria so most of the time when the stimulus is not present the subject will rightly say he/she “do not see”. When the criteria is strict most part of the N+S is above the criteria, this indicates that the probability that the person would say the he/she sees it, when the stimulus is present is high(a hit). When the N+S is below the criteria, the subject will say he/she do not see it when actually it is present (A miss)
- 32. Strict Criteria……. • With a high criteria you will get a few false alarm and many misses(few hits). • You can influence the subject by set his/her criteria high by giving penalties. • For example; if you say, I give you an electric shock if you see it when it is not there(stimulus). • The subject becomes strict in making decision and sets his/her criteria really high and only responds if he/she is absolutely sure he/she sees it. • From this explanation it is possible to modify a subject criteria by offering rewards and penalties. • Think about this clinically.
- 33. Reference • Schwatz SH Visual perception- Clinical Orientation, 3rd Edition, Appleton & Lange, Stamford Connecticut 2004