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System identification is of special interest in science and engineering. This article is concerned with a system identification problem arising in stochastic dynamic systems, where the aim is to estimate the parameters of a system along…
In tracking multiple objects, it is often assumed that each observation (measurement) is originated from one and only one object. However, we may encounter a situation that each measurement may or may not be associated with multiple objects…
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…
Bayesian nonparametrics are a class of probabilistic models in which the model size is inferred from data. A recently developed methodology in this field is small-variance asymptotic analysis, a mathematical technique for deriving learning…
Bayesian inference methods are applied within a Bayesian hierarchical modelling framework to the problems of joint state and parameter estimation, and of state forecasting. We explore and demonstrate the ideas in the context of a simple…
With the rapid advancement of information technology and data collection systems, large-scale spatial panel data presents new methodological and computational challenges. This paper introduces a dynamic spatial panel quantile model that…
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…
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…
In this paper we focus on spatial Markov population models, describing the stochastic evolution of populations of agents, explicitly modelling their spatial distribution, representing space as a discrete, finite graph. More specifically, we…
Markov chains are a natural and well understood tool for describing one-dimensional patterns in time or space. We show how to infer $k$-th order Markov chains, for arbitrary $k$, from finite data by applying Bayesian methods to both…
There is a lack of methodological results for continuous time change detection due to the challenges of noninformative prior specification and efficient posterior inference in this setting. Most methodologies to date assume data are…
Spatial generalized linear mixed models (SGLMMs) are popular and flexible models for non-Gaussian spatial data. They are useful for spatial interpolations as well as for fitting regression models that account for spatial dependence, and are…
Spatial connectivity is an important consideration when modelling infectious disease data across a geographical region. Connectivity can arise for many reasons, including shared characteristics between regions, and human or vector movement.…
We develop a class of nearest-neighbor mixture models that provide direct, computationally efficient, probabilistic modeling for non-Gaussian geospatial data. The class is defined over a directed acyclic graph, which implies conditional…
The Markov chain random field (MCRF) model/theory provides a non-linear spatial Bayesian updating solution at the neighborhood nearest data level for simulating categorical spatial variables. In the MCRF solution, the spatial dependencies…
Deterministic compartmental models are predominantly used in the modeling of infectious diseases, though stochastic models are considered more realistic, yet are complicated to estimate due to missing data. In this paper we present a novel…
Geographic Information Systems (GIS) and related technologies have generated substantial interest among statisticians with regard to scalable methodologies for analyzing large spatial datasets. A variety of scalable spatial process models…
Probabilistic modeling of multidimensional spatiotemporal data is critical to many real-world applications. As real-world spatiotemporal data often exhibits complex dependencies that are nonstationary and nonseparable, developing effective…
In spite of the diverse literature on nonstationary spatial modeling and approximate Gaussian process (GP) methods, there are no general approaches for conducting fully Bayesian inference for moderately sized nonstationary spatial data sets…
Traditional epidemic detection algorithms make decisions using only local information. We propose a novel approach that explicitly models spatial information fusion from several metapopulations. Our method also takes into account…