Random variation in default kernel parameters

[uremes]

Summary:

The default kernel used in GPyRegression is initialised based on batch_size observations. The initialisation varies a lot when batch_size=1.

Description:

The default initialisation in GPyRegression chooses some kernel parameters based on the discrepancies y that are provided as input to the first update call. This means that when the model is used in BOLFI or BOLFIRE, the kernel parameters are chosen based on the first batch_size simulations.

BOLFI or BOLFIRE are not expected to need surrogate model predictions until n_initial_evidence simulations have been carried out, so initialisation could be postponed until then and all the initial evidence could be used in initialisation. This should reduce variation between optimisation runs that use small batch sizes.

Reproducible Steps:

Run BOLFI notebook with seed=310522 vs seed=1 and check the priors in bolfi.target_model (cell 6).