# Interval predictor model

Interval Predictor Models (IPMs) are a class of meta-model which describe the expected spread of the output of a model whilst making very few assumptions about the model. The meta-model finds an upper and lower bound for the predicted output of the model using a function chosen by the user. Therefore, once trained, the meta-model can make predictions very quickly. Interval Predictor Models offer a robust quantification of uncertainty, even when few data points are available. This makes them useful when a very computationally expensive model limits the number of simulations which can be performed.

Creating an IPM of the performance function yields bounds on $g(\boldsymbol{x})$ ($\overline{g}(\boldsymbol{x})$ and $\underline{g}(\boldsymbol{x})$). Hence we obtain bounds on the failure probability $P_f$ by Monte Carlo simulation for $\overline{g}(\boldsymbol{x})$ and $\underline{g}(\boldsymbol{x})$.

### What do I need to train an Interval Predictor Model?

The minimal implementation requires at least one RandomVariable defined in the Input Object, and one Model.

### How do I perform a reliability Analysis with an Interval Predictor model?

In the standard Reliability Analysis workflow the Model should be replaced with a Model containing an Evaluator, in turn containing an @IntervalPredictorModel.

### Where are my results?

The results of the analysis are stored in a FailureProbability object

### How is the Interval Predictor Model object constructed?

See the page of @IntervalPredictorModel object for more details

 Theory A brief explanation of the design of Experiment methods is available on our wikipedia article