Decouple `prediction_window` from training in `IncomingAdmissionPredictor`

[zmek]

Problem

Both prediction_window and prediction_times are currently required at training time (fit()) for all three IncomingAdmissionPredictor subclasses (DirectAdmissionPredictor, ParametricIncomingAdmissionPredictor, EmpiricalIncomingAdmissionPredictor). However, neither fundamentally affects what is learned from the data — they only control which subset of the full 24-hour arrival-rate dictionary is stored.

time_varying_arrival_rates() already computes rates for every time-of-day interval across the full 24-hour cycle. The two parameters then truncate that complete dictionary along two axes:

• prediction_times truncates which starting times get stored
• prediction_window truncates how many intervals are stored per starting time

This coupling has several downsides:

1. A model must be retrained to use a different prediction window or set of prediction times, even though the underlying arrival rates and survival curves are independent of both.
2. Prediction-time validation is forced to reject mismatches — both predict/emergency_demand.py and predict/service.py raise errors when the requested prediction_window differs from yet_to_arrive_model.prediction_window, which would be unnecessary if the window were a predict-time concern.
3. Prediction times must fall back to the nearest trained time — _iter_prediction_inputs() uses find_nearest_previous_prediction_time() to snap to a trained time, losing precision. With the full rate dictionary, any time could be served exactly (snapping to the nearest yta_time_interval boundary instead).
4. Model naming is tied to the window — e.g. yet_to_arrive_{hours}_hours in train/emergency_demand.py — suggesting separate models for separate windows, when one model could serve them all.

Root cause

In _calculate_parameters() (incoming_admission_predictors.py, line 496), the full 24-hour arrival-rate dictionary is computed by time_varying_arrival_rates(), but then only a subset is kept — Ntimes intervals for each time in prediction_times:

Ntimes = int(prediction_window / yta_time_interval)

arrival_rates_dict = time_varying_arrival_rates(
    df, yta_time_interval, num_days, verbose=self.verbose
)

for prediction_time_ in prediction_times:
    arrival_rates = [
        arrival_rates_dict[
            (datetime(1970, 1, 1, prediction_time_hr, prediction_time_min)
             + i * yta_time_interval).time()
        ]
        for i in range(Ntimes)
    ]
    prediction_time_dict[(prediction_time_hr, prediction_time_min)] = {
        "arrival_rates": arrival_rates
    }

Everything downstream — self.weights, self.NTimes, self.prediction_window_hours, self.prediction_times — is then locked to those choices.

Proposed change

Defer both prediction_window and prediction_times to predict() / predict_mean() so that a single trained model can serve any window length (up to 24 hours) and any prediction time, given the same yta_time_interval.

After this change, fit() would only need from the user:

• train_df — the training data
• yta_time_interval — the granularity of arrival-rate buckets
• num_days — the number of days the training data spans
• epsilon — error tolerance for distribution support
• filters — (already on __init__) data categorization filters

Training side — simplify fit()

File / location	What changes
IncomingAdmissionPredictor.fit()	Remove prediction_window and prediction_times from signature.
_calculate_parameters()	Store the full arrival_rates_dict (keyed by time-of-day) instead of pre-slicing to Ntimes entries per prediction time. Remove prediction_window and prediction_times parameters.
Cached metadata	Remove self.prediction_window, self.prediction_window_hours, self.NTimes, self.prediction_times. Keep self.yta_time_interval and self.yta_time_interval_hours.
EmpiricalIncomingAdmissionPredictor.fit()	Drop prediction_window and prediction_times from the super().fit() call. The survival-curve calculation is already independent of both.
train/incoming_admission_predictor.py	Remove prediction_window and prediction_times from train_parametric_admission_predictor() and the yta_model.fit() call.
train/emergency_demand.py	Remove prediction_window and prediction_times from training paths. Model naming no longer needs the window suffix.

Prediction side — accept both in predict() / predict_mean()

File / location	What changes
_iter_prediction_inputs()	Accept prediction_window. Derive Ntimes on the fly and slice arrival rates from the stored full-cycle dict using datetime wrap-around arithmetic (currently in _calculate_parameters). The prediction_time is already passed via prediction_context — it now resolves against the full dict rather than the trained subset.
_get_window_and_interval_hours()	Accept prediction_window as an argument instead of reading self.prediction_window_hours and self.NTimes.
find_nearest_previous_prediction_time()	No longer needed for snapping to trained times. Could be replaced by snapping to the nearest yta_time_interval boundary, which is more precise.
DirectAdmissionPredictor.predict()	Accept prediction_window kwarg; pass through to iterator.
ParametricIncomingAdmissionPredictor.predict()	Accept prediction_window kwarg; use it to compute time_remaining_before_end_of_window and theta.
EmpiricalIncomingAdmissionPredictor.predict()	Accept prediction_window kwarg; pass to _calculate_survival_probabilities().
predict_mean() (base class)	Accept and forward prediction_window.
_get_admission_probabilities() (all subclasses)	Thread prediction_window through.
predict/emergency_demand.py	Pass prediction_window to .predict() / .predict_mean(). Remove the mismatch validation (prediction_window != yet_to_arrive_model.prediction_window).
predict/service.py	Same as above — pass window at predict time, remove mismatch checks for yet_to_arrive_model, non_ed_yta_model, and elective_yta_model.

Weights format change

The structure of self.weights changes from:

# Current: pre-sliced per prediction time
weights[filter_key][(hour, minute)] = {
    "arrival_rates": [rate_0, rate_1, ..., rate_{Ntimes-1}]
}

to:

# Proposed: full 24-hour arrival-rate dictionary
weights[filter_key] = {
    "arrival_rates_dict": {
        time(0, 0): rate,
        time(0, 30): rate,
        ...
        time(23, 30): rate,
    }
}

The per-prediction-time slicing moves into _iter_prediction_inputs() at predict time.

Note: This is a breaking change to the serialized model format. Any pickled models trained under the old format will need to be retrained after this change.

Backward compatibility

Consider a deprecation path:

1. Accept prediction_window and prediction_times in fit() as optional parameters with a deprecation warning.
2. If provided at training, store them as defaults that predict() uses when not passed explicitly — preserving existing call sites until they're migrated.
3. Remove the deprecated path in a future release.

Files affected

• src/patientflow/predictors/incoming_admission_predictors.py — core predictor classes
• src/patientflow/train/incoming_admission_predictor.py — training utility
• src/patientflow/train/emergency_demand.py — training orchestration
• src/patientflow/predict/emergency_demand.py — prediction with validation
• src/patientflow/predict/service.py — service-level prediction with validation
• src/patientflow/viz/pipeline_plots.py — if it accesses model.prediction_window
• Notebooks that call fit() with prediction_window / prediction_times

Benefits

• One model, any window, any time — a single trained model works for any prediction window and any prediction time without retraining.
• Simpler training API — fit() reduces to train_df, yta_time_interval, num_days, and epsilon.
• More precise prediction times — any time-of-day can be served exactly (snapping to the nearest interval boundary) rather than falling back to a trained subset.
• No mismatch errors — the predict-time validation that currently rejects window mismatches becomes unnecessary.
• Smaller stored models — the full arrival-rate dict is the same size regardless of how many prediction windows or times you plan to use.

[zmek]

Implemented in #162