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====== Calibration Demystified ======

Calibration is the process of calculating simulator input values for a historical time period which reproduce the observed simulator outputs over that period. To accomplish this, a distinct calibrator framework is created alongside the simulator framework, within a model family (see [[concepts:How it's Organized]]). There are two main motivations for calibration. The first is look back at history of a system through the same conceptual framework that is to be used to explore the future of the system - a prerequisite for trend analysis. The second is to get starting values - or initial conditions - of model stocks.

[Perhaps give a trivial example where the simulator model is //y = x + z//. If the historical observed value for y is 6, then a calibration solution for (x,y) could be (3,3), (2,4) or (1,5)...and so on. **Use population model as example instead.**  For real-world models this is a non-trivial problem and requires a separate calibrator framework because:

  * Simulators are dynamic and data-rich; they contain many inter-related, multidimensional time-series variables which constrain the calibration solution
  * Simulator variables in historical time may not be directly measured and therefore may have to be estimated, and/or there may be missing periods of observed data which require interpolation; or data quality issues; or when brought together the historical datasets may be inconsistent
  * [more?]

] FIXME

[Explain the diagram below wrt the frameworks, relative to time, inputs and outputs.  Break observed historical data btwn observed parameters and observed outputs.] FIXME

{{:concepts:calibration.png|}}

[Compare/contrast what we mean by calibration to other modelling paradigms: specification, estimate, calibration, etc. E.g. Choice model calibration.]
Note that the term calibration used in the whatIf? Platform / Design Approach context differs from specification and estimation of a statistical model. In particular, the use of data is different as in statistical modelling the data are used to estimate the parameters in the model using an appropriate statistical technique, while in the design approach, **data which have not been measured, such as lifetimes of capital stocks, are estimated and then the data set is used to calibrate the model** [clarify this with Bert] FIXME. The calibration is successful if the model reproduces the data, given a set of historical input variables, and this is considered a necessary but not sufficient condition for a valid model. [1]

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