PhD Funding Opportunities

July 14, 2020 Off By michellecarey_j50p0430

University College Dublin is pleased to invite applications for a fully-funded PhD studentship in the School of Mathematics and Statistics for entry in 2021. These studentships include a tax-free stipend of €18,000 per annum for four years, coverage of tuition fees, funds for conference travel, and an equipment allowance.

Spatial Functional Data Analysis

Supervisors: Dr. Michelle Carey, University College Dublin and Prof. Laura Maria Sangall, MOX - Dipartimento di Matematica, Politecnico di Milano.

Spatial data distributed over geographical locations and time are essential to the study of demographics, economies and the environment. These data are often distributed over irregularly shaped spatial domains with complex boundaries and interior holes. Figure (1) provides an example of such data, the population density recorded within the Island of Montreal.

The Island of Montreal census data. Dots indicate the population density. Two holes denote uninhabited regions which are highlighted by grey lines. The hole in the south-western part of the island is Dorval airport with some surrounding services and industries and the hole in the north-eastern end represents an area containing oil refineries and a water purification plant. A grey line also evidences the island's coastline; the stretches of coastline highlighted in blue are also uninhabited. These correspond to the harbour, in the east shore, and two public parks, in the south-west and north-west shore.

There are several features of the domain to note: (i) the irregular boundary defining the Island of Montreal; (ii) the two uninhabited regions indicated by the two holes in the island, that denote the airport in the south and an industrial park in the north-east; (iii) the four uninhabited coastlines highlighted in blue representing the harbour, in the east shore, and two public parks, in the south-west and north-west. Modelling approaches must account for spatial dependence of the underlying process, in this instance, the population density while adhering to the geometrical features of the domain listed in (i-iii).

Traditional spatial statistics methods, derived from time series analysis, express spatial processes descriptively in terms of first and second moments, i.e. means and covariances, see Cressie and Wikle (2015) for an excellent overview. In practice, the available classes of covariance functions are often too simplistic for real-world problems. Dynamical approaches incorporate problem-specific prior information about the spatial structure of the phenomenon under study, expressed in terms of a PDE. PDEs can naturally render complex spatial-temporal variation such as varied forms of anisotropy and non-stationarity. Additionally, PDEs efficiently handle complicated spatial domains, such as domains with strong concavities or holes, and domains with non-trivial geometries.

This PhD is devoted to the extension of a novel class of semiparametric regression models with differential regularisation. These models estimate and draw inference on spatial processes that evolve over complex geometries in the presence of incomplete measurements subject to observational error, and prior knowledge describing the complex spatial-temporal variation characterised by a PDE. They have been used to model the population density within the Island of Montreal (Sangalli et al., 2013); the blood-flow velocity field in carotid arteries (Azzimonti et al., 2014, 2015, Arnone et al.,2019); and rainfall across Switzerland (Bernardi et al., 2018).

THE POSITION:

The position is funded through Insight an SFI Research Centre for Data Analytics, one of the largest data analytics centres in Europe. Insight consists of 450 researchers across areas such as the Fundamentals of Data Science, Sensing and Actuation, Scaling Algorithms, Model Building, Multi-Modal Analysis, Data Engineering and Governance, Decision Making and Trustworthy AI.The University College Dublin is Ireland’s premier research university and its Statistics group is the highest-ranked in Ireland. University College Dublin is a campus-based university with excellent facilities, only a few kilometres from Dublin city centre.Politecnico di Milano is one of the most outstanding technical universities in Europe. The Laboratory for Modelling and Scientific Computing (MOX) is one of the largest University research laboratories devoted to applied mathematics and statistics in Italy. MOX is located in the city of Milan, Italy.

The successful candidate will be an Insight PhD student jointly supervised by Dr. Michelle Carey, University College Dublin and Prof. Laura Sangalli, Politecnico di Milano and therefore will have exposure to both leading institutions.

ENTRY REQUIREMENTS
A candidate must have reached a minimum of an upper second-class degree or equivalent in a relevant honour’s undergraduate degree/Master’s degree. All applicants are required to demonstrate a high level of competence in the English language. Applicants who have not undertaken their undergraduate degree/Master’s degree through English must provide evidence of their English proficiency by achieving a minimum standard in a recognised English language test such as IELTS.

Applicants should have experience in functional data analysis, spatial modelling, and/or applied mathematics. Applicants should have a numerate undergraduate degree. An MSc in Statistics, Data Analytics or Applied Mathematics is highly desirable.

APPLICATION DETAILS

An application consisting of a cover letter, curriculum vitae (including the names and contact details of two referees) and scanned copies of relevant academic transcripts should be sent to:

Dr Michelle Carey ( michelle.carey@ucd.ie)

I am a named supervisor in SFI Centre for Research Training in Foundations of Data Science. This large-scale collaborative initiative between the University of Limerick (UL), University College Dublin (UCD) and Maynooth University (MU) will train a cohort of PhD students with a world-class foundational understanding in the horizontal themes of Applied Mathematics, Statistics, and Machine Learning. These fundamental themes will be fused by applying them to real-world challenges in vertical themes, including Data Analytics, Privacy & Security, Smart Manufacturing, Networks, and Health & Wellbeing. Students will have work placements in relevant industries to develop cognisance of industry requirements, essential transversal skills, diversity and research impact.

For further details see  www.data-science.ie

I am a supervisor in the SFI Centre for Research Training in Genomics Data Science. The SFI Centre for Research Training in Genomics Data Science is a PhD training programme, linking together approx. ninety genomics data science group leaders based at six Irish institutions. Expertise within the group spans from statistical modelling and machine learning to the full range of applications of genomics. This Research Centre is focussed on 7 Research Themes:

For further details see: https://genomicsdatascience.ie/