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Nonstationary non-Gaussian spatial data are common in many disciplines, including climate science, ecology, epidemiology, and social sciences. Examples include count data on disease incidence and binary satellite data on cloud mask…

Geostatistical analysis of health data is increasingly used to model spatial variation in malaria prevalence, burden, and other metrics. Traditional inference methods for geostatistical modelling are notoriously computationally intensive,…

A novel extrapolation method is proposed for longitudinal forecasting. A hierarchical Gaussian process model is used to combine nonlinear population change and individual memory of the past to make prediction. The prediction error is…

Analysing non-Gaussian spatial-temporal data requires introducing spatial as well as temporal dependence in generalised linear models through the link function of an exponential family distribution. Unlike in Gaussian likelihoods, inference…

Statistical shape models (SSMs) represent a class of shapes as a normal distribution of point variations, whose parameters are estimated from example shapes. Principal component analysis (PCA) is applied to obtain a low-dimensional…

Graphical models are ubiquitous tools to describe the interdependence between variables measured simultaneously such as large-scale gene or protein expression data. Gaussian graphical models (GGMs) are well-established tools for…

Distributed Gaussian process (DGP) is a popular approach to scale GP to big data which divides the training data into some subsets, performs local inference for each partition, and aggregates the results to acquire global prediction. To…

Nonparametric regression for massive numbers of samples (n) and features (p) is an increasingly important problem. In big n settings, a common strategy is to partition the feature space, and then separately apply simple models to each…

This study introduces an integrated framework for predictive causal inference designed to overcome limitations inherent in conventional single model approaches. Specifically, we combine a Hidden Markov Model (HMM) for spatial health state…

Gaussian processes are a powerful framework for uncertainty-aware function approximation and sequential decision-making. Unfortunately, their classical formulation does not scale gracefully to large amounts of data and modern hardware for…

Gaussian process regression is a machine learning approach which has been shown its power for estimation of unknown functions. However, Gaussian processes suffer from high computational complexity, as in a basic form they scale cubically…

Despite the amount of research on disease mapping in recent years, the use of multivariate models for areal spatial data remains limited due to difficulties in implementation and computational burden. These problems are exacerbated when the…

Aggregated data is commonplace in areas such as epidemiology and demography. For example, census data for a population is usually given as averages defined over time periods or spatial resolutions (cities, regions or countries). In this…

Gaussian Graphical Models (GGMs) are widely used in high-dimensional data analysis to synthesize the interaction between variables. In many applications, such as genomics or image analysis, graphical models rely on sparsity and clustering…

Spatial generalized linear mixed models (SGLMMs) are popular for analyzing non-Gaussian spatial data. These models assume a prescribed link function that relates the underlying spatial field with the mean response. There are circumstances,…

This article focuses on drawing computationally-efficient predictive inference from Gaussian process (GP) regressions with a large number of features when the response is conditionally independent of the features given the projection to a…

We consider the edge-based compartmental models for infectious disease spread introduced in Part I. These models allow us to consider standard SIR diseases spreading in random populations. In this paper we show how to handle deviations of…

Gaussian processes (GPs) are a powerful tool for probabilistic inference over functions. They have been applied to both regression and non-linear dimensionality reduction, and offer desirable properties such as uncertainty estimates,…

Gaussian processes are a natural way of defining prior distributions over functions of one or more input variables. In a simple nonparametric regression problem, where such a function gives the mean of a Gaussian distribution for an…

Generalized additive models (GAMs) are a widely used class of models of interest to statisticians as they provide a flexible way to design interpretable models of data beyond linear models. We here propose a scalable and well-calibrated…