B7/B9: predictive uncertainty for an independent future participant¶

Experimental research API, not a stable release or calibrated prediction method. This research continuation extends the learned B7 Gaussian planar factor rather than the fixed-population B7 conditional-score benchmark.

Use eyetrajectoriespy.bayesian.predict_bayesian_planar_new_participant() with the returned BayesianPlanarFactorFit, exact evaluation-grid indices and two declared coordinate-specific noise scales:

from eyetrajectoriespy.bayesian import (
    fit_bayesian_planar_factor,
    predict_bayesian_planar_new_participant,
)

posterior = fit_bayesian_planar_factor(
    gaze,  # unique participant_id; x/y NaN means intentionally unobserved
    evaluation_grid=grid,
    observation_noise_sd=(0.04, 0.06),
    n_components=2,
    n_basis=5,
    n_chains=2,
    n_draws=60,
    warmup=90,
)
future = predict_bayesian_planar_new_participant(
    posterior,
    evaluation_indices_x=[3, 8, 12, 18],
    evaluation_indices_y=[5, 9, 14, 20],
    observation_noise_sd=(0.04, 0.06),
    random_state=100,
)
pointwise = future.summary_frame()

The call does not use the fitted training participant scores. For each stored Gibbs iteration it draws a new shared participant factor z_new ~ N(0,I_K) and combines it with the same iteration's learned population mean and both channel loading functions. It then adds independent Gaussian observation noise using supplied coordinate scales. Using a common z_new propagates temporal and x/y dependence rather than drawing each coordinate independently.

Predictions intentionally require exact integer positions in the fitted evaluation grid. Coordinates can have different observed index subsets. Nothing silently interpolates x/y onto a common observed clock, and there is no hidden time-unit conversion. This grid restriction is an explicit implementation boundary, not a universal limitation of Gaussian functional models.

The returned latent_draws and observed_draws arrays have shape (chain, population_posterior_draw, requested_channel_time_rows). row_frame records the source coordinate, time and index for each row. summary_frame() gives pointwise 5th/95th predictive quantiles; it does not construct simultaneous 90% prediction regions or certify 90% frequentist coverage.

Known-truth predictive check¶

The B7 refit pilot now additionally draws one completely new participant per simulation from the same prior/likelihood generating population, including a new latent factor and coordinate-specific observation noise. That participant is never part of the population posterior fit. For each participant it tests eight withheld coordinate-time outcomes (four x, four y), reports the mean within-participant pointwise inclusion fraction, and records whether all eight marginal bands happened to contain their outcomes.

The eight outcomes are strongly dependent. They must not be used as eight independent binomial simulation replications. An all-eight event is not itself a jointly calibrated functional 90% prediction band. Such a region and calibration remains new methodological work.

Engineering CI evaluates two prior-generated datasets per paired/async and rank-1/rank-2 combination. It is a smoke test, not a sample adequate to claim nominal predictive coverage.

Unresolved¶

Population noise, prior and rank learning; rich observation-process and missingness mechanisms; full posterior-convergence qualification; near-tied eigenspace sensitivity; conditional prediction after observing part of a new participant's trajectory; simultaneous x/y functional predictive bands; independent external benchmarks; and honest real-participant holdout studies. Existing scientific and release gates remain false. Development remains stacked and unpublished.