SepiaPredict

The SepiaPredict class is used to obtain predictions from the model based on MCMC samples. Three types of predictions are possible:

  • SepiaEmulatorPrediction: predictions from the emulator portion of the model

  • SepiaXvalEmulatorPrediction: cross-validated predictions from the emulator

  • SepiaFullPrediction: predictions from the full model (including discrepancy and observation noise)

The SepiaPredict classes handle transformation from u/w/v to the original output space.

class sepia.SepiaPrediction(x_pred=None, samples=None, model=None, t_pred=None, addResidVar=False, storeRlz=True, storeMuSigma=False, do_call=True)

Base class inherited for predictions. Contains:

Variables

  • model (sepia.SepiaModel) – SepiaModel instance

  • xpred (numpy.ndarray) – x values for which to predict, shape (npred, p) matrix, on original untransformed scale

  • t_pred (numpy.ndarray/NoneType) – t values for which to predict, shape (npred, q) matrix, optional for full model (if not provided, theta values from posterior samples will be used) but required for emulator.

  • samples (dict) – from SepiaModel.get_samples()

  • addResidVar (bool) – add the posterior residual variability to the samples?

  • storeRlz (bool) – make and store a process realizations for each x_pred / sample combination?

  • storeMuSigma (bool) – store the mean and sigma for the GP posterior for each x_pred / sample combination?

  • do_call (bool) – call wPred/uvPred upon initialization?

  • w (numpy.ndarray/NoneType) – simulation predictions on PCA weight space, shape (#samples, #x_pred, pu)

  • u (numpy.ndarray/NoneType) – observation predictions on PCA weight space, shape (#samples, #x_pred, pu)

  • v (numpy.ndarray/NoneType) – observation predictions on D weight space, shape (#samples, #x_pred, pv)

  • mu (numpy.ndarray/NoneType) – posterior mean, shape (#samples, #x_pred)

  • sigma (numpy.ndarray/NoneType) – posterior sigma, shape (#samples, #x_pred, #x_pred)

class sepia.SepiaXvalEmulatorPrediction(leave_out_inds=None, model=None, *args, **kwrds)

Cross-validated predictions from the emulator.

Instantiate SepiaXvalEmulatorPrediction object.

Parameters

  • leave_out_inds (list/NoneType) – optional, list of lists of indices to leave out in each fold; defaults to leave-one-out

  • x_pred (numpy.ndarray) – x values for which to predict, shape (npred, p) matrix, on original untransformed scale

  • samples (dict) – from SepiaModel.get_samples()

  • model (sepia.SepiaModel) – the SepiaModel object

  • t_pred (numpy.ndarray) – t values for which to predict, shape (npred, q) matrix, required.

  • addResidVar (bool) – add the posterior residual variability to the samples?

  • storeRlz (bool) – make and store a process realizations for each x_pred / sample combination?

  • storeMuSigma (bool) – store the mean and sigma for the GP posterior for each x_pred / sample combination?

  • do_call (bool) – call wPred upon initialization?

Raises

  • TypeError – if inputs are not expected types

  • ValueError – if inputs are not expected shapes

class sepia.SepiaEmulatorPrediction(*args, **kwrds)

Make predictions of the emulator (‘eta’) component of the model. This functions with an emulator-only model or a full model, but predicts the posterior simulation estimates. Predictions are performed on init and stored in the object for access methods.

Instantiate SepiaEmulatorPrediction object.

Parameters

  • x_pred (numpy.ndarray) – x values for which to predict, shape (npred, p) matrix, on original untransformed scale

  • samples (dict) – from SepiaModel.get_samples()

  • model (sepia.SepiaModel) – the SepiaModel object

  • t_pred (numpy.ndarray) – t values for which to predict, shape (npred, q) matrix, required.

  • addResidVar (bool) – add the posterior residual variability to the samples?

  • storeRlz (bool) – make and store a process realizations for each x_pred / sample combination?

  • storeMuSigma (bool) – store the mean and sigma for the GP posterior for each x_pred / sample combination?

  • do_call (bool) – call wPred upon initialization?

Raises

  • TypeError – if inputs are not expected types

  • ValueError – if inputs are not expected shapes

get_mu_sigma()

Returns the stored (if requested on init) mean (vector) and sigma (matrix) of the posterior process for each sample

Returns

tuple: posterior mean (#samples x #x_pred), sigma (#samples x #x_pred x #x_pred x )

get_w()

Returns predictions that were made on init in PCA weight space.

Returns

predictions of w, (#samples x #x_pred x pu) numpy.ndarray

get_y(std=False)

Project w through the K basis to provide predictions of y on native (or standardized) scale. (standardized refers to the mean=0 and sd=1 standardization process in model setup).

Parameters

std (bool) – return standardized (True) or native (default, False) scaling of predictions

Returns

predictions of y, (#samples x #x_pred x py) tensor

class sepia.SepiaFullPrediction(mode='Sep', *args, **kwrds)

Make predictions of the full model: both emulator (‘eta’) and discrepancy (‘delta’) == (u,v) Predictions are performed on init and stored in the object for access by methods.

Instantiate SepiaFullPrediction object.

Parameters

  • x_pred (numpy.ndarray) – x values for which to predict, shape (npred, p) matrix, on original untransformed scale

  • samples (dict) – from SepiaModel.get_samples()

  • model (sepia.SepiaModel) – the SepiaModel object

  • t_pred (numpy.ndarray) – t values for which to predict, shape (npred, q) matrix, optional (can take from theta samples).

  • addResidVar (bool) – add the posterior residual variability to the samples?

  • storeRlz (bool) – make and store a process realizations for each x_pred / sample combination?

  • storeMuSigma (bool) – store the mean and sigma for the GP posterior for each x_pred / sample combination?

Raises

  • TypeError – if inputs are not expected types

  • ValueError – if inputs are not expected shapes

get_discrepancy(as_obs=False, std=False, obs_ref=0)

return Dsim*v to provide predictions of discrepancy on the native scale at sim locations. (native refers to not the sd=1 standardization process in model setup)

Parameters

  • as_obs (bool) – provide discrepancy predictions at obs locations (defaults to sim locations)

  • std (bool) – provide discrepancy predictions on standardized scale (defaults to native scale)

  • obs_ref (int) – if this is a ragged_obs problem, selects the reference observation index to use for transformation parameters; default index 0

Returns

predictions of native discrepancy, (#samples x #x_pred x py_sim(or py_obs)) or (#samples x py_sim(or py_obs)) if ragged and obs_ref is specified

get_mu_sigma()

Returns the stored (if requested on init) mean (vector) and sigma (matrix) of the posterior process for each sample

Returns

tuple: posterior mean (#samples x #x_pred), sigma (#samples x #x_pred x #x_pred x )

get_u_v()

Returns predictions that were made on init

Returns

tuple: predictions of u (#samples x #x_pred x pu) , v (#samples x #x_pred x pv)

get_yobs(as_obs=False, std=False, obs_ref=0)

return y=Ksim*u+Dsim*v to provide predictions of y on the native scale at sim locations. (native refers to not the mean=0 and sd=1 standardization process in model setup)

Parameters

  • as_obs (bool) – provide discrepancy predictions at obs locations (defaults to sim locations)

  • std (bool) – provide discrepancy predictions on standardized scale (defaults to native scale)

  • obs_ref (int) – if this is a ragged_obs problem, selects the reference observation index to use for transformation parameters; default index 0

Returns

predictions of native y (Emulator+Discrepancy), (#samples x #x_pred x py_sim(or py_obs)) or (#samples x py_sim(or py_obs)) if ragged and obs_ref is specified

get_ysim(as_obs=False, std=False, obs_ref=0)

Project u through the K basis to provide predictions of ysim on the native scale. (native refers to not the mean=0 and sd=1 standardization process in model setup)

Parameters

  • as_obs (bool) – provide ysim predictions at obs locations (defaults to sim locations)

  • std (bool) – provide ysim predictions on standardized scale (defaults to native scale)

  • obs_ref (int) – if this is a ragged_obs problem, selects the reference observation index to use for transformation parameters; default index 0

Returns

predictions of native ysim, (#samples x #x_pred x py_sim(or py_obs)) or (#samples x py_sim(or py_obs)) if ragged and obs_ref is specified