Michael Stanley Smith, Weichang Yu, David J. Nott, David Frazier
arXiv 5 Oct 2023 · Statistics — Methodology · publishedJournal of the American Statistical Association (2025) · 2 citations (OpenAlex)
arXiv:2310.03521 · PDF · DOI · OpenAlex · Extracted main text
In copula models the marginal distributions and copula function are specified separately. We treat these as two modules in a modular Bayesian inference framework, and propose conducting modified Bayesian inference by "cutting feedback". Cutting feedback limits the influence of potentially misspecified modules in posterior inference. We consider two types of cuts. The first limits the influence of a misspecified copula on inference for the marginals, which is a Bayesian analogue of the popular Inference for Margins (IFM) estimator. The second limits the influence of misspecified marginals on inference for the copula parameters by using a pseudo likelihood of the ranks to define the cut model. We establish that if only one of the modules is misspecified, then the appropriate cut posterior gives accurate uncertainty quantification asymptotically for the parameters in the other module. Computation of the cut posteriors is difficult, and new variational inference methods to do so are proposed. The efficacy of the new methodology is demonstrated using both simulated data and a substantive multivariate time series application from macroeconomic forecasting. In the latter, cutting feedback from misspecified marginals to a 1096 dimension copula improves posterior inference and predictive accuracy greatly, compared to conventional Bayesian inference.
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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 | Smith, M. S. and Vahey, S. P (2016) Asymmetric forecast densities for us macroeconomic variables from a Gaussian copula model of cross-sectional and serial dependence self | 1.000 | 10 | 3 | 100% |
| 2 | Nelsen, R. B (2006) An Introduction to Copulas | 0.928 | 4 | 3 | 100% |
| 3 | Joe, H (2005) Asymptotic efficiency of the two-stage estimation method for copula-based models | 0.874 | 6 | 4 | 67% |
| 4 | Yu, X., Nott, D. J., and Smith, M. S (2023) Variational inference for cutting feedback in misspecified models self | 0.874 | 5 | 2 | 100% |
| 5 | Genest, C., Ghoudi, K., and Rivest, L.-P (1995) A semiparametric estimation procedure of dependence parameters in multivariate families of distributions | 0.843 | 4 | 3 | 75% |
| 6 | Pitt, M., Chan, D., and Kohn, R (2006) Efficient Bayesian inference for Gaussian copula regression models | 0.843 | 3 | 3 | 100% |
| 7 | Carmona, C. and Nicholls, G (2022) Scalable semi-modular inference with variational meta-posteriors | 0.843 | 3 | 3 | 100% |
| 8 | Joe, H. and Xu, J. J (1996) The estimation method of inference functions for margins for multivariate models | 0.843 | 3 | 3 | 100% |
| 9 | Hoff, P. D (2007) Extending the rank likelihood for semiparametric copula estimation | 0.811 | 4 | 2 | 100% |
| 10 | Plummer, M (2015) Cuts in Bayesian graphical models | 0.811 | 4 | 2 | 100% |
Showing the top 10 of 56 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Bayesian Modular Inference for Copula Models with Potentially Misspecified Marginals | 1.000 | 8 | 4 |