Add Introduction to Bayesian Methods lecture (#751) (#758)

* Add Introduction to Bayesian Methods lecture (#751)

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>

* Fix code bugs, add trapezoid figure and conditional-independence note

- 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>

---------

Co-authored-by: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

Author: jstac

lectures/_toc.yml

@@ -86,6 +86,7 @@ parts:
   chapters:
   - file: simple_linear_regression
   - file: mle
+  - file: bayes_intro
 - caption: Other
   numbered: true
   chapters: