Timeline for Probability that Null Hypothesis is True
Current License: CC BY-SA 3.0
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| Sep 29, 2017 at 21:25 | history | edited | Sextus Empiricus | CC BY-SA 3.0 |
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| Sep 28, 2017 at 14:44 | comment | added | Sextus Empiricus | Talking about the probabilities. Note that Bayes rule is about two stochastic variables: P(a|b) P(b) = P(b|a) P(a). You can relate the conditional probabilities. If one of those P(b|a) is a causal relationship, as in 'theory leads to distribution of outcomes', then you can calculate it exact. Such case is only because the (1directional) causality. The hypothesis allows to know (hypothetic) everything you need, the marbles in the vase. The other way around, does not work. An experimental outcome 4 red vs 1 blue, does not cause the probability distribution of marbles in the vase. | |
| Sep 28, 2017 at 14:34 | comment | added | Sextus Empiricus | That is more an epistemological question than a problem about probability. An expression like P(result|hypothesis) is in a similar way "false", I mean, it is a hypothetical expression. You can express the probability for a result, given a certain hypothetical believe about 'reality'. In the same way as a probability for an experimental outcome is hypothetical, an expression for the probability of some theory (with or without some observation of a result), requires a certain hypothetical believe about 'reality'. Yes, priors are somewhat arbitrary. But so is a hypothesis. | |
| Sep 28, 2017 at 14:04 | comment | added | Kalev Maricq | Your vase example makes sense. However, in real life, we almost never know how many marbles of each color are in the vase. I always find myself with a question more like "Are there more red marbles than blue" and my data is that I drew 4 red marbles and 1 blue marble from the vase. Now, I can make assumptions like "there are probably ~100 marbles and each marble is either red or blue with 50% probability" but in real life, I often find myself at a loss for how to non-arbitrarily and non-circularly get these priors. | |
| Sep 28, 2017 at 12:30 | history | edited | Sextus Empiricus | CC BY-SA 3.0 |
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| Sep 28, 2017 at 12:21 | history | answered | Sextus Empiricus | CC BY-SA 3.0 |