pymc_forecast.gaussian#

Correlated-over-time observation noise: the Gaussian prefix conditional.

For elementwise noise the forecast distribution is the horizon marginal (what predict() does implicitly). When the observation noise is a MultivariateNormal over the time axis — GP-style correlated residuals — the forecast must instead be the Gaussian conditional given the observed prefix. This module ports numpyro_forecast’s _mvn_prefix_condition (Cholesky of the prefix block, triangular solves for the conditional mean and covariance, jitter + symmetrization) to PyTensor and wires it into a predict-style primitive.

Univariate series only (the MVN event dimension is time), matching upstream.

pymc_forecast.gaussian.conditional_mvn(loc, cov, observed_prefix, *, jitter=1e-06)[source]#

Condition a length-t+f MVN on its first t observed values.

Parameters:

  • loc (numpy.ndarray or pytensor.tensor.TensorVariable) – Full-horizon mean, shape (t + f,); must be a tensor when observed_prefix is a tensor.

  • cov (numpy.ndarray or pytensor.tensor.TensorVariable) – Full-horizon covariance, shape (t + f, t + f); it is symmetrized before use.

  • observed_prefix (numpy.ndarray or pytensor.tensor.TensorVariable) – Observed values, shape (t,).

  • jitter (float, default 1e-6) – Additive diagonal term, added to the symmetrized joint covariance and again to the conditional covariance.

Returns:

  • cond_mean (pytensor.tensor.TensorVariable) – Mean of the forecast conditional, shape (f,).

  • cond_cov (pytensor.tensor.TensorVariable) – Covariance of the forecast conditional, shape (f, f).

pymc_forecast.gaussian.predict_mvn(h, loc, cov, *, jitter=1e-06)[source]#

Register MVN-over-time observation/forecast variables.

The correlated-noise counterpart of predict(): the likelihood is MvNormal over the observed window (the prefix block of cov) and — when forecasting — the "forecast" variable is the exact Gaussian conditional given the observed prefix, not the horizon marginal.

Only "obs" and (when forecasting) "forecast" are registered; unlike predict(), no "mu" / "mu_future" Deterministics are recorded.

Parameters:

  • h (pymc_forecast.model.Horizon) – The horizon of the current model build; its data, if any, must be 1-D.

  • loc (array_like or pytensor.tensor.TensorVariable) – Full-horizon mean with shape (duration,) (time on axis 0).

  • cov (array_like or pytensor.tensor.TensorVariable) – Full-horizon covariance with shape (duration, duration) — e.g. a GP kernel gram matrix over the time positions.

  • jitter (float, default 1e-6) – Additive diagonal term for numerical stability, added to the symmetrized covariance and again to the conditional forecast covariance (see conditional_mvn()).

Raises:

pymc_forecast.exceptions.HorizonError – If the data are multivariate (the MVN event dim must be time), or if forecasting without observed data.