Deep hierarchical generalized transformation models for spatio-temporal data with discrepancy errors

Article Statistics & Probability

Challenges in Markov Chain Monte Carlo for Bayesian Neural Networks

Theodore Papamarkou et al.

Summary: This paper reviews the challenges of using MCMC methods in Bayesian neural networks and shows that valuable posterior predictive distributions can be obtained through MCMC sampling.

STATISTICAL SCIENCE (2022)

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Article Mathematics, Interdisciplinary Applications

Joint Bayesian Analysis of Multiple Response-Types Using the Hierarchical Generalized Transformation Model

Jonathan R. Bradley

Summary: This article introduces a method to convert a Bayesian statistical model into a model suitable for handling multiple response-type datasets, and utilizes Bayesian inference to handle the uncertainty of the transformation. The flexibility and practicality of the method are demonstrated through applications to various models and real datasets.

BAYESIAN ANALYSIS (2022)

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Article Environmental Sciences

High-dimensional multivariate geostatistics: A Bayesian matrix-normal approach

Lu Zhang et al.

Summary: This article introduces a conjugate Bayesian framework for analyzing multivariate spatial data, addressing the computational challenges faced when modeling large spatial data sets. The differences between modeling the multivariate response itself as a spatial process and modeling a latent process in a hierarchical model are discussed. The computational and inferential benefits of this approach are demonstrated through simulation studies and analysis of a vegetation index data set with millions of spatially dependent observations.

ENVIRONMETRICS (2021)

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Article Statistics & Probability

A General Framework for Vecchia Approximations of Gaussian Processes

Matthias Katzfuss et al.

Summary: This study introduces a generalization of the Vecchia method as a framework for Gaussian process (GP) approximations, which includes many popular existing GP approximation methods. By representing models with directed acyclic graphs, the sparsity of matrices necessary for inference is determined, leading to a novel sparse general Vecchia approximation.

STATISTICAL SCIENCE (2021)

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Article Environmental Sciences

A Simple Model for Wildland Fire Vortex-Sink Interactions

Bryan Quaife et al.

Summary: The model explores fire-atmosphere interactions through simulating fire coordinates, boundary conditions, and different fire front geometries to examine their effect on fire spread and stability.

ATMOSPHERE (2021)

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Article Mathematics, Interdisciplinary Applications

Fast Exact Bayesian Inference for Sparse Signals in the Normal Sequence Model

Tim van Erven et al.

Summary: This study proposes an exact algorithm for Bayesian inference with model selection priors in the sparse normal sequence model, which is numerically stable for much larger sample sizes. The study also explores alternative approaches like approximate algorithms, shrinkage priors, and empirical Bayesian methods, and demonstrates the computational speed and numerical accuracy of the proposed methods in various experiments. Additionally, bounds on the numerical accuracy of all new algorithms are computed to ensure their reliability, highlighting the advantages over alternative methods based on long division.

BAYESIAN ANALYSIS (2021)

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Article Computer Science, Interdisciplinary Applications

FRK: An R Package for Spatial and Spatio-Temporal Prediction with Large Datasets

Andrew Zammit-Mangion et al.

Summary: FRK is an R software package for spatial/spatio-temporal modeling and prediction with large datasets, distinguishing itself by avoiding stationary and isotropic covariance and variogram models in favor of a spatial random effects (SRE) model. It offers the advantages of integrating multiple observations with different supports, obtaining precise predictions at millions of locations, and reliable quantification of uncertainty.

JOURNAL OF STATISTICAL SOFTWARE (2021)

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Article Forestry