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[GreedyAlgorithm]

I'm interested in distributions on the busses, not distributions about the Bayesian's uncertainty about his own knowledge. And that is because I am studying busses, not Bayesians.

You may have noticed we're having trouble figuring out what your question about busses is. I will propose a question, answer it as a Bayesian would, and see what you think about it.

Obviously real bus schedules are too complex to deal with here. How about this one. You are at a bus stop. You know one bus (the 42, maybe) stops here. You know that throughout your world, busses stop either at 15 minute intervals all day, at 30 minute intervals all day, or at 60 minute intervals all day. You have no idea what type the 42 is or when it last stopped here. One question you could ask is "with what probability will a bus stop here in the next 10 minutes?"

The Bayesian says to himself, "Since I have no idea what type of bus this is and have no idea how many of each type there are and have no idea about traffic patterns (which would give me an idea of which type would be best here), I'll set the probability of each type to be 1/3. I also have no idea when the last one stopped here so I'll put a uniform distribution on the time until the next one stops. So if it's a 15 minute bus, I have a 10/15 chance of it stopping in the next 10 minutes, if 30, then 10/30, and if 60, then 10/60. Together that's (10/15)*(1/3)+(10/30)*(1/3)+(10/60)*(1/3)=7/18."

Your objection, if I'm reading correctly, would be that the probability is either 10/15, or 10/30, or 10/60, right? That the actual probability cannot possibly be 7/18?

Please either reformulate the question as you wish, confirm that that's your objection, or provide a different objection.