mcmc-sampling-stan

MCMC convergence diagnostics assess whether your Stan sampling has run long enough. R-hat measures chain mixing (target < 1.01), ESS estimates effective sample size (target > 400), and divergences flag numerical problems. Stan reports these automatically after sampling; address any violations by increasing iterations, adjusting step size, or reparameterizing your model.

Environment setup verifies Stan toolchains, compilers, and dependencies before modeling. Install Stan or RStan with version-pinned packages, check compiler readiness, and validate installation by compiling a test model. This prevents build failures and ensures reproducible sampling across projects.

Stan model specification requires writing data, parameters, and model blocks with explicit priors. Define your data types and dimensions in the data block, declare parameters to estimate in the parameters block, and specify the likelihood and priors in the model block. Proper specification prevents sampling errors and improves diagnostics.

Yes, Stan supports hierarchical and multilevel modeling through nested parameter declarations and group-level priors. You define population-level hyperparameters and group-specific parameters, then use vectorized operations for efficiency. This enables pooling information across groups while capturing variation.

Divergences and high treedepth indicate numerical instability or inefficient sampling geometry. Common causes include poor prior choices, unscaled parameters, or insufficient adaptation. Address these by reparameterizing, standardizing inputs, increasing adapt_delta, or adjusting max_treedepth in your sampling configuration.