If the PESTMODE variable in the "control data" section of a PEST control file is set to "predict", then PEST runs in "predictive analysis" mode. PEST has been able to run in this mode for a long time. However this mode is not used as much now as it was in the past because it is now generally appreciated that uncertainty analysis generally requires the use of many parameters, and PEST's predictive analysis algorithm is not built for this.

However there definitely are cases where it can be of use. These include not just simulation contexts that are characterised by relatively few parameters, but also contexts where dimensional reduction has reduced parameters to a number that reflects the information content of field data. Data space inversion (DSI) is one such context. So it is possible that as the use of data space inversion grows, there may be a resurgence in the use of PEST's predictive analyser.

"Predictive analysis" mode is supported by PEST and BEOPEST. It is not supported by PEST_HP. If you ask PEST_HP to run in "predictive analysis" mode, it will tell you that it cannot do this.

Use of PEST's predictive analyser assumes that a model has already been calibrated, and that an objective function has been minimised. The fact that the objective function has a discrete minimum implies a well-posed inverse problem. Hence the inverse problem must either be naturally well-posed, or be supplemented by the addition of prior information equations whose weights express prior parameter probabilities.

We designate the minimised objective function as Φ0. Now let us designate the highest objective function at which the model can still be deemed to be acceptably calibrated (at a certain level of confidence) as Φ1. Theory is available to calculate this value; however it is often ok to guess Φ1 based on visual inspection of model-to-measurement misfit.

Now let us focus on a single prediction of management interest. We refer to this prediction using the letter s. When run in "predictive analysis" mode, PEST's job is to maximise or minimise s subject to the constraint that the objective function rises no higher than Φ1. If s is maximised and then minimised, its uncertainty range is thereby explored. Maximisation of s is depicted for a two parameter model below. This is a nonlinear model. If it were linear, then objective function contours would be ellipses and prediction contours would be straight lines.

When run in "predictive analysis" mode, PEST maximises/minimises a prediction subject to an objective function constraint.

Sometimes many model runs are required to solve the constrained maximisation/minimisation problem that PEST is asked to solve when run in "predictive analysis" mode. Nevertheless, this number is likely to be far fewer than that required by other Bayesian alternatives such as Markov chain Monte Carlo. Still, no method is perfect. PEST's performance when run in "predictive analysis" mode can suffer if model outputs are numerically granular and calculation of finite-difference derivatives suffers as a consequence.

General

If PEST is run in "predictive analysis" mode, then not only must the PESTMODE variable be set to "predict". The PEST control file must contain a "predictive analysis" section. This section informs PEST whether it must maximise or minimise a prediction, and the objective function value that must be respected when doing this. (This is the PEST control variable PD0.) Normally, predictive analysis should follow calibration; so the minimum value of the objective function should be known.

Like objective function minimisation, the constrained optimisation process that is solved by PEST's predictive analyser is an iterative one. Each iteration requires re-calculation of a Jacobian matrix. This is followed by a set of model runs in which upgraded parameter sets calculated using different values of the Marquardt lambda are tested. Optionally, a line search procedure can be invoked. This can be somewhat numerically expensive, and cannot be parallelised. However, it is generally worth doing this, despite its cost.

The prediction that must be maximised or minimised must feature in the "observation data" section of the PEST control file. It must be assigned to an observation group named "predict".

The ADDPRED1 utility

ADDPRED1 is to predictive uncertainty analysis what ADDREG1 is to regularisation. It adds prior information equations to the bottom of a PEST control file. These equations assign each parameter a value that is equal to its initial value.  ADDPRED1 also adds a "predictive analysis" section to the PEST control file.

ADDPRED1 is particularly useful if using PEST's predictive analyser in conjunction with the statistical model that is produced by the DSI2 program that is used by PEST for data space inversion. See Part 2 of the PEST manual for more details.