Perception and Bayesian Inference - Thinking - 1+2

Question 1

How can thinking be described?

Answer 1

Thinking: can be described as the flexible organization and manipulation of internal representations

Question 2

What theories try to understand how thinking representations are formed?

Answer 2

Rationalism vs Empiricism debate (e.g. René Descartes “vs” John Locke, David Hume) in the 17th century

Emphasis of constructivist nature (according to a priori existing concepts) of the human mind vs sensory driven

Question 3

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

Answer 3

No, Instead, the brain uses ‘algorithms’ and assumptions to actively construct an image of the world
- perceptual illusions, Gestalt laws law of good continuity, law of closure etc

Question 4

Why do we use algorithms and assumptions to percieve?

Answer 4

We do not have unambiguous information coming through our senses

Incomplete “projection” into the brain, e.g. 3D – 2D projection
Even perception of simple features like colour is ambiguous!! eg blue and black dress

Question 5

How does the brain integrate specific observations?

Answer 5

(e.g. for visual object recognition: contour lines / shape, colour)

-the probability of the occurrence of a particular ‘object’

-other available information, e.g. the sound the object makes

Question 6

How do we process info based on the probability of the occurrence of a particular ‘object’?

Answer 6

Depending on narrative context, observers either see the young (‘wife’) or the old woman (‘mother in law’) - old lady young woman illusion

Question 7

Who researched illusions in thinking?

Answer 7

Gregory: Seeing through illusions

Carbon (2014): “Understanding human perception by human-made illusions” Frontiers in Human Neurosci.

Question 8

What is the Ventrioquist effect?

Answer 8

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

Question 9

What is the McGurk effect?

Answer 9

The perceived sound of a spoken syllable is altered by an incongruent visual input of lip-movement

aka (visual) + apa(auditory) = ata(perception)

Question 10

How can we resolve ambiguity in the brain?

Answer 10

• the brain needs to integrate sensory signals from a given modality with contextual information
• The human mind ‘has evolved’ a battery of strategies to deal with this uncertainty – select and integrate information according to “set routines” – which may be prone to failure in certain situations: perceptual illusions

Question 11

What were Helmholtz and Wundts “best guess” about perception?

Answer 11

“Unconscious Inference”

Question 12

What did Daniel Kahneman say about Bayesian Cognition?

Answer 12

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

Question 13

What are the two opposing positions of Bayesian cognition?

Answer 13

Karl Friston and Daniel Kahneman

Question 14

What did Karl Friston say about Bayesian Cognition?

Answer 14

A wide range of studies and computational propositions, Human cognition is based on Bayesian algorithms and this is what brains have evolved to do

Question 15

look up bayes theorem ( probs dont need to know it)

Question 16

What is a Probability, “p”, Kolmogorov axioms in simple terms?

Answer 16

• Probabilities are non-negative (real) numbers between 0 and 1 {0 < p < 1}
• The probability of the certain event is 1.
• The probabilities of all separate events that comprise a set add up and they add up to p=1.

Question 17

What is an example of the Kolmogorov axioms “The probabilities of all separate events that comprise a set add up and they add up to p=1.”?

Answer 17

eg - Set of balls from 1-7,
in different subsets, one from 1-5, the other from 6-7

Probability of any given ball having one of the numbers from 1-5, or from 6-7

Ball has number from 1-5 p(B1) = 5/7
Ball has number 6 or 7: p(B2) = 2/7

he probability that any given ball has a number from 1-7 is precisely p = 1

Question 18

How do you read conditioned probability?

Answer 18

p ( B / A) : reads “the probability of B given A” OR “the conditional probability of B given A”

And vice versa p (A/B)

Question 19

What is a conditional probability?

Answer 19

A conditional probability is the probability of a particular (hypothetical or real) ‘event’, e.g. A=2 with in the set of another event, e.g. B1 = set{1,2,3,4,5}

Question 20

What is inference?

Answer 20

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

Question 21

What is posterior probability?

Answer 21

p(H1/0) = The posterior probability of hypothesis H1 being true given observation O being made i.e. the probability of the patient suffering from AIDS, given a positive test result

Question 22

refearch Bayesian inference cos wtf

Question 23

How important is bayes theorem?

Answer 23

Inference of ‘ground truth’ (the state of the world) on the basis of (limited) data always comes with uncertainty, since the likelihoods, e.g. p(A|B) are virtually never 0 or 1.
The data alone rarely ever tell us with 100% certainty whether Hypothesis 1 or 2 is correct

For judging which hypothesis is the most “likely”, consideration of the prior probability is often crucial. In other words, individual observations are rarely enough, but we need contextual information, e.g. prior probabilities, to make judgements better.

In order to make the best judgement / inference under uncertainty, the Bayes theorem is crucial

Question 24

How much impact does the prior probability have on the posterior probability?

Answer 24

The relative “impact” the prior probability has on the posterior probability also depends on the “strength of the observations.
For instance, if the likelihoods were deterministic (e.g. Hit-rate of 1, False alarm rate of 0) then the prior probability is entirely irrelevant.

Question 25

What happens if the prior properties are balanced?

Answer 25

With more balanced ‘prior probabilities’, their importance is relatively reduced and will depend greatly on the “strength” of the data.

Question 26

What is the concept of sensing threat from one person in different areas according to bayesian perception?

Answer 26

The threat of seeing a roadman at night in kensington (nice part of ldn) would be less scary than in hackney (scary ldn)

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

Question 27

how are sensory and prior information weighted?

Answer 27

Sensory and prior information weighted according to their ‘precision’ to compute posterior belief (subjective percept)

Question 28

how do you find bayesian perceptual inference?

Answer 28

Calculate the ‘posterior probability’ of perceptual hypotheses given the sensory evidence and prior probability of the causes

Question 29

what is the perceptual hypothesis in bayes theorem?

Answer 29

p (Hi/S)

Question 30

what is the prior probability of the causes in bayes theorem?

Answer 30

p(Hi)

Question 31

what is the sensory evidence in bayes theorem?

Answer 31

p(S/Hi)

Question 32

How can we increase certainty about objects in the real world?

Answer 32

One way to increase the certainty about objects in the real world from our sensory systems is to combine the signals from different sensory modalities

We know that this happens (ventriloquist / McGurk effect)

Question 33

How do we increase certainty about sensory systems using bayes theorem?

Answer 33

The 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”

Question 34

What is Excursion - probability distributions?

Answer 34

The standard deviation σ is here expressed by the slope:

wider pdf distribution, flatter slope in cdf

Question 35

How do humans integrate visual and haptic information in a statistically optimal fashion?

Answer 35

Visual and haptic 3D - virtual reality

The task is to compare the height of two ‘bars’ – presented in VR visually and haptically

Question 36

What does virtual reality measure?

Answer 36

Can measure the accuracy of judgement in the 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, judge how much their judgement depends on visual, how much on haptic perception

Question 37

What is the psychometric function?

Answer 37

The psychometric function is often modelled as a ‘cumulative Gaussian function’ (sometimes ‘Weibull’ function)

Question 38

How does the parametric function show performance?

Answer 38

Slope of the psychometric function indicates the ‘performance’ of an observer:
The better, the steeper
This is captured by the standard deviation – or variance!

Question 39

What is the 2 AFC task?

Answer 39

judge whether the second stimulus was larger than the first (“standard” stimulus)

Question 40

What were the variables in the 2AFC test?

Answer 40

Measure the psychometric function

under haptic stimulation only

under visual stimulation only

at diff different noise levels

Question 41

How tall was the standard stimulus in the 2AFC task serial comparison?

Answer 41

55mm

Question 42

How can you estimate empirical weight?

Answer 42

Now presenting the stimuli both visual AND haptically, often when the visual stimulus was different from the haptic stimulus (kind of a visuo-haptic McGurk effect), allows to estimate the empirical weight with which each sensory modality contributed to the joint estimate….

Question 43

How oes the human brain encode?

Answer 43

Strong evidence that the human brain encodes sensory information probabilistically

and applies Bayes-optimal computations for multi-sensory integration to optimally judge stimulus properties.

Question 44

How did Stocker & Simoncelli 2006 research noise characteristics in prior expectations in human vidual speed perception?

Answer 44

Presented moving (‘drifting’) Gabor patches composed of different contrast-levels

It is known that motion perception of low contrast stimuli is less accurate than at high contrasts

It is known 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