[kalman] Fix errors, modernize code, and unify notation (#908)
* [kalman] Fix errors, modernize code, unify notation
Review-driven pass over the Kalman filter lecture covering correctness
fixes, code modernization, a notation overhaul, and math layout.
- Fix an unterminated math span ($Y_{t+1}.), a measurement-equation
subscript (v -> v_t), and a stray figure label ($y$ -> $Y_t$).
- Replace the hand-rolled bivariate_normal density with
scipy.stats.multivariate_normal; switch the jet colormap to viridis;
drop redundant float(...item()) conversions.
- Reparameterize the Gaussian throughout as N(mu, Sigma) (xhat -> mu),
in math, prose, and code variables, with bridging notes tying mu_t to
the literature's xhat and the QuantEcon `x_hat` attribute.
- Set "new" subscripts upright (\mathrm{new}) and reflow two wide
derivations into aligned blocks.
Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
* misc
---------
Co-authored-by: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
1 file changed
Lines changed: 162 additions & 198 deletions
