(calibration_classes_functions_observations_data_and_distance)=
# Defining data, distance and likelihood functions

The different distance and likelihood functions already embedded in {{uranie}} can be found in 
[](#calibration_introduction_distance_compare_model) and are further discussed from a theoretical 
point of view in {{metho}}. From the user point of view, on the other hand, every distance or likelihood function 
inherits from the class `TDistanceLikelihoodFunction`, as can be seen in 
{numref}`calibration_Calibration_Class_Hierarchy`, which is purely virtual (meaning that no object 
can be instantiated as `TDistanceLikelihoodFunction`) and serves several main purposes:

- it loads the reference data once and stores them internally as a vector of vectors (or as a vector 
of `TMatrixD`, depending on the chosen formalism used to compute the distance or likelihood);

- once done, the following loop is executed as long as new configurations need to be tested (a 
configuration being defined as a new set of values for vector $\theta$):

    1. it runs the chosen model regardless of the nature of the object (`TRun`, `TCode`, etc.) on the 
   full reference dataset to get the new predictions;

    2. it loads the new model predictions for the configuration under study into a vector of vectors (or 
    as a vector of `TMatrixD` depending on the chosen formalism);

    3. it computes the distance or likelihood using both vectors as statd by the equations in 
    [](#calibration_introduction_distance_compare_model). This computation is done within the 
    `localeval` method (which is the only method that should be redefined if a user wants to create 
    its own distance or likelihood function, see dedicated discussion in 
    [](#calibration_classes_functions_observations_data_and_distance_distance_func)).

From a technical point of view, the `TDistanceLikelihoodFunction` inherits from the `TDoubleEval` class which is 
a part of the **Relauncher** module. This inheritance is not very important as its main appeal is to 
**considerably** simplify the implementation of the minimisation methods with the **Reoptimizer** 
module, allowing the straightforward use of all **TNlopt** algorithms as well as **Vizir** solutions (see 
[](#calibration_minimisation)).

Regardless of the calibration method considered, a distance or likelihood function must be used to compare data and 
model predictions. This is even true for the `TLinearBayesian` class, which directly computes the 
analytical posterior distribution, as the residuals are computed both *a priori* and *a posteriori* 
to assess the improvement of the prediction and their consistency within the 
uncertainty model (see discussion in {{metho}}). In most cases the object will be 
constructed with a recommended way (discussed in 
[](#calibration_classes_functions_observations_data_and_distance_recommended_distance)). 
Another possibility is also discussed in 
[](#calibration_classes_functions_observations_data_and_distance_distance_func)

Whatever the situation, once a calibration 
instance is created (for the sake of generality, we will use an instance named `cal`, of the 
mock class `TCalClass`, as if it inherited from the `TCalibration` class), the first method to 
be called is the `setDistance` or `setLikelihood` depending on the framework used (see the corresponding 
section), as this is the method which defines both the 
type of distance or likelihood function and the observation dataset. 

```{toctree}
data_and_distance/recommended_distance
data_and_distance/distance_func
data_and_distance/option_distance_func
```