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• W3187182912 abstract "A multivariate distribution can be described by a triangular transport map from the target distribution to a simple reference distribution. We propose Bayesian nonparametric inference on the transport map by modeling its components using Gaussian processes. This enables regularization and uncertainty quantification of the map estimation, while resulting in a closed-form and invertible posterior map. We then focus on inferring the distribution of a nonstationary spatial field from a small number of replicates. We develop specific transport-map priors that are highly flexible and are motivated by the behavior of a large class of stochastic processes. Our approach is scalable to high-dimensional distributions due to data-dependent sparsity and parallel computations. We also discuss extensions, including Dirichlet process mixtures for flexible marginals. We present numerical results to demonstrate the accuracy, scalability, and usefulness of our methods, including statistical emulation of non-Gaussian climate-model output. Supplementary materials for this article are available online." @default.
• W3187182912 created "2021-08-16" @default.
• W3187182912 creator A5038477614 @default.
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• W3187182912 date "2023-05-02" @default.
• W3187182912 modified "2023-10-09" @default.
• W3187182912 title "Scalable Bayesian Transport Maps for High-Dimensional Non-Gaussian Spatial Fields" @default.
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• W3187182912 doi "https://doi.org/10.1080/01621459.2023.2197158" @default.
• W3187182912 hasPublicationYear "2023" @default.
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