[navy_captain, likelihood_ratio_process] Typo fixes and update non-IID likelihood ratio processes

[HumphreyYang]

This PR fixes typos in navy_captain and adds an section discussing non-IID likelihood ratio processes with models generated by two Markov chains.

[github-actions]

🚀 Deployed on https://6892cb82d3f268dfaa1506dc--nostalgic-wright-5fa355.netlify.app

[Copilot]

Pull Request Overview

This PR addresses typos in the navy_captain lecture and adds a substantial new section to likelihood_ratio_process covering non-IID likelihood ratio processes with Markov chain models.

• Corrects typos and improves clarity in the navy captain lecture
• Updates variable names from Greek letters (α, β) to Latin letters (A, B) for consistency
• Adds a comprehensive section on Markov chain likelihood ratio processes with theoretical analysis and simulations

Reviewed Changes

Copilot reviewed 2 out of 2 changed files in this pull request and generated 2 comments.

File	Description
lectures/navy_captain.md	Fixes typos, updates references to wald_friedman_2, changes variable names from α/β to A/B, and corrects mathematical formulations
lectures/likelihood_ratio_process.md	Adds new section on Markov chain models with KL divergence rate analysis and simulation code

[Copilot]

The condition checks if P_f > 0 where P_g == 0, but this creates a logical issue. When P_g has zero entries where P_f is positive, the KL divergence should be infinite, but the function should handle this consistently with proper mathematical treatment of log(0) cases.

Suggested change

	if np.any((P_f > 0) & (P_g == 0)):
	return np.inf
	valid_mask = (P_f > 0) & (P_g > 0)
	log_ratios = np.zeros_like(P_f)
	log_ratios[valid_mask] = np.log(P_f[valid_mask] / P_g[valid_mask])
	# Use np.errstate to handle log(0) cases gracefully
	with np.errstate(divide='ignore', invalid='ignore'):
	# Where P_f == 0, set log ratio to 0 (since 0 * log(0/q) = 0 by convention)
	log_ratios = np.where(P_f > 0, np.log(P_f / P_g), 0.0)

[mmcky]

@HumphreyYang this doesn't inspire confidence either

Updates variable names from Greek letters (α, β) to Latin letters (A, B) for consistency