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Statistical models for spatial processes play a central role in analyses of spatial data. Yet, it is the simple, interpretable, and well understood models that are routinely employed even though, as is revealed through prior and posterior predictive checks, these can poorly characterise the spatial heterogeneity in the underlying process of interest. Here, we propose a new, flexible class of spatial-process models, which we refer to as spatial Bayesian neural networks (SBNNs). An SBNN leverages the representational capacity of a Bayesian neural network; it is tailored to a spatial setting by incorporating a spatial “embedding layer” into the network and, possibly, spatially-varying network parameters. An SBNN is calibrated by matching its finite-dimensional distribution at locations on a fine gridding of space to that of a target process of interest. That process could be easy to simulate from or we may have many realisations from it. We propose several variants of SBNNs, most of w ....
In applications of optically stimulated luminescence (OSL) dating to unconsolidated sediments, the burial age of a sample of grains is estimated using statistical models of the distribution of the experimentally determined equivalent doses of the grains, together with estimates of the environmental dose rate. For grains that have been vertically mixed after deposition (e.g., due to bioturbation), existing dose models may fail to appropriately account for the complexity of the mixing process, thus producing inaccurate age estimates of the original time of deposition of the ‘native’ grains in any particular sample (usually the quantity of most interest). Here we introduce a new dose model, the asymmetric Laplacian mixture model (ALMM), developed for vertically mixed samples with single-grain dose distributions. The approach is based on a continuous statistical mixture that models the displacement of grains in both upward and downward directions. The central dose of the native grains ....
Density tempering (also called density annealing) is a sequential Monte Carlo approach to Bayesian inference for general state models which is an alternative to Markov chain Monte Carlo. When applied to state space models, it moves a collection of parameters and latent states (which are called particles) through a number of stages, with each stage having its own target distribution. The particles are initially generated from a distribution that is easy to sample from, e.g. the prior; the target at the final stage is the posterior distribution. Tempering is usually carried out either in batch mode, involving all the data at each stage, or sequentially with observations added at each stage, which is called data tempering. Efficient Markov moves for generating the parameters and states for each stage of particle based density tempering are proposed. This allows the proposed SMC methods to increase (scale up) the number of parameters and states that can be handled. Most current methods use ....
Yuansi Chen, assistant professor of Statistical Science, and Kevin Welsher, associate professor of Chemistry, have been named Sloan Research Fellows for 2023. Awarded annually since 1955, Sloan Research Fellowships are one of the most prestigious awards available to U.S. and Canadian researchers. Yuansi Chen ....