TY - JOUR
A1 - Seelig, Stefan A.
A1 - Rabe, Maximilian Michael
A1 - Malem-Shinitski, Noa
A1 - Risse, Sarah
A1 - Reich, Sebastian
A1 - Engbert, Ralf
T1 - Bayesian parameter estimation for the SWIFT model of eye-movement control during reading
JF - Journal of mathematical psychology
N2 - Process-oriented theories of cognition must be evaluated against time-ordered observations. Here we present a representative example for data assimilation of the SWIFT model, a dynamical model of the control of fixation positions and fixation durations during natural reading of single sentences. First, we develop and test an approximate likelihood function of the model, which is a combination of a spatial, pseudo-marginal likelihood and a temporal likelihood obtained by probability density approximation Second, we implement a Bayesian approach to parameter inference using an adaptive Markov chain Monte Carlo procedure. Our results indicate that model parameters can be estimated reliably for individual subjects. We conclude that approximative Bayesian inference represents a considerable step forward for computational models of eye-movement control, where modeling of individual data on the basis of process-based dynamic models has not been possible so far.
KW - dynamical models
KW - reading
KW - eye movements
KW - saccades
KW - likelihood function
KW - Bayesian inference
KW - MCMC
KW - interindividual differences
Y1 - 2020
U6 - https://doi.org/10.1016/j.jmp.2019.102313
SN - 0022-2496
SN - 1096-0880
VL - 95
PB - Elsevier
CY - San Diego
ER -
TY - JOUR
A1 - Engbert, Ralf
A1 - Rabe, Maximilian Michael
A1 - Kliegl, Reinhold
A1 - Reich, Sebastian
T1 - Sequential data assimilation of the stochastic SEIR epidemic model for regional COVID-19 dynamics
JF - Bulletin of mathematical biology : official journal of the Society for Mathematical Biology
N2 - Newly emerging pandemics like COVID-19 call for predictive models to implement precisely tuned responses to limit their deep impact on society. Standard epidemic models provide a theoretically well-founded dynamical description of disease incidence. For COVID-19 with infectiousness peaking before and at symptom onset, the SEIR model explains the hidden build-up of exposed individuals which creates challenges for containment strategies. However, spatial heterogeneity raises questions about the adequacy of modeling epidemic outbreaks on the level of a whole country. Here, we show that by applying sequential data assimilation to the stochastic SEIR epidemic model, we can capture the dynamic behavior of outbreaks on a regional level. Regional modeling, with relatively low numbers of infected and demographic noise, accounts for both spatial heterogeneity and stochasticity. Based on adapted models, short-term predictions can be achieved. Thus, with the help of these sequential data assimilation methods, more realistic epidemic models are within reach.
KW - Stochastic epidemic model
KW - Sequential data assimilation
KW - Ensemble Kalman
KW - filter
KW - COVID-19
Y1 - 2020
U6 - https://doi.org/10.1007/s11538-020-00834-8
SN - 0092-8240
SN - 1522-9602
VL - 83
IS - 1
PB - Springer
CY - New York
ER -
TY - JOUR
A1 - Engbert, Ralf
A1 - Rabe, Maximilian Michael
A1 - Schwetlick, Lisa
A1 - Seelig, Stefan A.
A1 - Reich, Sebastian
A1 - Vasishth, Shravan
T1 - Data assimilation in dynamical cognitive science
JF - Trends in cognitive sciences
N2 - Dynamical models make specific assumptions about cognitive processes that generate human behavior. In data assimilation, these models are tested against timeordered data. Recent progress on Bayesian data assimilation demonstrates that this approach combines the strengths of statistical modeling of individual differences with the those of dynamical cognitive models.
Y1 - 2022
U6 - https://doi.org/10.1016/j.tics.2021.11.006
SN - 1364-6613
SN - 1879-307X
VL - 26
IS - 2
SP - 99
EP - 102
PB - Elsevier
CY - Amsterdam
ER -
TY - JOUR
A1 - Malem-Shinitski, Noa
A1 - Opper, Manfred
A1 - Reich, Sebastian
A1 - Schwetlick, Lisa
A1 - Seelig, Stefan A.
A1 - Engbert, Ralf
T1 - A mathematical model of local and global attention in natural scene viewing
JF - PLoS Computational Biology : a new community journal
N2 - Author summary
Switching between local and global attention is a general strategy in human information processing. We investigate whether this strategy is a viable approach to model sequences of fixations generated by a human observer in a free viewing task with natural scenes. Variants of the basic model are used to predict the experimental data based on Bayesian inference. Results indicate a high predictive power for both aggregated data and individual differences across observers. The combination of a novel model with state-of-the-art Bayesian methods lends support to our two-state model using local and global internal attention states for controlling eye movements.
Understanding the decision process underlying gaze control is an important question in cognitive neuroscience with applications in diverse fields ranging from psychology to computer vision. The decision for choosing an upcoming saccade target can be framed as a selection process between two states: Should the observer further inspect the information near the current gaze position (local attention) or continue with exploration of other patches of the given scene (global attention)? Here we propose and investigate a mathematical model motivated by switching between these two attentional states during scene viewing. The model is derived from a minimal set of assumptions that generates realistic eye movement behavior. We implemented a Bayesian approach for model parameter inference based on the model's likelihood function. In order to simplify the inference, we applied data augmentation methods that allowed the use of conjugate priors and the construction of an efficient Gibbs sampler. This approach turned out to be numerically efficient and permitted fitting interindividual differences in saccade statistics. Thus, the main contribution of our modeling approach is two-fold; first, we propose a new model for saccade generation in scene viewing. Second, we demonstrate the use of novel methods from Bayesian inference in the field of scan path modeling.
Y1 - 2020
U6 - https://doi.org/10.1371/journal.pcbi.1007880
SN - 1553-734X
SN - 1553-7358
VL - 16
IS - 12
PB - PLoS
CY - San Fransisco
ER -
TY - JOUR
A1 - Schütt, Heiko Herbert
A1 - Rothkegel, Lars Oliver Martin
A1 - Trukenbrod, Hans Arne
A1 - Reich, Sebastian
A1 - Wichmann, Felix A.
A1 - Engbert, Ralf
T1 - Likelihood-based parameter estimation and comparison of dynamical cognitive models
JF - Psychological Review
N2 - Dynamical models of cognition play an increasingly important role in driving theoretical and experimental research in psychology. Therefore, parameter estimation, model analysis and comparison of dynamical models are of essential importance. In this article, we propose a maximum likelihood approach for model analysis in a fully dynamical framework that includes time-ordered experimental data. Our methods can be applied to dynamical models for the prediction of discrete behavior (e.g., movement onsets); in particular, we use a dynamical model of saccade generation in scene viewing as a case study for our approach. For this model, the likelihood function can be computed directly by numerical simulation, which enables more efficient parameter estimation including Bayesian inference to obtain reliable estimates and corresponding credible intervals. Using hierarchical models inference is even possible for individual observers. Furthermore, our likelihood approach can be used to compare different models. In our example, the dynamical framework is shown to outperform nondynamical statistical models. Additionally, the likelihood based evaluation differentiates model variants, which produced indistinguishable predictions on hitherto used statistics. Our results indicate that the likelihood approach is a promising framework for dynamical cognitive models.
KW - likelihood
KW - model fitting
KW - dynamical model
KW - eye movements
KW - model comparison
Y1 - 2017
U6 - https://doi.org/10.1037/rev0000068
SN - 0033-295X
SN - 1939-1471
VL - 124
IS - 4
SP - 505
EP - 524
PB - American Psychological Association
CY - Washington
ER -