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Traffic forecasting problem remains a challenging task in the intelligent transportation system due to its spatio-temporal complexity. Although temporal dependency has been well studied and discussed, spatial dependency is relatively less…
Mechanistic statistical models are commonly used to study the flow of biological processes. For example, in landscape genetics, the aim is to infer spatial mechanisms that govern gene flow in populations. Existing statistical approaches in…
Latent space models (LSMs) are often used to analyze dynamic (time-varying) networks that evolve in continuous time. Existing approaches to Bayesian inference for these models rely on Markov chain Monte Carlo algorithms, which cannot handle…
Coming up with Bayesian models for spatial data is easy, but performing inference with them can be challenging. Writing fast inference code for a complex spatial model with realistically-sized datasets from scratch is time-consuming, and if…
Spatial-temporal forecasting has attracted tremendous attention in a wide range of applications, and traffic flow prediction is a canonical and typical example. The complex and long-range spatial-temporal correlations of traffic flow bring…
We study maximum likelihood estimation for spatial generalized linear mixed models with Gaussian process approximations using a stochastic Newton-Raphson algorithm. We consider two Gaussian Process approximations in this context: spectral…
Traffic prediction has drawn increasing attention in AI research field due to the increasing availability of large-scale traffic data and its importance in the real world. For example, an accurate taxi demand prediction can assist taxi…
Spatio-temporal graph neural networks (STGNN) have become the most popular solution to traffic forecasting. While successful, they rely on the message passing scheme of GNNs to establish spatial dependencies between nodes, and thus…
Modeling stochastic traffic behaviors at the microscopic level, such as car-following and lane-changing, is a crucial task to understand the interactions between individual vehicles in traffic streams. Leveraging a recently developed theory…
Representing the nodes of continuous-time temporal graphs in a low-dimensional latent space has wide-ranging applications, from prediction to visualization. Yet, analyzing continuous-time relational data with timestamped interactions…
Spherically embedded spatial data are spatially indexed observations whose values naturally reside on or can be equivalently mapped to the unit sphere. Such data are increasingly ubiquitous in fields ranging from geochemistry to demography.…
To date, VANET research efforts have relied heavily on simulations, due to prohibitive costs of deploying real world testbeds. Existing channel models implemented in discrete-event VANET simulators are by and large simple stochastic radio…
This thesis deals with applications of experimental mathematics to a number of problems. The first problem is related to random graph statistics. We consider a certain class of Galton-Watson random trees and look at the total height…
We introduce a nonstationary spatio-temporal statistical model for gridded data on the sphere. The model specifies a computationally convenient covariance structure that depends on heterogeneous geography. Widely used statistical models on…
Self-exciting point processes are widely used to model the contagious effects of crime events living within continuous geographic space, using their occurrence time and locations. However, in urban environments, most events are naturally…
A non-stationary spatial Gaussian random field (GRF) is described as the solution of an inhomogeneous stochastic partial differential equation (SPDE), where the covariance structure of the GRF is controlled by the coefficients in the SPDE.…
Accurately forecasting urban development and its environmental and climate impacts critically depends on realistic models of the spatial structure of the built environment, and of its dependence on key factors such as population and…
State-space models have been successfully used for more than fifty years in different areas of science and engineering. We present a procedure for efficient variational Bayesian learning of nonlinear state-space models based on sparse…
In this work, we study a family of wireless channel simulation models called geometry-based stochastic channel models (GBSCMs). Compared to more complex ray-tracing simulation models, GBSCMs do not require an extensive characterization of…
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…