How I would pack in one sentence the intuition for why ‘changing priors’ is ok: “Sometimes the number you wrote down as your prior is not your real prior, and looking at the data helps you sort that out.”
Yes, that’s how Bayesianism is supposed to work. It’s called Bayesian Updating.
You don’t wake up every day with a child’s naivete about whether the sun will rise or not, you have a prior belief that is refined by knowledge combined with the weight of previous evidence.
Then, upon observing that the sun did in fact rise on this new morning, your belief that the sun rises every day gets that much stronger going into the next day.
Why is this not the case? I thought the shortest summary of the bayesian process was prior → new evidence / arguments → posterior → posterior becomes new prior. I assumed that considering the quality of your evidence is a way to update your priors. What an I missing?
Sorry for being cursory, by “No” I meant to reply to the question in yourAorou’s comment “Isn’t this post an elaborate way of saying that today’s posteriors are tomorrow’s priors?” ⇒ “No, I don’t think that’s the point of the post”. I separately think that yes, today’s posteriors are tomorrow’s priors.
I liked this!
Isn’t this post an elaborate way of saying that today’s posteriors are tomorrow’s priors?
As in- all posteriors eventually get baked into the prior.
How I would pack in one sentence the intuition for why ‘changing priors’ is ok: “Sometimes the number you wrote down as your prior is not your real prior, and looking at the data helps you sort that out.”
Yes, that’s how Bayesianism is supposed to work. It’s called Bayesian Updating.
You don’t wake up every day with a child’s naivete about whether the sun will rise or not, you have a prior belief that is refined by knowledge combined with the weight of previous evidence.
Then, upon observing that the sun did in fact rise on this new morning, your belief that the sun rises every day gets that much stronger going into the next day.
No.
Why is this not the case? I thought the shortest summary of the bayesian process was prior → new evidence / arguments → posterior → posterior becomes new prior. I assumed that considering the quality of your evidence is a way to update your priors. What an I missing?
Sorry for being cursory, by “No” I meant to reply to the question in
yourAorou’s comment “Isn’t this post an elaborate way of saying that today’s posteriors are tomorrow’s priors?” ⇒ “No, I don’t think that’s the point of the post”. I separately think that yes, today’s posteriors are tomorrow’s priors.