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Title: Bayesian adaptive sparse copula Authors:  Martin Burda - University of Toronto (Canada) [presenting]
Artem Prokhorov - University of Sydney (Australia)
Abstract: A new method is proposed for Bayesian multivariate nonparametric density estimation that is both adaptive and sparse. Our approach extends recent work on univariate multiscale nonparametric densities by requiring sparsity via an alternative functional approximation implemented with a spike-and-slab prior structure. Implementation of the resulting sparse multiscale density model has a flavor of multiscale importance sampling whereby major functional approximation components are preserved while minor components known to fall below a given threshold are not evaluated. As a result, the nonparametric density approximation requires only a fraction of the implementation time and memory size relative to its non-sparse counterpart at the expense of a negligible loss of precision controlled by the user. This makes our approach suitable for multivariate scenarios and usage in wider structural models; indeed so far the multiscale density methods proposed in the literature have been univariate. We further embed the sparse multiscale estimator within a multivariate nonparametric copula density model with countably infinite mixtures of location-scale marginals.