pseudo-code or proof of concept implementation of updated time handling

[dylanhmorris]

Needs

• All three signals can fit to arbitrary timeseries (with missing observed days, etc).
• Consistent, safe conversion between model time ("days since $t_0$") and human time (dates)
• Posterior prediction of full timeseries (including any days with missing values from the fitting timeseries and any requested forecast days).

To-do once implemeneted

• Simplify application of day-of-week effects, right truncation adjustments, etc accordingly.

What exists

Right now, H and E expect complete timeseries (i.e. no missing observations) and are keyed by a first observation date:

pyrenew-hew/pyrenew_hew/pyrenew_hew_model.py

Lines 513 to 516 in 85b13d8

	observed_hospital_admissions = hospital_admissions_obs_rv(
	mu=predicted_weekly_admissions[offset_first_obs_weeks:],
	obs=data_observed,
	)

W, in contrast, has nullable data, and takes an explicit vector of observed times:

pyrenew-hew/pyrenew_hew/pyrenew_hew_model.py

Lines 703 to 706 in 85b13d8

	expected_obs_log_v_site = (
	expected_obs_viral_genomes[ww_observed_times, ww_observed_subpops]
	+ mode_ww_site[ww_observed_lab_sites]
	)

What we want

The same system for H and E as W

• user passes in two vectors of equal length: one representing the observed dates (dates_obs_hospital_admissions, dates_obs_ed_visits, etc) and one representing the observed values (values_obs_hospital_admissions, values_obs_ed_visits etc).
• Model generates predictions for all dates from the earliest observation date across signals to the last observation date across signals, but only performs the observation process for the user-specified observed dates for each signal.

Details

• Model determines what date corresponds to model $t_0$. By convention, this is the date of the first observation across all available signals. Note that some vectors in the model will not begin at $t_0$ including the vector of infections. This should be a @property (named model_t0_date) of PyrenewHEWData

• Model determines the model time indices (rel to $t_0$, zero indexed) of the observed dates for all three signals. This should be a class method of PyrenewHEWData (named, e.g. date_to_model_time()) that uses the value of model_t0_date to perform the computation. Name these vectors model_t_obs_hospital_admissions, model_t_obs_ed_visits etc.

• Model computes the latent_infections vector. Model computes the time index of the first entry of the latent_infections vector (in model time, i.e. relative to $t_0$. It will be negative.

• Model computes the predicted signal value vectors (i.e. latent_hospital_admissions, latent_ed_visits, etc.) via the compute_delay_ascertained_incidence() or wastewater equivalent. Model uses offsets of the start of these predicted signal vectors relative to the latent_infections vector to compute the (integer) time indices in model time of those vectors' first entries (model_t_first_latent_ed_visit, etc).

• Model indexes latent_{signal} vectors by model_t_obs_{signal} vectors with the appropriate offset given by model_t_first_latent_{signal} integer, and performs the observation, e.g.

        which_obs_ed_visits = model_t_obs_ed_visits - model_t_first_latent_ed_visit  
       # minus because the first entry of the latent_ed_visits vector corresponds to model_t >= 0
        observed_ed_visits_admissions = ed_visits_obs_rv(
            mu=latent_ed_visits[which_obs_ed_visits],
            obs=data_observed_ed_visits,
        )

• For posterior prediction (including forecasting), indexing by which_obs_{signal} should return all the values of latent_{signal} (i.e. which_obs_{signal} should be the vector range(latent_{signal}.size) and data_observed_{signal} should be None. The to_forecast_data() method of PyrenewHEWData should be configured accordingly.

[dylanhmorris]

@sbidari