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Bayesian Adaptive Sparse Copula
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DOI：10.1080/10618600.2026.2648594.png)
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Abstract
En 中文
Bayesian nonparametric density estimation procedures are typically based on single-scale priors, such as Dirichlet process mixtures. Alternative multiscale density priors built on decision trees have many well-known advantages, including the ability to characterize abrupt local changes and to provide an estimate with a desired level of resolution. Despite their theoretical appeal, multiscale methods have typically been developed in the literature as univariate. Their multivariate versions are generally costly to implement in applications due to rapidly increasing number of mixture components. We propose a random Bernstein polynomial prior on the unit hypercube of arbitrary dimension with a spike-and-slab shrinkage structure. The prior induces posterior sparsity of the multiscale decision tree, alleviating the curse of dimensionality. We embed the proposed model in the form of a copula link function along with nonparametric marginals in a composite prior over general spaces of densities. We provide conditions for posterior consistency under the weak topology and assess the finite-sample properties in a simulation study. We further illustrate the practical use of the model in an application to forecasting the Value at Risk and Expected Shortfall of a financial portfolio in a scenario where sampling from the non-sparse posterior would be infeasible.
Keywords:
Bernstein polynomial
Multiscale estimation
Nonparametric copula
Journal
J
IF:
1.8
Papers:
116
Citations:
6.4K
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Cited Papers