Add Introduction to Bayesian Methods lecture (#751)#758
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New lecture introducing Bayesian updating through a microloan default example. Builds from conditional probability and Bayes' law to a Bernoulli/beta conjugate model, covering: - numerical grid-based posterior updating via the trapezoidal rule - the beta closed form and conjugacy - iterative (sequential) updating and the equivalent batch binomial update - loan pricing: expected loss and the break-even interest rate r = θ/(1-θ) - two exercises (prior sensitivity, credible interval) Slotted under the Estimation part of the table of contents after mle. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
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- Fix variable-name mismatches (y_outcomes/outcomes, current/current_vals) and define prior_vals at module scope - Normalize each iterated posterior against the running density rather than the original prior - Fix two prose typos - Add a note explaining that sequential updating also relies on conditional independence, just implicitly - Add a hidden-input figure visualizing the trapezoidal rule - Rename the conditional-probability example label to bayes_ex_cond Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
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Closes #751.
Adds a new lecture, Introduction to Bayesian Methods, motivated by a microloan default-risk story (a development bank entering a new lending market).
The lecture builds up gradually for a relatively unsophisticated audience:
normalizing_constanthelper and anupdatestepMCMC is deliberately left for a subsequent lecture.
Slotted under the Estimation part of
_toc.yml, aftermle.All code cells were run end-to-end (including under
-W error::DeprecationWarning); usesnp.trapezoidand matplotlib default colors.🤖 Generated with Claude Code