perception and bayesian inference

Question 1

what is thinking?

Answer 1

can be described as the flexible organisation and manipulation of internal representations

Question 2

is perception a one-to-one mapping of the physical world into the mind?

Answer 2

no

Question 3

what does the brain use to actively construct an image of the world?

Answer 3

“algorithms” and assumptions

perceptual illusions, Gestalt laws (law of good continuity, closure)

Question 4

why do we need algorithms and assumptions?

Answer 4

do not have unambiguous information coming through our senses

even perceptions of simple features like colour is ambiguous

Question 5

what does brain integrate?

Answer 5

specific observations with all kinds of contextual information

the expectancy of the occurrence of a particular “object”

other available information

Question 6

what is the ventriloquist effect?

Answer 6

the perceived location of a sound is shifted in space by a simultaneously occurring visual stimulus at incongruent location

Question 7

what is the McGurk effect?

Answer 7

the perceived sound of a spoken syllable is altered by an incongruent visual input of lop-movement

Question 8

how does the brain resolve ambiguity?

Answer 8

needs to integrate sensory signals from a given modality with contextual information

human mind “has evolved” battery of strategies to deal with this uncertainty - select and integrate information according to “set routines”, may be prone to failure in certain situations (perceptual illusions)

Question 9

who was Hermann von Helmholtz?

Answer 9

physicist and early experimental and theoretical work on perception

handbook of physiological optics (1867)

Question 10

who was Wilhelm Wundt?

Answer 10

founder of first academic institute for psychology in history (1879, Leipzig)

foundations of physiological psychology

Question 11

what is Bayesian inference?

Answer 11

possible way of implementing the contextual integration of specific observations through Bayesian inference

infer what is going on in the “outside world” on the basis of observations and expectations

takes observations and expectations into account

choose the scenario/hypothesis that is maximally satisfying both at the same time

all formulated in (mathematical) probabilities

Question 12

what is Bayes theorem?

Answer 12

P(B|A) = (p(B) * p(A|B)) / p(A)

Question 13

what are probabilities?

Answer 13

Kolmogorov axioms in simplified terms

probabilities are not negative (real) number between 0 and 1

probability of certain event is 1

probabilities of all separate events that comprise a set add up and they add up to p = 1

Question 14

what is conditional probability?

Answer 14

probability of a particular (hypothetical or real) “event” within the set of another event

P(A|B) = probability A given B

Question 15

what is inference?

Answer 15

to infer from observations to the (probability of the) hypothesis

Question 16

what are we really interested in Bayes theorem?

Answer 16

what the probability of a certain hypothesis is, given the observations we have made

Question 17

what does the inference of “ground truth” come with?

Answer 17

ground truth = the state of the world

inference of ground truth on basis of (limited) data always comes with uncertainty since likelihoods are virtually never 0 or 1

data alone rarely ever tell us with 100% certainty whether hypothesis 1 or 2 is correct

Question 18

what does Bayes theorem do?

Answer 18

allows use to make best judgement/inference under uncertainty

for judging which hypothesis is most “likely”, consideration of prior probability is often crucial - individual observations rarely enough, need contextual information to make judgements better

relative “impact” the prior probability has on the posterior probability also depends on the “strength” of the observations - with more balanced “prior probabilities” their importance is relatively reduced and will depend greatly on the “strength” of the data

Bayes theorem gives equation how to calculate the (posterior) probability of a hypothesis given particular observations/data

Question 19

what do decisions under uncertainty require us to look at?

Answer 19

not only data supporting each of the hypotheses but also at prior probability of hypotheses

ignoring prior probability can lead to seriously wrong decisions - choice of wrong options/hypotheses

Question 20

who was Daniel Kahneman?

Answer 20

Nobel Laureate (2002)

humans fail spectacularly in taking prior probabilities (= base rate) into account

Question 21

what is Bayesian perception?

Answer 21

use of prior/contextual information will almost certainly considerably influence the perceived level of threat from one and same person

Question 22

what is Bayesian perceptual inference?

Answer 22

calculate “posterior probability” of perceptual hypothesis (p(Hi|S)) given the sensory evidence (p(S|Hi)) and prior probability of the causes (p(Hi))

p(Hi|S) = (p(S|Hi) * p(Hi)) / p(S)

sensory and prior information weighted according to their “precision” to compute posterior belief (subjective percept)

Question 23

what is one way to increase certainty about objects in the real world from our sensory systems?

Answer 23

combine signals from different sensory modalities

know this happens - ventriloquist effect, McGurk effect

Bayes theorem allows to derive how these are ideally combined to come to a common judgement, in the same way as individual observations and prior probability are “combined”

combined sensation = subjective percept

Question 24

what was Ernst & Banks’s (2002) study?

Answer 24

visual and haptic 3D - virtual reality

task is to compare the height of two bars - presented in VR visually or haptically

can measure accuracy of judgement in visual domain and somatosensory domain (presented separately)

can estimate a person’s accuracy in each modality (separately) for vision also under various levels of noise

in combined presentations, measure how much their judgement depends on visual, how much on haptic perception

Question 25

what is the psychometric function?

Answer 25

2AFC task - judge whether the second stimulus larger than the first ("standard" stimulus) often modelled as a "cumulative Gaussian function" (sometimes "Weibull" function) slope of psychometric function indicates "performance" of observer - better, steeper - captured by standard deviation or variance

Question 26

what is a 2AFC?

Answer 26

serial comparisons "standard stimulus" S (55mm) comparison stimulus ↑↓

Question 27

how is the psychometric function measured?

Answer 27

under haptic stimulation only under visual stimulation only - at different noise levels

Question 28

what does presenting the stimuli both visually and haptically do?

Answer 28

often when visual stimulus was different from haptic stimulus allows us to estimate the empirical weight with which each sensory modality contributed to the joint estimate followed (pretty) much exactly the optimal weight as derived from Bayes theorem

Question 29

what does the visual and haptic task present strong evidence for?

Answer 29

that the human brain encodes sensory information probabilistically and applies Bayes-optimal computations for multi-sensory integration to optimally judge stimulus properties

Question 30

what was Stocker & Simoncelli's (2006) study?

Answer 30

presented moving ("drifting") Gabor patches composed of different contrasts levels known that motion perception of low contrast stimuli is less accurate than at high contrasts know that there is a general bias to underestimate motion speeds and this is thought to be due to the fact that lower speeds are more present in natural environments low contrast stimuli will be perceived as more ambiguous participants will be biased to perceive motions as slower than they are therefore the perceived motion of low contrast gratings (ambiguous) will be slower than those of high contrast hypotheses were confirmed - Bayesian observer model could explain behavioural data for different motion speeds and contrast levels sufficiently well and better than other models

Question 31

what did Ernst & Banks show clear and strong evidence for?

Answer 31

that human observers are capable of integrating vision and touch signals as expected from "Bayes-optimal observer"

Question 32

what did Stocker & Simoncelli show?

Answer 32

that a Bayesian model can account for the data of human observers in a speed judgement task

Question 33

what is a criticism of Ernst & Banks?

Answer 33

did not investigate whether participants integrate sensory signals and prior probability of the causes

Question 34

what is a criticism of Stocker & Simoncelli?

Answer 34

could not manipulate the prior probability distribution but had to assume these/estimates from the data only show that Bayesian model can explain data very well (and better than other models) yet there may be better models out there

Question 35

why does the question of perception reflecting Bayes-optimal inference remain under intense investigation?

Answer 35

definitely range of spectacularly positive results, in particular in domain of multisensory integration, also studies that addressed the integration of different sensory modalities and prior probability - multisensory illusions can be explained by Bayesian integration of senses but there are methodological shortcomings in studies investigating this for the combination of true prior probabilities and sensory information