rxmc.predictive.total_predictive_band#

rxmc.predictive.total_predictive_band(mean_fn, kernel, x_train, y_train, x_pred, draws, n_model_params, *, theta_cols=None, noise_std=0.0, train_noise_var=None, levels=(16, 84), n_draws=400, rng=None)[source]#

Data-space predictive band that propagates total uncertainty.

For each posterior draw q it splits out the model parameters and the kernel log-theta, forms the residual y_train - mean_fn(x_train, *model_params), conditions the GP discrepancy at x_pred, and samples

\[y_*^{(s)} = \mathrm{mean\_fn}(x_*) + \bar f_*^{(s)} + \mathcal N\!\big(0,\ \mathrm{var}_*^{(s)} + \sigma^2\big),\]

returning the requested percentile band over the samples. Only the GP’s posterior variance is propagated per point (the off-diagonal posterior covariance is not used for the marginal band).

Parameters:

  • mean_fn (callable) – mean_fn(x, *model_params) -> y on a raw x array (e.g. a model’s .y plotting helper).

  • kernel (sklearn-style kernel) – The discrepancy kernel (as passed to kernel_term()).

  • x_train, y_train, x_pred (array-like) – Training inputs/outputs and the prediction grid.

  • draws (array-like, shape (n_samples, n_draw_cols)) – Posterior chain rows.

  • n_model_params (int) – Number of leading model parameters in each draw (consumed by mean_fn).

  • theta_cols (array-like of int, optional) – Column indices selecting the kernel log-theta within each draw row, in kernel.theta order. When None (default) the kernel theta is taken as the trailing columns q[n_model_params:] and the row width is validated against len(kernel.theta). Pass explicit columns when the draw also carries other covariance/likelihood nuisances.

  • noise_std (float, optional) – Observation noise std-dev, used both to condition the GP and as the prediction-point noise (overridden for conditioning by train_noise_var if given).

  • train_noise_var (float or array-like, optional) – Training-noise covariance for conditioning (defaults to noise_std**2).

  • levels (sequence of float, optional) – Percentile levels for the returned band.

  • n_draws (int, optional) – Number of posterior rows to subsample (if the chain is longer).

  • rng (np.random.Generator, optional)

Returns:

np.ndarray, shape (len(levels), len(x_pred))

Raises:

ValueError – If the kernel-theta selection does not have len(kernel.theta) columns.