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The sigma (residual variance) sampling had an incorrect parameterization: Before: sigma = 1.0 / Gamma((n+p)/2, scale=1) / err = InvGamma(a,1)/err After: sigma = err / Gamma((n+p)/2, scale=1) = err * InvGamma(a,1) The original PRS-CS (Ge et al., getian107/PRScs) samples sigma as 1/Gamma(a, scale=1/err) = InvGamma(a, rate=err), which has mean err/(a-1). The buggy version gave mean 1/(err*(a-1)), differing by err^2. This caused incorrect posterior variance estimation. Also add a signal recovery test for prs_cs with realistic binomial genotype data and verify sigma is in a reasonable range. Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
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Summary
src/prscs_mcmc.hline 262)err²vs the original PRS-CS (Ge et al., getian107/PRScs)Bug details
The original PRS-CS samples:
sigma = 1/Gamma((n+p)/2, scale=1/err)=InvGamma(a, rate=err)with meanerr/(a-1).The buggy code had:
sigma = 1.0 / Gamma((n+p)/2, scale=1) / errwhich givesInvGamma(a, rate=1) / errwith mean1/(err*(a-1)). These differ byerr².Fix:
sigma = err / Gamma((n+p)/2, scale=1)which giveserr * InvGamma(a, rate=1)=InvGamma(a, rate=err). ✅Validation
Cross-method benchmark on simulated data (n=1000, p=50, 4 causal SNPs):
PRS-CS stability across 5 seeds: mean cor = 0.92, sd = 0.015. Sigma estimates ~0.95 (reasonable for the simulation).
Test plan
devtools::test(filter="regularized_regression")🤖 Generated with Claude Code