Related papers: Modeling and Predicting Spatio-temporal Dynamics o…
Spatial heteroskedasticity refers to stochastically changing variances and covariances in space. Such features have been observed in, for example, air pollution and vegetation data. We study how volatility modulated moving averages can…
In this paper we explore a covariance spectral modelling strategy for spatial-temporal processes which involves a spectral approach for time but a covariance approach for space.It facilitates the analysis of coherence between the temporal…
A variational inference-based framework for training a multi-output Gaussian process latent variable model, specifically tailored to the tails-up spatio-temporal stream network, is developed. Training, given a censored observational data…
Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from biology to…
Gaussian processes (GPs) are important probabilistic tools for inference and learning in spatio-temporal modelling problems such as those in climate science and epidemiology. However, existing GP approximations do not simultaneously support…
We introduce a Bayesian approach for analyzing high-dimensional multinomial data that are referenced over space and time. In particular, the proportions associated with multinomial data are assumed to have a logit link to a latent…
With the advancement of GPS and remote sensing technologies, large amounts of geospatial and spatiotemporal data are being collected from various domains, driving the need for effective and efficient prediction methods. Given spatial data…
Probabilistic forecasting of multivariate time series is essential for various downstream tasks. Most existing approaches rely on the sequences being uniformly spaced and aligned across all variables. However, real-world multivariate time…
The rate of strong convergence is investigated for an approximation scheme for a class of stochastic differential equations driven by a time-changed Brownian motion, where the random time changes $(E_t)_{t\ge 0}$ considered include the…
Inverse problems with spatiotemporal observations are ubiquitous in scientific studies and engineering applications. In these spatiotemporal inverse problems, observed multivariate time series are used to infer parameters of physical or…
We introduce a flexible and scalable class of Bayesian geostatistical models for discrete data, based on the class of nearest neighbor mixture transition distribution processes (NNMP), referred to as discrete NNMP. The proposed class…
We present a fully Bayesian statistical approach to the problem of compartmental modelling in the context of Positron Emission Tomography. We cluster homogeneous region of interest and perform kinetic parameter estimation simultaneously. A…
This thesis focuses on data that has complex spatio-temporal structure and on probabilistic graphical models that learn the structure in an interpretable and scalable manner. We target two research areas of interest: Gaussian graphical…
Modeling correlation (and covariance) matrices can be challenging due to the positive-definiteness constraint and potential high-dimensionality. Our approach is to decompose the covariance matrix into the correlation and variance matrices…
In spatio-temporal analysis, we often record data at specific time intervals but with varying spatial locations between these timepoints. We propose a conditional model to analyze such spatio-temporal data that accommodates the dependencies…
High-dimensional spatially correlated covariates are common in regression models encountered in environmental sciences and other fields. In such models, the regression coefficients often exhibit a sparse structure with spatial dependence.…
I present an approach for modeling areal spatial covariance by considering the stationary distribution of a spatio-temporal Markov random walk. In the areal data case, this stationary distribution corresponds to an intrinsic simultaneous…
Explosive growth in spatio-temporal data and its wide range of applications have attracted increasing interests of researchers in the statistical and machine learning fields. The spatio-temporal regression problem is of paramount importance…
Recent years have seen a huge development in spatial modelling and prediction methodology, driven by the increased availability of remote-sensing data and the reduced cost of distributed-processing technology. It is well known that…
This work is focused on constructing space-time covariance functions through a hierarchical mixture approach that can serve as building blocks for capturing complex dependency structures. This hierarchical mixture approach provides a…