Extend statistical inference backends

[Konrad1991]

• Linear Mixed Models (LMM)
  Support hierarchical and split-plot experimental structures (random intercepts/slopes) and enable simulation from fitted models for power analysis.

• Randomization / permutation tests
  Provide design-based inference aligned with the randomization engine, including restricted permutations for blocked and stratified designs.
  Anderson2001, Anderson2003, and Enrst2004

• Bootstrap inference
  Add nonparametric, residual, and parametric bootstrap methods as robust alternatives to classical parametric tests and for simulation-based sample-size estimation. Using boot::boot and/or car::Boot

• Bayesian models
  Introduce Bayesian linear and hierarchical models with posterior predictive simulation to support adaptive and optimization-driven experimental workflows (maybe using brms)

All methods should integrate with the existing Monte-Carlo simulation framework used for power and sample-size determination.