Lucas Kock, David T. Frazier, Michael Stanley Smith, David J. Nott
arXiv 12 Mar 2026 · Statistics — Methodology
arXiv:2603.11457 · PDF · DOI · OpenAlex · Extracted main text
Copula models of multivariate data are popular because they allow separate specification of marginal distributions and the copula function. These components can be treated as inter-related modules in a modified Bayesian inference approach called ”cutting feedback” that is robust to their misspecification. Recent work uses a two module approach, where all $d$ marginals form a single module, to robustify inference for the marginals against copula function misspecification, or vice versa. However, marginals can exhibit differing levels of misspecification, making it attractive to assign each its own module with an individual influence parameter controlling its contribution to a joint semi-modular inference (SMI) posterior. This generalizes existing two module SMI methods, which interpolate between cut and conventional posteriors using a single influence parameter. We develop a novel copula SMI method and select the influence parameters using Bayesian optimization. It provides an efficient continuous relaxation of the discrete optimization problem over $2^d$ cut/uncut configurations. We establish theoretical properties of the resulting semi-modular posterior and demonstrate the approach on simulated and real data. The real data application uses a skew-normal copula model of asymmetric dependence between equity volatility and bond yields, where robustifying copula estimation against marginal misspecification is strongly motivated.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Carmona, Chris U and Nicholls, Geoff K (2022) Scalable semi-modular inference with variational meta-posteriors | 1.000 | 12 | 3 | 100% |
| 2 | Carmona, Christian and Nicholls, Geoff (2020) Semi-Modular Inference: enhanced learning in multi-modular models by tempering the influence of components | 1.000 | 10 | 3 | 100% |
| 3 | Smith, Michael Stanley and Yu, Weichang and Nott, David J and Frazie… (2025) Cutting feedback in misspecified copula models self | 1.000 | 8 | 4 | 100% |
| 4 | Frazier, David T and Nott, David J (2025) Posterior risk of modular and semi-modular Bayesian inference self | 1.000 | 6 | 3 | 100% |
| 5 | Yu, Xuejun and Nott, David J and Smith, Michael Stanley (2023) Variational inference for cutting feedback in misspecified models self | 0.737 | 3 | 2 | 100% |
| 6 | Liu, Yang and Goudie, Robert J B (2025) A general framework for cutting feedback within modularized Bayesian inference | 0.737 | 3 | 2 | 100% |
| 7 | Loaiza-Maya, Rubén and Smith, Michael S (2019) Variational Bayes Estimation of Discrete-Margined Copula Models with Application to Time Series self | 0.644 | 2 | 2 | 100% |
| 8 | Plummer, Martyn (2015) Cuts in Bayesian graphical models | 0.644 | 2 | 2 | 100% |
| 9 | Frazier, David T and Nott, David J (2025) Cutting feedback and modularized analyses in generalized Bayesian inference self | 0.644 | 2 | 2 | 100% |
| 10 | Garnett, Roman (2023) Bayesian Optimization | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 42 scored citations.