Overview

Adds support for count observations aggregated to a weekly grid while the renewal equation continues to be evaluated daily. Two design pieces:

1. Weekly observation likelihood path. Daily predicted counts are summed to the weekly observation grid before the likelihood is scored. Aggregation lives inside the numpyro-traced graph so the noise model and the likelihood operate on the same scale.
2. Independent parameter cadence. The temporal process for $\mathcal{R}(t)$ may be parameterized daily or weekly (or any stepwise cadence) and is broadcast to the daily axis. The renewal equation and all observation transforms run daily either way.

End-to-end flow for a weekly signal

• $\mathcal{R}(t)$ sampled by a temporal process at the chosen cadence and broadcast to the daily model axis if needed.
• Daily renewal equation consumes daily $\mathcal{R}(t)$ and produces the daily infection trajectory.
• Daily predicted counts computed via ascertainment + delay convolution.
• Daily predicted counts summed to the weekly observation grid via pyrenew.time.daily_to_weekly.
• Likelihood scored at weekly scale against weekly observations.

Relationship to pyrenew-hew

The production pyrenew-hew model parameterizes $\mathcal{R}(t)$ weekly and aggregates daily predicted hospital admissions to a weekly grid. This PR brings the same capability into PyRenew while making parameter cadence a user choice rather than a fixed coupling:

• Match pyrenew-hew today: wrap the inner temporal process in StepwiseTemporalProcess(step_size=7, alignment="calendar_week", week_start_dow=...).
• Daily parameterization for the same signals: drop the wrapper and use the inner process directly.
• Mixed cadences: weekly hospital admissions and daily ED visits in one model regardless of the Rt parameter cadence.

Observation cadence and parameter cadence are independent design choices; the builder no longer enforces a pairing rule between them.

Reviewer guide

Review bottom-up through the dependency chain. Each unit's changes are self-contained.

1. Synthetic data refresh (120 → 126 days)

• Files: datagen_he_CA_126.py, synthetic_CA_126/*.csv, synthetic_data.py, test_datagen_he_CA_126.py, test_datasets_synthetic.py.
• Six extra days yields 18 full weeks. No API change.
• Verify true_parameters.json matches the generating process.

2. Observation base validators — pyrenew/observation/base.py

• New: _validate_aggregation_params, _compute_period_offset, _validate_period_end_times.
• Generalized _validate_shapes_match replaces _validate_obs_times_shape.
• _validate_dow_effect now uses the shared require_shape helper.
• Focus: offset arithmetic (period_end_dow + 1 - first_day_dow) % 7 and period-boundary alignment.

3. Latent: temporal processes — pyrenew/latent/temporal_processes.py

• New class StepwiseTemporalProcess; step_size attr added to the TemporalProcess Protocol and to AR1 / DifferencedAR1 / RandomWalk.
• Alignment options: "model_index" (default) starts blocks at model index 0; "calendar_week" aligns weekly blocks to a declared week_start_dow.
• Calendar-week broadcast delegates to pyrenew.time.weekly_to_daily; coarse trajectory recorded as {name_prefix}_coarse.
• first_day_dow threaded through the Protocol so calendar-aligned wrappers can use the model-axis day-of-week; standard processes ignore it.

4. Latent: shape contracts — pyrenew/latent/{population,subpopulation}_infections.py

• Both sample() methods accept first_day_dow and forward it to their temporal processes.
• Output shape of every temporal process is validated via the shared pyrenew.arrayutils.require_shape helper.

5. Count observation path — pyrenew/observation/count_observations.py

• New ctor params aggregation_period, reporting_schedule, period_end_dow.
• New _aggregate wraps pyrenew.time.daily_to_weekly.
• Branching in validate_data / sample for regular vs. irregular schedules.
• Confirm all in-tree SubpopulationCounts call sites updated; times → period_end_times rename consistent.

6. Measurement observations — pyrenew/observation/measurement_observations.py

• One-line refactor to use the renamed shape validator.

7. Builder + model coherence — pyrenew/model/{pyrenew_builder,multisignal_model}.py

• MultiSignalModel.sample() accepts first_day_dow and forwards it to the latent process.
• _validate_coherence enforces calendar-anchor and structural coherence:
  • All observations sharing an aggregation_period > 1 must agree on period_end_dow.
  • Every temporal-process step_size must be a positive integer.
  • Calendar-week-aligned temporal processes must have week_start_dow consistent with weekly period_end_dow: period_end_dow == (week_start_dow + 6) % 7.
• first_day_dow required at validate_data when any obs has aggregation_period > 1.
• The previous "step_size ≤ finest aggregation_period" rule was deliberately removed — see the in-body comment.

8. Integration test — test/integration/test_population_infections_he_weekly.py

• End-to-end MCMC: weekly admissions + daily ED visits, calendar-week-aligned weekly Rt.
• Prior-predictive shape check and posterior recovery for I0 + baseline R(t).
• Uses numpyro.enable_x64() + set_host_device_count(4).

9. Test fixtures + config — test/conftest.py, pyproject.toml, _typos.toml

• 196-line conftest promotes repeated setup to fixtures, including reusable temporal-process stubs (WrongShapeTemporalProcess, ConstantTemporalProcess, InvalidStepSizeTemporalProcess).
• Pytest integration marker added so -m "not integration" skips MCMC tests.

10. Tutorial — docs/tutorials/building_multisignal_models.qmd

• New section explaining the three independent choices: parameter cadence, model time axis, observation cadence.
• Worked example pairing weekly Rt (alignment="calendar_week", week_start_dow=6) with weekly observations (period_end_dow=5).

Where to focus review attention

• Offset math in _compute_period_offset and the period-boundary check in _validate_period_end_times — these govern correctness of weekly alignment.
• StepwiseTemporalProcess calendar-week broadcasting — weekly_to_daily is reused; sanity check with n_timepoints=17, first_day_dow=3, week_start_dow=6 produces 3 coarse samples broadcast to [c0×3, c1×7, c2×7].
• The three coherence rules in _validate_coherence — each has pass + distinct-failure tests in test_pyrenew_builder.py.
• CountObservation._aggregate runs inside the numpyro-traced graph — likelihood scoring is at weekly scale, not post-hoc.

Incidental fixes (not directly tied to #789)

Found while implementing aggregation; small enough that separating them would create churn.

• _validate_index_array empty-array guard (observation/base.py) — jnp.any(indices < 0) on empty arrays returned False; now returns early on size == 0.
• _validate_index_array / _validate_obs_dense ndim check — previously accepted non-1D arrays and relied on silent broadcasting; now rejects with a clear error.
• AR(p) stationary-SD bound in test_ar_process_asymptotics — the bound |long_ts[-1]| < 3 * noise_sd was too tight (stationary SD strictly > innovation SD when autoregressive coefficients are non-zero) and latently flaky; replaced with closed-form stationary SD per order.
• _validate_obs_times_shape → _validate_shapes_match rename — prerequisite refactor; same shape-match logic needed for (obs, period_end_times) pairs.
• _typos.toml: allow dows. pyproject.toml: register integration pytest marker.