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Chapter7.2_PerceptionasaBayesianproblem-createdfor3rdedition.ppt

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Chapter 7.2:
Perception as a Bayesian problem

Inferential model of perception

How do our perceptual systems get from proximal sensory stimulation to a full-blown model of the distal environment?

Irving Rock: offered a distinctive inferential model of perception

Influenced by the Gestalt school of perceptual psychology: perceptual inference is largely top-down and holistic.

What the visual system does is impose structure on an essentially unstructured retinal image.

The visual system uses general principles about how objects and groups of objects form organized patterns.

Cognitive Science  José Luis Bermúdez / Cambridge University Press 2020

Gestalt principles of grouping

Cognitive Science  José Luis Bermúdez / Cambridge University Press 2020

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http://www.skidmore.edu/~hfoley/PercLabs/Shape.htm

Cognitive Science  José Luis Bermúdez / Cambridge University Press 2020

Bayesian model of perception

How do Gestalt principles of grouping operate to structure how we see the world?

The Bayesian answer: perceptual systems make probabilistic inferences, so that perceptual systems exploit a constantly updated body of probabilistic knowledge.

Cognitive Science  José Luis Bermúdez / Cambridge University Press 2020

Probabilistic inferences in perception

Perceptual systems aim to derive a hypothesis (H) about the environment based on the evidence (E) provided by sensory stimulation at the retina, or at the membrane window of the cochlea.

Each perceptual system aims for the hypothesis that is most probable given the evidence: posterior probabilities p(H/E)

Perceptual systems store information about the likelihood of different environmental set-ups: prior probabilities p(H); and how likely different types of sensory stimulation are, given different layouts of the distal environment: likelihoods p(E/H).

Cognitive Science  José Luis Bermúdez / Cambridge University Press 2020

Gestalt principles as Bayesian priors

Cognitive Science  José Luis Bermúdez / Cambridge University Press 2020

A Bayesian prior: A hypothesis about the lay-out of objects in the environment that contains abrupt changes should have a lower prior probability than one with fewer or no abrupt changes.

Perceptual systems make probabilistic inferences that end up in a model of how things are in the external environment using Bayes’s rule.

Cognitive Science  José Luis Bermúdez / Cambridge University Press 2020

Case study: binocular rivalry

When separate images are presented to each eye, what you actually perceive alternates between the two images

Cognitive Science  José Luis Bermúdez / Cambridge University Press 2020

The Bayesian explanation of binocular rivalry

Question: Does the distal environment contain a red iron (H1), a green violin (H2), or some sort of mish-mash composite object that is part iron, part violin, colored both red and green (H3)?

Evidence (E): Picture of red iron (L eye) and picture of green violin (R eye)

The task is to compare p(H1/E), p(H2/E), and p(H3/E).

Cognitive Science  José Luis Bermúdez / Cambridge University Press 2020

Comparison without numerical assignments

Posterior probability of the hypothesis =

Likelihood of the evidence  Prior probability of the hypothesis

––––––––––––––––––––––––––––––––––––––––––– Probability of the evidence

The probability of the evidence is the same for all three hypotheses. So we just need to compare the numerator.

It is reasonable that the hypothesis that there is a red iron and that there is a green violin is the same [p(H1)=p(H2)] and that both are more likely than the hypothesis that there is a composite object [p(H1)=p(H2)>p(H3)].

Cognitive Science  José Luis Bermúdez / Cambridge University Press 2020

Comparison of the likelihoods

It is reasonable that the likelihoods of the evidence are the same for H1 and H2 [p(E/H1)=p(E/H2)] .

If H1 holds, then that explains why there is a red iron image on the left. But the green violin is a complete mystery.

If H2 holds, then that explains why there is a green violin image on the right. But the red iron image is a complete mysterious.

Cognitive Science  José Luis Bermúdez / Cambridge University Press 2020

Comparison of the likelihoods (cont.)

p(E/H3) is the likelihood that you would get the evidence (a red iron image on the left and a green violin image on the right) if what were in the world were a red-green violin-iron.

This is not very likely. If the visual system is reliable, you would expect your eyes to generate an image of what is in the world, i.e., a red-green iron-violin. It seems unlikely that a composite object would yield two distinct retinal images.

So, p(E/H1)=p(E/H2)>p(E/H3)

Cognitive Science  José Luis Bermúdez / Cambridge University Press 2020

Coming to the conclusion

p(H1)=p(H2)>p(H3)

p(E/H1)=p(E/H2)>p(E/H3)

So, p(H1/E)=p(H2/E)>p(H3/E)

The eyes are unable to decide between between H1 and H2. The visual system switches between them at random.

This creates the characteristic effect of binocular rivalry, as a rational response to a process of Bayesian updating.

Cognitive Science  José Luis Bermúdez / Cambridge University Press 2020