Bayesian Inference for Joint Tail Risk in Paired Biomarkers via Archimedean Copulas with Restricted Jeffreys Priors
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| Autores principales: | , , , |
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| Formato: | Preprint |
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2026
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| _version_ | 1866915841614807040 |
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| author | Aich, Agnideep Murshed, Md. Monzur Hewage, Sameera Aich, Ashit Baran |
| author_facet | Aich, Agnideep Murshed, Md. Monzur Hewage, Sameera Aich, Ashit Baran |
| contents | We propose a Bayesian copula-based framework to quantify clinically interpretable joint tail risks from paired continuous biomarkers. After converting each biomarker margin to rank-based pseudo-observations, we model dependence using one-parameter Archimedean copulas and focus on three probability-scale summaries at tail level $α$: the lower-tail joint risk $R_L(θ)=C_θ(α,α)$, the upper-tail joint risk $R_U(θ)=2α-1+C_θ(1-α,1-α)$, and the conditional lower-tail risk $R_C(θ)=R_L(θ)/α$. Uncertainty is quantified via a restricted Jeffreys prior on the copula parameter and grid-based posterior approximation, which induces an exact posterior for each tail-risk functional. In simulations from Clayton and Gumbel copulas across multiple dependence strengths, posterior credible intervals achieve near-nominal coverage for $R_L$, $R_U$, and $R_C$. We then analyze NHANES 2017--2018 fasting glucose (GLU) and HbA1c (GHB) ($n=2887$) at $α=0.05$, obtaining tight posterior credible intervals for both the dependence parameter and induced tail risks. The results reveal markedly elevated extremal co-movement relative to independence; under the Gumbel model, the posterior mean joint upper-tail risk is $R_U(α)=0.0286$, approximately $11.46\times$ the independence benchmark $α^2=0.0025$. Overall, the proposed approach provides a principled, dependence-aware method for reporting joint and conditional extremal-risk summaries with Bayesian uncertainty quantification in biomedical applications. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_15319 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bayesian Inference for Joint Tail Risk in Paired Biomarkers via Archimedean Copulas with Restricted Jeffreys Priors Aich, Agnideep Murshed, Md. Monzur Hewage, Sameera Aich, Ashit Baran Methodology Applications We propose a Bayesian copula-based framework to quantify clinically interpretable joint tail risks from paired continuous biomarkers. After converting each biomarker margin to rank-based pseudo-observations, we model dependence using one-parameter Archimedean copulas and focus on three probability-scale summaries at tail level $α$: the lower-tail joint risk $R_L(θ)=C_θ(α,α)$, the upper-tail joint risk $R_U(θ)=2α-1+C_θ(1-α,1-α)$, and the conditional lower-tail risk $R_C(θ)=R_L(θ)/α$. Uncertainty is quantified via a restricted Jeffreys prior on the copula parameter and grid-based posterior approximation, which induces an exact posterior for each tail-risk functional. In simulations from Clayton and Gumbel copulas across multiple dependence strengths, posterior credible intervals achieve near-nominal coverage for $R_L$, $R_U$, and $R_C$. We then analyze NHANES 2017--2018 fasting glucose (GLU) and HbA1c (GHB) ($n=2887$) at $α=0.05$, obtaining tight posterior credible intervals for both the dependence parameter and induced tail risks. The results reveal markedly elevated extremal co-movement relative to independence; under the Gumbel model, the posterior mean joint upper-tail risk is $R_U(α)=0.0286$, approximately $11.46\times$ the independence benchmark $α^2=0.0025$. Overall, the proposed approach provides a principled, dependence-aware method for reporting joint and conditional extremal-risk summaries with Bayesian uncertainty quantification in biomedical applications. |
| title | Bayesian Inference for Joint Tail Risk in Paired Biomarkers via Archimedean Copulas with Restricted Jeffreys Priors |
| topic | Methodology Applications |
| url | https://arxiv.org/abs/2602.15319 |