ﻻ يوجد ملخص باللغة العربية
Spatial processes with nonstationary and anisotropic covariance structure are often used when modelling, analysing and predicting complex environmental phenomena. Such processes may often be expressed as ones that have stationary and isotropic covariance structure on a warped spatial domain. However, the warping function is generally difficult to fit and not constrained to be injective, often resulting in `space-folding. Here, we propose modelling an injective warping function through a composition of multiple elemental injective functions in a deep-learning framework. We consider two cases; first, when these functions are known up to some weights that need to be estimated, and, second, when the weights in each layer are random. Inspired by recent methodological and technological advances in deep learning and deep Gaussian processes, we employ approximate Bayesian methods to make inference with these models using graphics processing units. Through simulation studies in one and two dimensions we show that the deep compositional spatial models are quick to fit, and are able to provide better predictions and uncertainty quantification than other deep stochastic models of similar complexity. We also show their remarkable capacity to model nonstationary, anisotropic spatial data using radiances from the MODIS instrument aboard the Aqua satellite.
We use the theory of normal variance-mean mixtures to derive a data augmentation scheme for models that include gamma functions. Our methodology applies to many situations in statistics and machine learning, including Multinomial-Dirichlet distributi
Applications such as the analysis of microbiome data have led to renewed interest in statistical methods for compositional data, i.e., multivariate data in the form of probability vectors that contain relative proportions. In particular, there is con
Approximate Bayesian Computation (ABC) methods are used to approximate posterior distributions in models with unknown or computationally intractable likelihoods. Both the accuracy and computational efficiency of ABC depend on the choice of summary st
Automated sensing instruments on satellites and aircraft have enabled the collection of massive amounts of high-resolution observations of spatial fields over large spatial regions. If these datasets can be efficiently exploited, they can provide new
Gaussian processes are popular and flexible models for spatial, temporal, and functional data, but they are computationally infeasible for large datasets. We discuss Gaussian-process approximations that use basis functions at multiple resolutions to