Peter Thompson

My research addresses the problem of identifiability. Systems of ordinary differential equations (ODEs) are often used to model biological processes, with variables representing physical quantities like the concentration of a particular chemical. Some quantities are measured by the experimenter (outputs), some are controlled by the experimenter (inputs), and the rest may or may not be deduced from this information. Whether the value of a particular quantity can be deduced in this context is precisely the question of whether that quantity is identifiable.

Physical quantities are assumed to be functions of time, and one can view the ODEs they satisfy as elements of an abstract algebraic object, such as a differential ring, and apply techniques from differential algebra and symbolic computation. Much of my prior research has centered around how one can obtain equations involving only input and output variables and exactly what information these give (and do not give) about what quantities are identifiable.

Identifiability analysis is often divided into roughly two categories. Structural identifiability is based only on the form of the ODEs and assumes that measurements are known perfectly. This has the advantage that it can be done before time and money are spent collecting data. Practical identifiability is assessed after data collection, but it takes into account the presence of noise as well as prior knowledge of an interval in which a quantity lies. My current research is based on developing techniques that incorporate the presence of noise and prior knowledge into structural identifiability analysis.

I hold a PhD in Mathematics from the CUNY Graduate Center in New York.