feat: add dynamic regression (time-varying coefficients)

[YuminosukeSato]

Summary

Add Dynamic Regression (time-varying coefficients β_t), equivalent to R CausalImpact's AddDynamicRegression.

β_t = β_{t-1} + η_t, η_t ~ N(0, diag(σ²_β))

Regression coefficients follow a random walk over time. This provides better counterfactual predictions than static regression when the pre-intervention relationship undergoes structural changes.

Changes

Rust (src/)

• kalman.rs: Multivariate FFBS (Durbin-Koopman simulation smoother). Cholesky-solve based backward pass for numerical stability (avoids explicit matrix inversion)
• sampler.rs: Extended Block Gibbs loop via run_single_chain_dynamic() — samples β_t, σ²_β and propagates random walk predictions in post-period
• lib.rs: Added dynamic_regression=false PyO3 argument

Python (python/)

• options.py: Added ModelOptions.dynamic_regression: bool = False field
• main.py: Added default to DEFAULT_MODEL_ARGS, passthrough in _run_sampler

Tests

• test_dynamic_regression.py: 16 tests (option validation 2, basic behavior 3, boundary 5, statistical quality 3, integration 3)
• Rust tests: 6 new tests (kalman 3 + sampler 3)
• All 193 existing tests pass with no regressions

Design Decisions

• Spike-and-slab is automatically disabled when dynamic_regression=True (variable selection is incompatible with time-varying coefficients)
• β_t / σ²_β are internal variables, not exposed in V1 (YAGNI)
• σ²_β prior: InvGamma(16, 16 × (y_sd/√T_pre)²), matching R AddDynamicRegression defaults
• init_beta_var = 100 (sufficiently vague prior for standardized data)
• Static/dynamic paths are fully separated via run_single_chain_static / run_single_chain_dynamic — zero risk of regression

Usage

ci = CausalImpact(
    df, pre_period, post_period,
    model_args={"dynamic_regression": True}
)

Test plan

• cargo fmt --check && cargo clippy -- -D warnings passes
• cargo test — 26 tests pass
• ruff check && ruff format --check passes
• .venv/bin/pytest tests/ -v — 193 tests pass
• End-to-end verification with structural break data