signal detection theory (sdt) théorie de la détection du signal (tds)

Signal Detection Theory (SDT)

Théorie de la Détection du Signal (TDS)

Screenplay and realization : Antoine Deplancke (doctor in cognitive science)Interpreted by : Laurent Sparrow

Signal Detection Theory (SDT)

Théorie de la Détection du Signal (TDS)- Signal Detection Theory (SDT) has had, and continues to have, an enormous impact on many branches of psychology and in other areas : radiology, air traffic control…- Used to study two different processes : the sensory process (changes in physical stimulation,

external stimulation) and the strategic process (decision) .- Used to quantify the ability to discern between an external physical information (signal) and

random information (called noise, consisting of random neural activity of the nervous system – internal noise - or a physical degradation of signal – external noise).

- It is a statistical model but very similar to neurophysiological models: concepts of activation threshold => trigger response ...

sensorial variability

--> Ratio signal/noise

decisional variability

--> strategies

Classical representation of the SDT with separation of sensory and decision processes :

Signal detection theory (SDT) is used when we want to measure the way we make decisions under conditions of uncertainty.

On peut distinguer 3 grandes étapes dans la perception :

a- La sensationInformations de bases fournies par les récepteurs sensoriels (visuels, auditifs, gustatifs, olfactifs, tactiles). Les stimulations externes (physiques, par exemple, des longueurs d’onde) sont transcodées par ces récepteurs sensoriels en impulsions nerveuses.

L’organisme contient aussi de nombreux autres dispositifs de détection : récepteurs de la pression sanguine, récepteurs du taux de sucre, récepteurs des muscles et tendons... Ceci permet au cerveau de disposer en permanence d’informations concernant l’état de l’organisme. Un système de régulation automatique fonctionne en permanence, permettant de maintenir un équilibre dans les fonctions vitales, ce qu’on appelle l’homéostasie. Certaines de ces données peuvent générer un percept (mal au ventre quand on a faim).

a- La sensationb- L’organisation perceptuelle : à quoi l’objet ressemble

Les informations transmises par les récepteurs sensoriels sont élémentaires, simples, basiques. Par exemple, dans le cas de la vision, les processus perceptuels élémentaires donnent des indications de taille, de forme, de couleur, de contraste, d’orientation. Ces informations élémentaires sont ensuite synthétisées (intégrées et combinées, c’est à dire, organisées) ce qui donne naissance au percept. Ces activités mentales sont automatiques et inconscientes.

a- La sensationb- L’organisation perceptuelle : à quoi l’objet ressemblec- Identification et reconnaissance : Quel est cet objet, quel est sa fonction

La troisième étape du processus perceptuel consiste à donner un sens à ces percepts: Un objet rond, circulaire peut devenir un ballon, une pièce de monnaie. On identifie l’objet mais en même temps, on lui attribue une fonction. Cette étape est consciente et fait appel à des processus dits « supérieurs ». Notre personnalité, nos souvenirs, nos valeurs, nos croyances peuvent influencer l’identification et la reconnaissance.

L’activation sensorielle, interne ou externe, peut aussi déclencher des réflexes émotionnels. Certains objets ont la particularité de mettre l’organisme en état d’alerte. Il existe une liaison directe entre perception et émotion.L’étape d’identification et de reconnaissance peut être mise en défaut. On parle dans ce cas d’illusions perceptives. Par exemple, une même image sensorielle peut donner lieu à différentes interprétations, c’est l’ambiguïté.

Théorie de la Détection du Signal (SDT)1 Variability of responses, concepts of signal and noise …

2 General principle and historical

3 Model Description

4 Some examples

5 Experimentation

6 Conclusion

There is a wide variability in the human responses, even in repeated or identical situations or when we perform a very simple task.

Especially with motor responses.

Less evident with a purely perceptual task (and yet, the variability is + + +):

Sometimes we see a vase, sometimes we see two faces : we do not know why, but suddenly, we switch from one percept to another

You (probably) learned in school (among other things) that elephants have 4 legs, but your perception does not help you to

verify this fact

Say to your perception that this circle does not rotate

Some see a dancer turning clockwise, and

some, counterclockwise.

The illusion derives from the lack of visual cues for

depth

If the foot touching the ground is perceived to be the left foot, the dancer appears to be spinning clockwise; if it is taken to be the right foot, then she

appears to be spinning counterclockwise.

sensorial variabilityRatio signal/noise

Noisy or not ?

decisional variability

--> strategies

If the signal is noisy or ambiguous then the perceptual processes will still attempt to interpret

signal noise ratio:

Every system is subject to a set of random noise.

-> It's a physical reality: there is no pure signal. There are two kinds of noise factors that contribute to the uncertainty: internal noise and external noise. External noise can be filtered and it is possible to attenuate it (but not to suppress it totally). But it is very difficult to reduce internal noise

after filtering

Internal noise refers to the fact that neural responses are noisy : it’s a random activity of neurons that is not associated with encoding of behaviorally relevant variables (signal).

Transformation des signaux reçus par les

In the context of decision models, we define the signal as being relevant information to the task or the behavior and noise as being any other information that disrupt processing of that signal

Environment = signal + noise

noise signalEnvironment

Low signal/noise ratio High signal/noise ration

Low contrast High contrast

« pop out » effectnumerous distractors

Main sources of noise in sensory processing :

Internal noise

External noise

external noise and irrelevant signals (eg distractors)

Transformation des signaux reçus par les

Transformations of informations coming from the sensory organs in percepts

Cognitive interference caused by brain processes unrelated to

the current task

Main sources of noise in sensory processing :

Internal noise

External noise

external noise and irrelevant signals (eg distractors)

Transformation des signaux reçus par les

Transformations of informations coming from the sensory organs in percepts

Cognitive interference caused by brain processes unrelated to

the current task

The transformation of information in percepts is a complex process that generates noise at all levels : some examplesAt the most peripheral level: retinal persistence (fix the black dot in the center of the picture)

Optical illusion black & white color

Google is your friend : « Jesus illusion »

at a more central level, The physical reality of the environment is sometimes transformed by the perception… This create also some noise !

this is not a spiral

all the lines are straight

nothing move !

Make some saccades on this picture…

Masking = Flushed face illusion

Google : « Drug illusions »

Main sources of noise in sensory processing :

Internal noise

External noise

external noise and irrelevant signals (eg distractors)

Transformation des signaux reçus par les

Transformations of informations coming from the sensory organs in percepts

Cognitive interference caused by brain processes unrelated to

the current task

Stroop effect : When the name of a color (e.g., "blue," "green," or "red") is printed in a color not denoted by the name (e.g., the word "red" printed in blue ink instead of red ink), naming the color of the word takes longer and is more prone to errors than when the color of the ink matches the name of the color.

vert bleu jaune rougebleu rouge jaune vertrouge jaune vert bleujaune vert bleu rougevert rouge bleu jaune jaune bleu vert rougevert rouge jaune bleujaune bleu vert rouge

naming the ink colordont read the word

This interference was explained by the automation of reading, where the mind automatically determines the semantic meaning of the word (it reads the word "red" and thinks of the color "red"), and then must

intentionally check itself and identify instead the color of the word (the ink is a color other than red), a process that is not automatized.

vert bleu jaune rougebleu rouge jaune vertrouge jaune vert bleujaune vert bleu rouge

it is impossible to name the ink color without reading the word

The participant must estimate the distance.

But first, he must take the object in hand.

This object can be heavy or light.

Perceived distance is altered for heavy object : influence of memory

to summarize

2 sources of sensorial noise:

Internal noise

External noise

external noise and irrelevant signals (eg distractors)

Transformation des signaux reçus par les

Transformations of informations coming from the sensory organs in percepts

Cognitive interference caused by brain processes unrelated to

the current task

Depends on the Signal to Noise ratio

Depends on the ability to discriminate

sensorial variabilityRatio signal/noise

Noisy or not ?

decisional variability

--> strategies

Decisional variability

Decisional variability : Strategy (or method) that we used to perform a task. It is consciously "controlled" opposed to sensory variability. ≠ noise

e.g. : search strategy by scanningfind this character

Decisional variability : Strategy (or method) that we used to perform a task. It is consciously "controlled" opposed to sensory variability.

≠ noise

1) A priori knowledge of the stimulus with respect to which we must respond2) Consign (instructions given to the participant): focus on speed or accuracy3) Reinforcement / punishment: Cost of good responses / errors

The decisional strategy depends of:

1) A priori knowledge of the stimulus :

You know this person, you know he likes to be near a tent for example, or you know he loves boating.

1) A priori knowledge of the stimulus :

you know that in this kind of task, the signal appears mostly in one precise region of the picture,

75%0%

5% 20%

2) Consign :

One can influence the strategy through the instructions given to the participant:

emphasize speed: this may increase errors

emphasize on accuracy: the participant may be slower

3) Reinforcement / punishment :

Reinforcement and punishment, the core tools of operant conditioning, are either positive (delivered following a response), or negative (withdrawn following a response)

E.g. : Reinforcement of rapid responses in a detection task

--> Decrease in the average latency of response.

Théorie de la Détection du Signal (SDT)1 Variability of responses, concepts of signal and noise …

2 General principle and historical

3 Model Description

4 Some examples

5 Experimentation

6 Conclusion

In World War II radar waves were used to detect enemy aircraft. The soldiers had to determine if the little spots of light are enemies, or simple noise (I.e. birds). There was no clearly defined criteria for making these kinds of decisions. If a enemy went undetected, people could be killed. If noise was interpreted as an enemy, time and money would be lost and people will be alerted for nothing.

Psychophysics of the 40s and 50s

Green, D.M., Swets J.A. (1966) Signal Detection Theory and Psychophysics. New York: Wiley.

used in many areas :

- air traffic control- medicine- radiology- quality control- Alarm Systems- Human Machine Interface- Experimental psychology.

Théorie de la Détection du Signal (SDT)1 Variability of responses, concepts of signal and noise …

2 General principle and historical

3 Model Description

4 Some examples

5 Experimentation

6 Conclusion

- Signal detection theory (SDT) is used when psychologists want to measure the way we make decisions under conditions of uncertainty.

Sensitivity (d’) : Measures of the sensitivity of the sensory process (pronounced ‘d-prime’):

The criterion (c ou c’) : Decision threshold that reflects the strategy of the subject (response bias)

- SDT assumes that the decision maker is not a passive receiver of information, but an active decision-maker who makes difficult perceptual judgments under conditions of uncertainty- There are two main components to the decision-making process: information

acquisition (sensitivity) and criterion.

SDT in experimental psychology:

medical example : radiology for the detection of cancers

Imagine that a radiologist is examining a CT scan (computed tomography, medical imaging), looking for evidence of a tumor.

Interpreting images is hard and it takes a lot of training. Because the task is so hard, there is always some uncertainty as to what is there or not.

Either there is a tumor (signal present) or there is not (signal absent).

Either the doctor sees a tumor (they respond "yes'') or does not (they respond "no'').

There are four possible outcomes:

hit (tumor present and doctor says "yes'')

miss (tumor present and doctor says "no'')

false alarm (tumor absent and doctor says "yes")

correct rejection (tumor absent and doctor says "no").

Hits and correct rejections are good.

False alarms and misses are bad.

F(Bruit) signalnoise

Probability

Internal response

The curve on the left is for the noise-alone (healthy lung) trials, and the curve on the right is for the signal-plus-noise (tumor present) trials. The horizontal axis is labeled internal response (or perceived stimulus intensity) and the vertical axis is labeled probability. The height of each curve represents how often that level of internal response will occur.

several possibilities

noise signalprobability

Example : stimulus is noise…Response : NOISE SIGNAL

reality

percept

noise signalprobability

Example : stimulus is signal…Response : SIGNAL BRUIT

reality

percept

The distance between the two distributions will be assimilated to the measure of the individual sensory processes (discrimination ability) ...

d’ = is the difference between the means of the noise (mN) and the signal+noise (mSN) distributions

Modulated by the signal / noise ratio

Discrimination :

d’

If d’ is low, then this means there is low discriminability.The noise and stimulus are highly overlapping. d’ = 0: pure chance

If d’ is high, then this means there is high discriminability.

d’ = 1: moderate performance

d’ > 4: “optimal” (corresponds to hit rate=0.99, false alarm rate=0.01)

Interpreting d’ :

If d’ is low, then this means there is low discriminability.If d’ is high, then this means there is high discriminability.

Sensitivity (d’) : Measures of the sensitivity of the sensory process (pronounced ‘d-prime’):

The criterion (c ou c’) : Decision threshold that reflects the strategy of the subject (response bias)

Response bias is based on a participant’s preference for a particular outcome. Preferences are based on costs and rewards. The strategy of the participant is expressed via the choice of this threshold.

C = Criterion Level below this criterion = choice will be « noise »above this criterion = choice will be « signal »

Response = noise Response = signal

There are four possible outcomes: (as we see with the doctor example) :

HITMISS

FACR

False alarmHit

Miss Correct Rejection

To summarize :If we present NOISE = Correct rejection or False Alarm

If we present SIGNAL = Miss or Hit

It depends on the criterion

Fausse Alarme

Hit

Miss

Rejet Correct

no yes

Effect of shifting the criterion :

Théorie de la Détection du Signal (SDT)1 Variability of responses, concepts of signal and noise …

2 General principle and historical

3 Model Description

4 Some examples

5 Experimentation

6 Conclusion

Estimation of d’

Converting hit & false alarm rates (which are probabilities) to z scores from tables of z distribution:

Hit rate = P(yes|Signal) => z( yes|signal )

False alarm rate = P(yes|Noise) => z( yes|Noise)

d’ = z( yes|Signal ) - z( yes|Noise )

d’ = z(HIT) – z(FA)

Criterion = = -0.5*z(hit) +z(fa))

signal

noise

DetectionNo

Detection

40 Hit 60 Miss

20 FA 80 CR

Exemple : responses

100

100

signal

noise

DetectionNo

Detection

0.4 0.6

0.2 0.8

Example : propability

1

1

signal

noise

DetectionNo

Detection

0.4 0.6

0.2 0.8

Example : calcul

1

1

d’ = z(.4)-z(.2) = .58

c=-0.5*(z(.4)+z(.2)) = 0.54

Théorie de la Détection du Signal (SDT)1 Variability of responses, concepts of signal and noise …

2 General principle and historical

3 Model Description

4 Some examples

5 Experimentation

6 Conclusion

Théorie de la Détection du Signal (SDT)1 Variability of responses, concepts of signal and noise …

2 General principle and historical

3 Model Description

4 Some examples

5 Experimentation http://www.cogs.indiana.edu/software/SigDetJ2/index.html

6 Conclusion

SDT Review :

• Perceptual decisions are made in the real world, which is full of noise.

• Perceptual responses are biased with respect to a criterion.

• A criterion level can change based on the preference for particular outcomes.

• There is a trade-off between hit rate and false alarm rate.

• Sensitivity/discriminability - the ability to discriminate a stimulus from noise - it is independent of the criterion.

• d’ is a measure of discriminability that is insensitive to the criterion level.

• d’ can be computed from the hit rate (proportion of stimuli detected when present) and the false alarm rate (proportion of stimuli reported when not present)