Regularized Gaussian extension: RegularizedUniform and Constraints/Nonnegative Gaussian/GMRF alternatives

[jeverink]

Closes #436

Sub PR from #424

• Added RegularizedUniform implicit prior
• Added ConstrainedGaussian/GMRF and NonnegativeGaussian/GMRF as simplified alternatives

Explanation of RegularizedUniform: Consider a regularized Gaussian posterior of the form: $\min{x} \text{likelihood}(x, \hat{b}) + \frac12 ||x - \hat{\mu}||{\Sigma^{-1}}^2 + f(x) $. In various cases, we might not want the randomized linear least squares term from the RegularizedGaussian prior, but only the penalty $f(x)$. To make the randomized prior term disappear, we let $\Sigma^{-1} = 0$, or more precisely, $\Sigma^{-\frac{1}{2}} = 0$, such that the posterior takes the form:

$\min_{x} \text{likelihood}(x, \hat{b}) + f(x) $.

This, the RegularizedUniform can be interpreted as a RegularizedGaussian with infinitely flat underlying Gaussian, i.e., a uniform "distribution" on the unbounded parameter space.

By letting the RegularizedUniform inherit from RegularizedGaussian, set the sqrtprec to zero, RegularizedLinearRTO will accept this implicit prior without modification.

To-do:

• [x] Add tests

[jeverink]

Hi @nabriis , I've added an explanation as to why I have designed the RegularizedUniform class as such above, hope it helps.

[jakobsj]

PS, should this PR remain a draft or be changed?

[jeverink]

Thanks for the comment @jakobsj , I have now updated all the documentation and added some tests.

[jeverink]

I have now renamed RegularizedUniform to RegularizedUnboundedUniform

[jakobsj]

Thanks @jeverink. I've rerequested review from Nicolai.