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Bayesian Statistics: The three cultures

(statmodeling.stat.columbia.edu)
309 points luu | 1 comments | 26 Jul 24 17:15 UTC | HN request time: 0.208s | source
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prmph ◴[26 Jul 24 22:49 UTC] No.41083029[source]▶
So my theory is that probability is an ill-defined, unfalsifiable concept. And yet, it _seems_ to model aspects of the world pretty well, empirically. However, might it be leading us astray?

Consider the statement p(X) = 0.5 (probability of event X is 0.5). What does this actually mean? It it a proposition? If so, is it falsifiable? And how?

If it is not a proposition, what does it actually mean? If someone with more knowledge can chime in here, I'd be grateful. I've got much more to say on this, but only after I hear from those with a rigorous grounding the theory.

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1. canjobear ◴[27 Jul 24 02:20 UTC] No.41084029[source]▶
You’re right that a particular claim like p(X=x)=a can’t be falsified in general. But whole functions p can be compared and we can say one fits the data better than another.

For example, say Nate Silver and Andrew Gelman both publish probabilities for the outcomes of all the races in the election in November. After the election results are in, we can’t say any individual probability was right or wrong. But we will be able to say whether Nate Silver or Andrew Gelman was more accurate.