Support prior distributions

[matthiaskoenig]

Full support for (parameter) prior distributions for

• parameter optimization (Bayes)
• uncertainty propagation (sensitivity)
• sensitivity calculation

Currently, all parameters are handled via lb, ub, i.e. by providing an interval with uniform distributed probability.

[kushvinth]

Hi @matthiaskoenig,

I’d be happy to work on this issue if it’s available.

Proposed approach:

• Introduce a Distribution base class and start with Normal and LogNormal implementations (these should cover the majority of use cases).
• Extend SensitivityParameter with an optional distribution field while keeping the existing lower_bound / upper_bound logic for backward compatibility (defaulting to uniform when no distribution is provided).
• Update the sampling layer to support distribution-aware sampling instead of assuming uniform LHS.
• Once sampling is stable, expose these distributions as priors for parameter fitting / Bayesian optimization.

I plan to implement this incrementally:

1. Core distribution abstractions + Normal/LogNormal
2. Integration with SensitivityParameter and sampling
3. Optional extension to additional distributions (e.g., TruncatedNormal, Beta, Gamma) if needed

Let me know if this direction aligns with your expectations, or if there are design constraints or prior discussions I should be aware of before starting.