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Accurate estimation of the change in crime over time is a critical first step towards better understanding of public safety in large urban environments. Bayesian hierarchical modeling is a natural way to study spatial variation in urban…
The increased demand for online prediction and the growing availability of large data sets drives the need for computationally efficient models. While exact Gaussian process regression shows various favorable theoretical properties…
The log Gaussian Cox process is a flexible class of point pattern models for capturing spatial and spatio-temporal dependence for point patterns. Model fitting requires approximation of stochastic integrals which is implemented through…
We develop a Bayesian modeling framework to address a pressing real-life problem faced by the police in tackling insurgent gangs. Unlike criminals associated with common crimes such as robbery, theft or street crime, insurgent gangs are…
Learning time-series models is useful for many applications, such as simulation and forecasting. In this study, we consider the problem of actively learning time-series models while taking given safety constraints into account. For…
In this paper, we introduce the notion of Gaussian processes indexed by probability density functions for extending the Mat\'ern family of covariance functions. We use some tools from information geometry to improve the efficiency and the…
This paper proposes a log-linear model for the latent intensity functions of a replicated spatio-temporal point process. By simultaneously fitting correlated spatial and temporal Karhunen-Lo\`eve expansions, the model produces spatial and…
Spatio-temporal covariances are important for describing the spatio-temporal variability of underlying random processes in geostatistical data. For second-order stationary processes, there exist subclasses of covariance functions that…
Many natural phenomena exhibit power law behaviour in the distribution of event size. This scaling is successfully reproduced by Self Organized Criticality (SOC). On the other hand, temporal occurrence in SOC models has a Poisson-like…
An unbinned statistical test on cluster-like deviations from Poisson processes for point process data is introduced, presented in the context of time variability analysis of astrophysical sources in count rate experiments. The measure of…
A validated simulation model primarily requires performing an appropriate input analysis mainly by determining the behavior of real-world processes using probability distributions. In many practical cases, probability distributions of the…
In environmental science applications, extreme events frequently exhibit a complex spatio-temporal structure, which is difficult to describe flexibly and estimate in a computationally efficient way using state-of-art parametric…
Event cameras, inspired by biological vision systems, provide a natural and data efficient representation of visual information. Visual information is acquired in the form of events that are triggered by local brightness changes. Each pixel…
Urban systems often exhibit scale-invariant properties, with power-law distributions observed in various spatial and temporal patterns of human behavior. A prominent example is the distribution of commercial activities and other Points of…
Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…
Severe Ionosphere magnetic storms are feared events for integrity and continuity of navigation systems such as EGNOS, the European SBAS (Satellite-Based Augmentation System) complementing GPS and an accurate modelling of this event…
It is common in nature to see aggregation of objects in space. Exploring the mechanism associated with the locations of such clustered observations can be essential to understanding the phenomenon, such as the source of spatial…
We present a survey of some of our recent results on Bayesian nonparametric inference for a multitude of stochastic processes. The common feature is that the prior distribution in the cases considered is on suitable sets of piecewise…
Halting a computer or biological virus outbreak requires a detailed understanding of the timing of the interactions between susceptible and infected individuals. While current spreading models assume that users interact uniformly in time,…
In this paper, the panel count data analysis for recurrent events is considered. Such analysis is useful for studying tumor or infection recurrences in both clinical trial and observational studies. A bivariate Gaussian Cox process model is…