Reduce repetition of the beta posterior derivation#912
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Move the closed-form beta posterior into the main text of prob_meaning (before the exercise, which now asks the reader to recover it), and replace the duplicated derivation in bayes_nonconj's "Analytical posterior" section with a back-reference. Reduces repetition across the two lectures. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
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The class only bundled a few parameters with three short methods; its state (draws, posterior_list, prior) reads more clearly as plain values produced by small functions. Refactor into simulate_flips and form_posterior, update the call sites and the exercise prompt. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
Like the Bayesian class, this only bundled parameters with methods that stashed results on self. Refactor into simulate_head_counts and compare_frequencies, and update the comparison loops and exercise prompt to call them directly. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
Replace the n!/(k!(n-k)!) form with the standard \binom{n}{k} in the
binomial pmf definition (and its restatements) across prob_meaning and
bayes_nonconj.
Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
Replace the {youtube} embeds with a bullet list of links in prob_meaning.
Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
- Drop "please" from each exercise prompt in pm_ex1 and pm_ex2. - Update the remaining "Python class" references (part h prompt and solution) to match the function-based refactor. - Define f_k^I with an indicator-function sum instead of words. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
Convert the "Comparison with different theta/n/I" headings and "Code for answering questions" from bold paragraphs to ### subsections. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
Give simulate_flips, simulate_head_counts, and compare_frequencies a seed=1234 default and build the generator with default_rng(seed), dropping the `rng = rng or np.random.default_rng()` guard. Call sites pass seed (seed=i in the comparison loops) instead of constructing and threading an rng object. Also fixes a stray undefined-rng line left in simulate_head_counts. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
The lead-in promised a derivation that the exercise never asked for. Now pm_ex2 keeps parts (a) and (b) and adds a new (c) asking the reader to derive the closed-form Beta(alpha+k, beta+n-k) posterior; the solution's existing n-flip generalization becomes solution part (c). The coding problems move to a new exercise pm_ex3 (parts a-f) with its own solution. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
(a) Reword the Overview to frame the lecture around the two meanings of probability (dropping the unfulfilled frequentist-confidence-interval promise), and add a "Comparing the two interpretations" synthesis section that contrasts the two answers before the conjugate-prior discussion. (c) Add ### subsections to the Bayesian half for parity with the Frequentist half, and add a caveat explaining the shape of the "different n" comparison (zero for n<10, peak near n=14). Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
# Conflicts: # lectures/bayes_nonconj.md
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What
prob_meaning.md: state the closed-form beta posterioreq:beta_posterior. The exercisepm_ex2now asks the reader to recover this result rather than being the only place it appears.bayes_nonconj.md: replace the duplicated three-step integral derivation in the "Analytical posterior" section with a back-reference to the result derived inprob_meaning(noting theWhy
The closed-form beta posterior was previously only stated inside
prob_meaning's exercise solution and then re-derived from scratch inbayes_nonconj. Stating it once as a first-class result and referencing it removes the repetition.Prose/math only — no code cells were modified.
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