Numerical reference checks

The optional checker compares the Python workflow with installed R mashr 0.2.79. Fixed cases cover EE and EZ, supplied and estimated mixture weights, null-biased fitting, and explicit scale expansion. Compared outputs include posterior means, standard deviations, covariances, local false sign rates and local false discovery rates. An uncentered PCA comparison checks the matched helper convention.

The reference export records package versions and library origin. The checker uses absolute and relative tolerances of 2e-10 for fixed-prior cases and 2e-5 for fitted-weight cases. PCA matrices use 1e-12. See tools/export_mashr_reference.R and tools/check_mashr_reference.py in the repository.

Reproduce the comparison

With mashr and jsonlite available in an isolated R library, run from the repository root:

Rscript tools/export_mashr_reference.R reference.json
python tools/check_mashr_reference.py reference.json

R is not a runtime dependency of the Python package. The checker reads a fresh export instead of treating an old success report as current evidence.

Differences and limits

Area	Interpretation
Missing conditions	Python uses exact observed-block Gaussian likelihoods; R's large-SE substitution is an approximation
PCA	Match EE/EZ preprocessing, centering and selected rows before comparing matrices
Scales	Python inputs are SD multipliers; covariance multipliers are their squares
Covariance learning	Independent analytic checks cover noisy-mixture updates; an installed-R extreme-deconvolution comparison is not claimed
Uncertainty	Numerical agreement does not establish repeated-dataset coverage or include all hyperparameter uncertainty

R mashr converts finite-degrees-of-freedom inputs to normal scores. JointShrink instead provides a separate native multivariate Student-t likelihood, checked against independent convolution integrals and distribution formulas. The installed-R comparisons above apply only to Gaussian summaries. See methods and limits.