prob_meaning: state equivalence of sequential and batch posterior updates
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- 1/5
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- Under an hour
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- Documentation
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- Quiet
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- markdown
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Open lectures/prob_meaning.md and read the n-step posterior derivation alongside the exercise solution's binomial likelihood. Add a brief remark explaining that sequential Bernoulli updates and one Binomial update produce the same posterior because the sufficient statistic is the number of heads, regardless of order.
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Description
In lectures/prob_meaning.md, the lecture updates the posterior sequentially (one Bernoulli observation at a time), but the exercise solutions use the binomial likelihood over n draws. The equivalence between these two approaches — that updating n times after each Bernoulli observation gives the same posterior as updating once using a Binomial over n draws — is never stated explicitly.
This follows from Beta-Binomial conjugacy: the posterior depends only on the sufficient statistic (k heads in n flips), not on the order of updating. A brief remark after the n-step posterior derivation would make this connection clear for the reader.
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