Statistics of geometric features and new data types

Isaac Newton Institute for Mathematical Sciences, Cambridge, UK

19th March - 23rd March 2018

Had a great time at the workshop on statistics of geometric features and new data types. Many thanks to John Aston, Richard Davis and Axel Munk for the invite.

Geo spatial data are observations of a process that are collected in conjunction with reference to their geographical location. This type of data is abundant in many scientific fields, some examples include: population census, social and demographic (health, justice, education), economic (business surveys, trade, transport, tourism, agriculture, etc.) and environmental (atmospheric and oceanographic) data. They are often distributed over irregularly shaped spatial domains with complex boundaries and interior holes. Modelling approaches must account for the spatial dependence over these irregular domains as well as describing there temporal evolution.

Dynamic systems modeling has a huge potential in statistics, as evidenced by the amount of activity in functional data analysis. Many seemingly complex forms of functional variation can be more simply represented as a set of differential equations, either ordinary or partial.

In this talk, I present a class of semiparametric regression models with differential regularization in the form of PDEs. This methodology will be called Data2PDE “Data to Partial Differential Equations". Data2PDE characterizes spatial processes that evolve over complex geometries in the presence of uncertain, incomplete and often noisy observations and prior knowledge regarding the physical principles of the process characterized by a PDE.

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