---
myst:
    substitutions:
        sentence1: "is fairly simple from an algorithm point of view as it"
        sentence2: "as discussed in {{metho}}"
---
```{include} /../core/calibration/linear_bayesian.md
```

In practice, this technique is applied by following the procedure provided 
in [](#calibration_classes_functions_observations) with one important difference, however: the code or 
function passed through the constructor of the `TLinearBayesian` object is not strictly necessary.
The parameter estimate is analytical so the main point of providing an assessor is 
to get both the *a priori* and *a posteriori* residuals distributions.

The usage of the `TLinearBayesian` class can be summarised in a few key steps:

1. Prepare the data and the model:
   - Select the assessor type to be used and construct the `TLinearBayesian` object with the appropriate likelihood function via `setLikelihood` method (see [](#calibration_linear_bayesian_tlinearbayesian)).
  
2. Set the algorithm properties:
   - Provide the input covariance matrix, *i.e.*, the reference observation covariance (in {{metho}}, 
   this corresponds to $\Sigma$). This step is mandatory, as the covariance matrix is used to compute the posterior distribution, as discussed in {{metho}};
   - Specify the name of the regressors. This is also a key step as a regressor can be an input 
   variable, but also any function of one or several input variables. This is discussed in 
   [](#calibration_linear_bayesian_linear_model);
   - A transformation function may be provided, although this is optional. This is discussed in 
   [](#calibration_linear_bayesian_transform).

3. Perform the estimate and analyse the results:
   - Run the estimate process;
   - Extract the results and visualise them with the standard plotting tools (see [](#calibration_linear_bayesian_results)).


```{toctree}
linear_bayesian/tlinearbayesian
linear_bayesian/linear_model
linear_bayesian/results
linear_bayesian/pred_variance
```

An example is also provided in the use-case section (see [](#use_cases_macro_calibration_linBayes)).