# Bayes rule P[s(t)|x(t)] = P[x(t)|s(t)] P(s(t)] / P[x(t)] s(t) - incoming stimulus that describes the object x(t) – activity in the system resulting from.

## Presentation on theme: "Bayes rule P[s(t)|x(t)] = P[x(t)|s(t)] P(s(t)] / P[x(t)] s(t) - incoming stimulus that describes the object x(t) – activity in the system resulting from."— Presentation transcript:

Bayes rule P[s(t)|x(t)] = P[x(t)|s(t)] P(s(t)] / P[x(t)] s(t) - incoming stimulus that describes the object x(t) – activity in the system resulting from the stimulus our ferret needs P[s(t)|x(t)] – probability of the stimulus given the data our ferret learns P[x(t)|s(t)] – probability of the data given the stimulus P[s(t)] - probability of the stimulus P[x(t)[ - probability of the data

Questions Detection: Is anything there ? Discrimination: Is this different from that one ? Scaling: How much of it is there? Recognition: What is it ?

Detection Concept Reality

Proportion of false alarms 1.0 0 Proportion of hits very sensitive no sensitivity Receiver operating curve (ROC) Response can be modulated by other means too importance of the response (payoff) Curve is given only by the system sensitivity for a given experiment, the ROC curve is unique the observer merely chooses the operating point on the curve response signalyesno presenthitmiss absentfalse alarm correct negative response signalyesno present0.720.28 absent0.400.60 stimulus present 50% of time response signalyesno present0.960.04 absent0.800.20 stimulus present 90% of time response signalyesno present0.390.61 absent0.050.95 stimulus present 10% of time

The model behind ROC sensor activity probability of the activity signal absent equal error rate low misses low false alarms signal present d’

sensor activity criterion

Discrimination How similar (different) are two different stimuli? – how much they need to differ to discriminated as being not the same? same or different ? (JND at 50%) forced-choice (JND at 75%) – which one is larger (brighter, heavier,…) A B time 100 g standard

Weber’s Law Just noticeable difference (JND) is proportional to the magnitude of the stimulus  I/I = const

Scaling (Psychological scales) nominalred ants = 1 black ants = 2 numbers are meaningless ordinalshortest = 1 taller = 2. tallest = N order meaningful values meaningless categorize stimuli used in category scaling intervalfarenheit celsius differences meaningful ratios meaningless origin meaningless 40 Celsius is not twice the heat of 20 C ratioheight = 183 cm ratios meaningful absolute value meaningless 183 cm = 72 inch rare scale in psychophysics absolutenumber of objects in the group absolute values meaningful

Fechner’s law S = K log I increase in intensity of stimulus I sensation S 1 JND Psychometric function sensation = f (intensity)

Scaling by category judgments ? very soft (1) soft (2) normal (3) loud (4) very loud (5) unbearable (6)

Power law of human perception sensation = intensity power Magnitude estimation 1.Present “standard stimulus” (magnitude 10) 2.Present new stimulus and ask for its “magnitude” Fechner sensation = K log (intensity) Stevens log(sensation) = power log (intensity)

Linear axislog-log axis