Related papers: Fast Variational Bayes for Large Spatial Data

Gaussian processes (GPs) are non-linear probabilistic models popular in many applications. However, na\"ive GP realizations require quadratic memory to store the covariance matrix and cubic computation to perform inference or evaluate the…

The availability of data sets with large numbers of variables is rapidly increasing. The effective application of Bayesian variable selection methods for regression with these data sets has proved difficult since available Markov chain…

With the growing capabilities of Geographic Information Systems (GIS) and user-friendly software, statisticians today routinely encounter geographically referenced data containing observations from a large number of spatial locations and…

Latent Gaussian models (LGMs) are perhaps the most commonly used class of models in statistical applications. Nevertheless, in areas ranging from longitudinal studies in biostatistics to geostatistics, it is easy to find datasets that…

While spatially varying coefficient (SVC) modeling is popular in applied science, its computational burden is substantial. This is especially true if a multiscale property of SVC is considered. Given this background, this study develops a…

Bayesian inference provides a methodology for parameter estimation and uncertainty quantification in machine learning and deep learning methods. Variational inference and Markov Chain Monte-Carlo (MCMC) sampling methods are used to…

While much research effort has been dedicated to scaling up sparse Gaussian process (GP) models based on inducing variables for big data, little attention is afforded to the other less explored class of low-rank GP approximations that…

Bayesian model selection enables comparison and ranking of conceptual subsurface models described by spatial prior models, according to the support provided by available geophysical data. Deep generative neural networks can efficiently…

In image reconstruction, an accurate quantification of uncertainty is of great importance for informed decision making. Here, the Bayesian approach to inverse problems can be used: the image is represented through a random function that…

This paper presents the development of a spatial block-Nearest Neighbor Gaussian process (block-NNGP) for location-referenced large spatial data. The key idea behind this approach is to divide the spatial domain into several blocks which…

Inverse problems involving partial differential equations (PDEs) are widely used in science and engineering. Although such problems are generally ill-posed, different regularisation approaches have been developed to ameliorate this problem.…

Recently, Stochastic Gradient Markov Chain Monte Carlo (SG-MCMC) methods have been proposed for scaling up Monte Carlo computations to large data problems. Whilst these approaches have proven useful in many applications, vanilla SG-MCMC…

This paper introduces the R package sgmcmc; which can be used for Bayesian inference on problems with large datasets using stochastic gradient Markov chain Monte Carlo (SGMCMC). Traditional Markov chain Monte Carlo (MCMC) methods, such as…

Non-linear hierarchical models are commonly used in many disciplines. However, inference in the presence of non-nested effects and on large datasets is challenging and computationally burdensome. This paper provides two contributions to…

Practitioners of Bayesian statistics have long depended on Markov chain Monte Carlo (MCMC) to obtain samples from intractable posterior distributions. Unfortunately, MCMC algorithms are typically serial, and do not scale to the large…

The generalized linear mixed model (GLMM) is widely used for analyzing correlated data, particularly in large-scale biomedical and social science applications. Scalable Bayesian inference for GLMMs is challenging because the marginal…

A near-field motion parameter estimation method is proposed. In contract to far-field sensing systems, the near-field sensing system leverages spherical-wave characteristics to enable full-vector location and velocity estimation. Despite…

Stochastic gradient Markov Chain Monte Carlo (SG-MCMC) has been developed as a flexible family of scalable Bayesian sampling algorithms. However, there has been little theoretical analysis of the impact of minibatch size to the algorithm's…

Variational Bayes (VB) is a popular tool for Bayesian inference in statistical modeling. Recently, some VB algorithms are proposed to handle intractable likelihoods with applications such as approximate Bayesian computation. In this paper,…

Spatial concurrent linear models, in which the model coefficients are spatial processes varying at a local level, are flexible and useful tools for analyzing spatial data. One approach places stationary Gaussian process priors on the…