Add adaptive sampling parameters and early stopping for optimization

[xiki-tempula]

Summary

• Add adaptive defaults for sample_size and warmup_steps that scale with problem dimensionality
• Implement early stopping for hyperparameter optimization to improve efficiency
• Add comprehensive tests for the new adaptive parameter functionality

Changes

Adaptive sample_size

• Changed default from fixed 1000 to None (adaptive)
• When None, automatically computed as max(1000, 100 * (m - 1)) where m is the number of states
• Ensures adequate posterior sampling for high-dimensional problems

Adaptive warmup_steps

• Changed default from fixed 500 to None (adaptive)
• When None, automatically computed as max(500, sample_size // 2) following Stan-like heuristics
• Scales appropriately with sample size for better NUTS adaptation

Early Stopping for Optimization

• Renamed optimize_steps to max_optimize_steps (breaking change for keyword argument users)
• Added optimize_patience (default: 500) - steps without improvement before stopping
• Added optimize_min_delta (default: 1e-4) - minimum loss improvement threshold
• Tracks best parameters during optimization and restores them at convergence
• Prints early stopping message when triggered (if verbose=True)

New Parameters

Parameter	Default	Description
sample_size	None	Adaptive: max(1000, 100 * (m - 1))
warmup_steps	None	Adaptive: max(500, sample_size // 2)
max_optimize_steps	10000	Maximum optimization iterations
optimize_patience	500	Early stopping patience
optimize_min_delta	1e-4	Minimum improvement threshold

Breaking Changes

• optimize_steps parameter renamed to max_optimize_steps