The role of computer-based modelling as third methodological approach in research has an increasing influence also in psychology and cognitive neuroscience. This is true not only for modelling of low level cellular neuronal activity, but also for processes of higher cognition such as deciding, learning, or problem solving. The major obstance to a widespread adoption of modelling and model based research here is an inverse problem, namely the fact that very often we find a multitude of cognitive models with similarly good reproduction of behavioural data. Then, advanced mathematical methods for systematically exploring, evaluating, validating, and selecting models from a space of possible candidates is required in order to apply and further develop the field. To date, this process of model building is almost exclusively a manual one that does not provide objective indicators for optimality or sub-optimality of the thus made choice of a working basis model.
This twinning projects focuses on investigating planning and problem solving processes in patients with schizophrenia, because
(1) this task is already a well define one (e.g. tower of Hanoi problems) and established reference models exist and can be used as ground truth for developing methods
(2) planning and problem solving is, not only for this group of patients, a daily activity of high relevance,
(3) a detailed understanding of cognitive deficits is instrumental for prognosis and tailored therapeutic remedy,
(4) we expect, that on the basis of mathematical model building and testing, we may eventually improve the efficiency of diagnosis,
(5) a clear contrast in behavioural features as opposed to healthy individuals provides for a well suited aim of quantitative mathematical modelling.
From the point of view of scientific computing, these questions may be sorted into three fundamental mathematical problem classes. Mathematical and computer-based methods for parameter estimation solve inverse problems for determining behavioural parameters. This research question arises for individual patients as well as for groups of patients with similar behavioural patterns. Methods of optimum experimental design yield model- and optimization-base indications that show through which kind of experiment (“test”) real-world data can be obtained that then allows for fast and reliable parameter estimation. This in particular means reducing uncertainty within the testing framework. Whenever during modelling multiple candidate models are available that possibly reproduce observed behavioural features, mathematical and statistical methods of model discrimination can be applied. The key idea here is the design of test that maximize differences in model response, thus allowing to sequentially rule out model candidates one by one.
In this twinning project, scientific computing is faced with a new kind of model structure coming from large, structured behavioural psychological models that are significantly different from more classical engineering applications. This means huge implications for numerical methods for optimization, parameter estimation, optimum experimental design, and model discrimination.
Name and contact of project responsible(s):
Daniel Holt (Experimental and Theoretical Psychology, Heidelberg University)
Christian Kirches (Interdisciplinary Center for Scientific Computing, Heidelberg University)
Stefan Koerkel (Interdisciplinary Center for Scientific Computing, Heidelberg University)
Additionally involved scientists and partners
Nadia Said (Experimental and Theoretical Psychology and Interdisciplinary Center for Scientific Computing, Heidelberg University)
Michael Engelhart (University of Magdeburg and Interdisciplinary Center for Scientific Computing Heidelberg)
Joachim Funke (Experimental and Theoretical Psychology, Heidelberg University)