Supervisor: Prof. Jorge Mateu, Department of Mathematics, University Jaume I of Castellon Spain). Visit http://www3.uji.es/~mateu.
Salary: 1300 euros/month approx
Topic: Statistical analysis of events in space and time with a focus on networks and trajectories
New technologies have witnessed the era of massive data (big data) and with it the emergence of data science field. In a massive world of information, the need for statistical treatment of events that evolve in space-time over a network system is increasingly common. When these events are monitored over time they give information about the movement and provide trajectories over networks. The theory of space-time stochastic processes on networks provide theoretical and methodological support for this type of data.
This project aims to address the statistical modeling of this type of events in these new scenarios. We start with parametric analysis of first order characteristics, which are necessary to build second order and higher order ones. We intend to characterise all orders (as far as possible) of a point process on networks to determine the underlying structure of space-time interaction existing on the network. With this, we propose parametric theoretical models of specific processes on networks beyond the Poisson models. One of these models is Cox processes on networks that combine random fields (geostatistics) with point processes. We will develop Bayesian inference methods for these models. These constructions open the way to the analysis of trajectories. We will first determine simple trajectories of origin-destination type by proposing Bayesian probabilistic models. We will extend this context to the case of marked functional processes where the marks will represent the trajectories.
The project is motivated by real problems from the field of Criminology, where the events are types of crimes occurring in cities, traffic accidents, movement of people within a city, or car thefts and their recoveries. We will provide probabilistic predictive models for the criminal activity over city networks. We will build our own software that can be used by external institutions (EPOs) that support the project.
Requirements for candidates:
1) Undergraduate in Mathematics and/or Statistics (main option). Computer Science could also be accepted as a secondary option.
2) Master in Maths, statistics, computer Science or related disciplines.
3) The undergraduate degree has to be obtained from 2016 to now.
4) Knowledge on stochastic processes, spatial and spatio-temporal statistics, and R-coding will be appreciated and up-weighted in the candidate assessment.
Deadlines: Official call will be open around 23-24 June and it will remain open for only the next 10 days.
Contact: Those candidates interested in applying, please send an email to firstname.lastname@example.org as soon as possible to fix details of the application.