Teaching Bayesianism

JQuinton

I've had a bit of success with getting people to understand Bayesianism at parties and such, and I'm posting this thought experiment that I came up with to see if it can be improved or if an entirely different thought experiment would be grasped more intuitively in that context:

Say there is a jar that is filled with dice. There are two types of dice in the jar: One is an 8-sided die with the numbers 1 - 8 and the other is a trick die that has a 3 on all faces. The jar has an even distribution between the 8-sided die and the trick die. If a friend of yours grabbed a die from the jar at random and rolled it and told you that the number that landed was a 3, is it more likely that the person grabbed the 8-sided die or the trick die?

I originally came up with this idea to explain falsifiability which is why I didn't go with say the example in the better article on Bayesianism (i.e. any other number besides a 3 rolled refutes the possibility that the trick die was picked) and having a hypothesis that explains too much contradictory data, so eventually I increase the sides that the die has (like a hypothetical 50-sided die), the different types of die in the jar (100-sided, 6-sided, trick die), and different distributions of die in the jar (90% of the die are 200-sided but a 3 is rolled, etc.). Again, I've been discussing this at parties where alcohol is flowing and cognition is impaired yet people understand it, so I figure if it works there then it can be understood intuitively by many people.

Say there is a jar that is filled with dice. There are two types of dice in the jar: One is an 8-sided die with the numbers 1 - 8 and the other is a trick die that has a 3 on all faces. The jar has an even distribution between the 8-sided die and the trick die. If a friend of yours grabbed a die from the jar at random and rolled it and told you that the number that landed was a 3, is it more likely that the person grabbed the 8-sided die or the trick die?

If you have an epistemic conception of probability, then it makes sense to talk about the probability distribution of a theoretical parameter, such as the mean of some variable in a population.

Please go on with an example of how it is practically relevant, so that the frequentism fails.

The Bayesianism here with the Solomonoff induction as a prior, is identical to frequentism over Turing machines anyway (or at least should be; if you make mistakes it won't be)

With the local trope, the local trope seem to be a complete misunderstanding of books such as the one you linked.

Please go on with an example of how it is practically relevant, so that the frequentism fails.

For an actual scientific example of Bayesian and frequentist methods yielding different results when applied to the same problem, see Wagenmakers et al.'s criticisms [PDF] of Bem's precognition experiments.

Here's a toy example that (according to Bayesians, at least) illustrates a defect of frequentist methodology. You draw two random values from a uniform distribution with unknown mean m and known width 1. Let these values be v1 and v2, with v1 < v2. If you ... (read more)

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That's not what frequentists actually do. See e.g. Probability Theory: The Logic of Science by E.T. Jaynes.