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This paradox is a good motivator for when Bayesian probability is a useful. Your confidence is a posterior probability which is conditioned on some prior inform
by fractionalhare 6y ago
This paradox is a good motivator for when Bayesian probability is a useful. Your confidence is a posterior probability which is conditioned on some prior information. Initially you have little prior information, except for an interval of time and distance. When you receive information about the derivative of speed throughout the trip, this meaningfully updates your priors, and so the posterior changes.
- jmoss20 6y agoThe upshot here is that choosing the max entropy distribution as your prior isn't enough, you also need to choose some particular way to formulate the problem. Particular formulations (travel time vs. speed, here) imply different max entropy priors, even though the formulations are equivalent. Worse, there are infinite equivalent formulations, all with different implied max entropy priors. You can get around this by choosing a non-max entropy prior, like [1], or by deciding on the One True Formulation for your problem. But (Bayesian) updating on the other formulations of the problem won't do it, because there isn't any information in the other formulations -- they're equivalent (by def). [1]: https://en.wikipedia.org/wiki/Jeffreys_prior https://en.wikipedia.org/wiki/Jeffreys_prior