In cognitive modelling, we investigate mathematical and computational approaches to explain human behaviour by a set of basic assumptions on principles of information pro- cessing of mind and brain. In this approach, model fitting and comparison are becoming more and more important due to increasingly complex models and the existence of competing modelling approaches. This is particularly important in the case of dynamical cognitive models, where parameter identification and model comparison must be based on time-ordered data (time series).
The focus of the current project is on dynamical models of eye-movement control. Eye- movement control is an important area of cognitive modelling, since the eyes are both sensory and motor systems and, therefore, are among the best experimental measures of ongoing cognition. We will investigate dynamical models that generate sequences of eye movements in (i) reading, (ii) scene perception, and (iii) fixational eye movements. Work packages are (WP1) likelihood-based parameter estimation and Bayesian inference, (WP2) efficient algorithms for parameter inference in cognitive models, and (WP3) Bayesian model comparison and random effects (to get a flavour for the type of work planned in this project, see reference  below).
The mathematically oriented PhD student will work at the Institute of Mathematics. Candidates with a degree in applied/computational mathematics or statistics will be preferred.
- Probabilistic forecasting and Bayesian data assimilation
S. Reich and C.J. Cotter, Cambridge University Press, 2015
- Likelihood-based parameter estimation and comparison of dynamical cognitive models
H.H. Schütt, L.O.M. Rothkegel, H.A. Trukenbrod, S. Reich, F.A. Wichmann and R. Engbert, University of Potsdam, 2016
- Spatial statistics and attentional dynamics in scene viewing
R. Engbert, H.A. Trukenbrod, S. Barthelme, and F.A. Wichmann, Journal of Vision, 15(1):14, 1-17, 2015.
Malem-Shinitski, N., Opper, M., Reich, S., Schwetlick, S., Seelig S. A., and Engbert, R (2020). A Mathematical Model of Exploration and Exploitation in Natural Scene Viewing.arXiv: 2004.04649
Rabe, M. M., Chandra, J., Krügel, A., Seelig, S. A., Vasishth, S., and Engbert, R. (2019). A Bayesian approach to dynamical modeling of eye-movement control in reading of normal, mirrored, and scrambled texts. psyarXiv
Seelig, S. A., Rabe, M. M., Malem-Shinitski, N., Risse, S., Reich, S., and Engbert, R. (2020). Bayesian parameter estimation for the SWIFT model of eye-movement control during reading. Journal of Mathematical Psychology, 95, 102313. doi:10.1016/j.jmp.2019.102313; arXiv: 1901.11110.
Schütt, H. H., Rothkegel, L. O. M., Trukenbrod, H. A., Reich, S., Wichmann, F. A. and Engbert, R. (2017). Likelihood-based parameter estimation and comparison of dynamical cognitive models. Psychological Review, 124, 505-524. doi:10.1037/rev0000068