[AHMETHAKANBEZIR1]

LinearAutoregressiveHMM.sample(..., prev_emissions=...) reads the supplied history in the opposite lag order from compute_inputs. The documented history is chronological (y[-L+1:0]), while the sampling scan expects newest-to-oldest lag blocks. Default zero history and one-lag models hide the discrepancy.

Reverse the initial history once on entry to the sampler, and clarify the shared oldest-to-newest convention in both docstrings. Keep the random keys, transition sampling, and subsequent scan updates unchanged.

For two lags, weights [2, 3] and history [1, 10], the first conditional mean should be 2*10 + 3*1 = 23; the existing sampler uses 2*1 + 3*10 = 32. With the same key, the sampled values differ by approximately 9.

Validation on Windows / Python 3.12.14 / JAX 0.12.0 / tfp-nightly 0.26.0-dev20261020, CPU:

• New regressions on unchanged main: 8 failed / 5 controls passed; with this fix: 13 passed.
• Cover 1/2/3 lags, scalar/vector emissions, eager/JIT execution, and explicit/omitted zero history. Each of five sampled timesteps is compared with its conditional distribution using independently assembled lag inputs and the same random keys.
• Full pytest --cov=./: 250 passed (737 warnings), 81% coverage.
• Configured docstring check: 99.2%, above the required 66%; git diff --check passes.

Prepared autonomously with OpenAI Codex, including code and tests; no independent human review is claimed.