Please read:

• Daniel Kersten and Alan Yuille, Bayesian models of object perception
• Chapter 1 of Stochastic models, estimation, and control (volume 1) by Peter Maybeck, 1979
• (optional) Hermann von Helmholtz, Concerning the perceptions in general

Figure 4 in Kersten and Yuille’s paper describes four categories of probabilistic inference and illustrates each category using an example from vision. They describe each category by giving

1. an intuitive, if vague, name for the inference, such as “cue integration”;
2. an influence diagram (that is, a Bayes net) in which each node is labeled by a random variable (that is, a component of the sample space), such as “stereo disparity”;
3. an English description of how the inference arises in practice, such as “the same factor in a scene influences two different features or cues”;
4. the probability formula that corresponds to the influence diagram, such as “p(S,I₁,I₂) = p(I₁,I₂|S) p(S)”;
5. a sample measurement (that is, observed evidence), such as the image inputs to the left and right eyes; and
6. an English explanation of how the example instantiates the inference, such as “The shadow means that the lower two green squares appear to be further from the checkerboard; however, when seen in stereo (with eyes crossed), the disparity and shadow cues combine, and the upper green square is seen to be further from the checkerboard.”

In an email to the class mailing list, please follow or extend this pattern to give a different example of probabilistic inference. (To depict an influence diagram over email, it’s probably the least hassle to use punctuation symbols from a monospaced font.) You may draw your example from vision or any other domain, be it perceptual, cognitive, robotic, strategic, or none of the above. Your example may instantiate one of Kersten and Yuille’s four categories or any other influence diagram. Your example need not match what people or (other) machines actually do, such as predict how people actually integrate visual cues. (But how would you find out or argue whether it does match?)