3 ms·
You are using priors to decide that B is more likely than A, that is, you are saying that the frequent bus hypothesis is likely because buses with frequent inte
by pliny 10y ago
You are using priors to decide that B is more likely than A, that is, you are saying that the frequent bus hypothesis is likely because buses with frequent intervals are common.
If the bus shows up within 1 second of your arrival then there can be no discussion of "frequent buses", you were definitely lucky, but only because the prior for buses with frequency of Order-of (1 second) is so low.
The analogy here is time-to-life and we have 1 data point for that, not enough to establish credible priors for minimum\mean time-to-life under any circumstances.
- whack 10y agoThe point of the thought experiment is to avoid using any priors. If you have a single data-point of an event E, taking time T to occur, then there are 2 possibilities: A) Event E usually takes much much longer than T (>100T), and what you just witnessed is an anomaly, or B) Event E usually does take roughly time T to occur, and what you witnessed is within the range of what usually occurs. Both conclusions have an extremely high likelihood of being wrong, since the sample size is so small. But between the 2, conclusion B is more likely to be true than conclusion A.