Allow multivariate parameters to be passed via pybamm.ParameterValues and define multivariate distributions in model space

[SarahRo]

Description

The changes in the PR allow multivariate parameters to be passed via pybamm.ParameterValues. Moreover, multivariate distributions are now defined in the model space instead of the search space.

Introduces a MarginalDistribution class (subclass of Distribution) that is constructed from a BaseMultivariateDistribution. This is achieved by adding a method called 'marginal' to the multivariate distributions that returns the marginal distribution. The pybop.MarginalDistribution retains the original multivariate distribution in the parent_distribution attribute.

Introduces a MultivariateLogNormal class in order to define the distribution in the model space for the ep-bolfi example.

The MultivariateParameters class is removed. Instead, a check_multivariate method is added to pybop.Parameters() that checks whether a MarginalDistribution is present and if so whether all parameters have a MarginalDistribution with the same parent_distribution. This method is called in the constructor, the set method and the add method. The call to the method can be disabled in the add and set method by setting the parameter check_multivariate to false. This is, for example, used in the constructor in order to only call the method once all parameters have been added.

Fixes #856

Type of change

Please add a line in the relevant section of CHANGELOG.md to document the change (include PR #).

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• Tests added that prove fix is effective or that feature works

[codecov]

Codecov Report

❌ Patch coverage is 99.31034% with 1 line in your changes missing coverage. Please review.
✅ Project coverage is 92.46%. Comparing base (4628a65) to head (3f779cb).
⚠️ Report is 28 commits behind head on develop.

Files with missing lines	Patch %	Lines
pybop/parameters/parameter.py	97.82%	1 Missing ⚠️

Additional details and impacted files

@@             Coverage Diff             @@
##           develop     #862      +/-   ##
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+ Coverage    89.41%   92.46%   +3.04%     
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  Files           63       71       +8     
  Lines         4857     5495     +638     
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+ Hits          4343     5081     +738     
+ Misses         514      414     -100     

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[SarahRo]

Warning

The order of multivariate parameters is currently not verified inside pybop.Parameters(). They are assumed to be passed in order of the position property of the pybop.MarginalDistribution.

[NicolaCourtier]

Suggested change

	self.properties["cov"], np.zeros(self._n_parameters)
	self.properties["cov"], mean

As far as I understand, the Jacobian should be evaluated at the transformed mean for this conversion.