Reasoning under uncertainty #8 - weighting, expectation

A weighting metaphore to explain rule number 6 is developed. A few examples using die throws and the rain/overcast case is used. In addition to give a picture of rule 6, Pr(D)=sum Pr(Mi) Pr(D|Mi), the weight balancing principle can also be used for giving a picture of probabilistic expectation. Expectation is explained for dice throws.

Errata: The weighting picture in the middle of the video should have the oppositve labels in order to comply to the content of my speech.

Category:

Howto & Style

Tags:

• Bayesian
• Bayes
• weighting
• unconditional
• marginal
• data
• expectation
• risk
• probability
• reasoning
• model

[trondreitan]

Thanks. It's a bit frightening to have a reader of Cox in the audience. I bought the book, since Jaynes referred to it, but haven't read through it, yet. What you mention is a good illustration of expectancy, yes. There's also the thing about the minimizing quadratic error in an estimation problem, which yields expectancy. The difference between most likely and expectancy is something I'm planning on mentioning in the next clip.

[clray123]

I find the lottery metapher nice because it helps distinguish between "most likely" and "expected" - which are easily confused due to their intuitive similarity. A lottery can have a tiny "most likely" win (many worthless tickets), but still a pretty high expected value (a single ticket with a grand prize). With limited financial resources the "most likely" value seems to be more useful in spending decisions than the "expected" value.

[clray123]

Cox explains the meaning of "expected value" in "Algebra of Probable Inference" using a lottery example. There are winnable prizes of n different values in a lottery with m tickets. Each ticket may win one prize (or none). The "expected value" of the lottery is the break-even ticket price. Asking anything lower than that price makes the lottery organizer lose money after all tickets have been sold. Asking anything higher turns him a profit.