Bayesian extend/resume

[rozyczko]

Support for resuming and extending Bayesian MCMC chains using the BUMPS DREAM sampler.
Added ability to save and reload sampler state and continue chains across sessions.

• Resume and extend MCMC chains:

  • Added resume_state parameter to mcmc_sample and sample methods in both fitter.py and minimizer_bumps.py, allowing users to continue sampling from a saved chain state. This includes documentation of the "ring-buffer contract" for extending chains without losing samples.

• Population/chains argument resolution:

  • Introduced _resolve_population_alias method to handle both chains and population arguments, raising an error if both are set with different values, improving API clarity and preventing silent bugs.

[codecov]

Codecov Report

❌ Patch coverage is 93.87755% with 12 lines in your changes missing coverage. Please review.
✅ Project coverage is 83.30%. Comparing base (6efc17e) to head (013e834).

Files with missing lines	Patch %	Lines
src/easyscience/fitting/sampler.py	92.59%	10 Missing ⚠️
.../easyscience/fitting/minimizers/minimizer_bumps.py	96.36%	2 Missing ⚠️

Additional details and impacted files

@@             Coverage Diff             @@
##           develop     #257      +/-   ##
===========================================
+ Coverage    82.92%   83.30%   +0.37%     
===========================================
  Files           62       63       +1     
  Lines         5084     5253     +169     
===========================================
+ Hits          4216     4376     +160     
- Misses         868      877       +9     

Flag	Coverage Δ
integration	45.45% <89.79%> (+1.51%)	⬆️
unittests	81.00% <45.40%> (-1.42%)	⬇️

Flags with carried forward coverage won't be shown. Click here to find out more.

Files with missing lines	Coverage Δ
src/easyscience/fitting/__init__.py	100.00% <100.00%> (ø)
src/easyscience/fitting/fitter.py	96.92% <ø> (-0.38%)	⬇️
src/easyscience/fitting/minimizers/__init__.py	100.00% <100.00%> (ø)
src/easyscience/fitting/multi_fitter.py	98.52% <ø> (-0.03%)	⬇️
.../easyscience/fitting/minimizers/minimizer_bumps.py	96.95% <96.36%> (+1.00%)	⬆️
src/easyscience/fitting/sampler.py	92.59% <92.59%> (ø)

[damskii9992]

Just gonna stop my review here as there is already plenty to work on.
As we discussed in-person, I also think we should refactor the bayesian sampling to a seperate "samplers" module. This should help us when we add other Bayesian samplers in the future as well as provide a cleaner user API (the user doesn't create a "Fitter" when doing sampling).
It also more cleanly separates responsibility in the code. A Minimizer minimizes a function to the data, a Sampler samples the parameters to create distributions.
To avoid duplicating code, it might be smart to move shared functionality to new base-classes.