@article{NueskenPavhotis2019,
  author    = {N{\"u}sken, Nikolas and Pavhotis, Grigorios A.},
  title     = {Constructing Sampling Schemes via Coupling},
  series = {SIAM ASA journal on uncertainty quantification / Society for Industrial and Applied Mathematics ; American Statistical Association},
  volume    = {7},
  journal   = {SIAM ASA journal on uncertainty quantification / Society for Industrial and Applied Mathematics ; American Statistical Association},
  number    = {1},
  publisher = {Society for Industrial and Applied Mathematics},
  address   = {Philadelphia},
  issn      = {2166-2525},
  doi       = {10.1137/18M119896X},
  pages     = {324 -- 382},
  year      = {2019},
  abstract  = {In this paper we develop a general framework for constructing and analyzing coupled Markov chain Monte Carlo samplers, allowing for both (possibly degenerate) diffusion and piecewise deterministic Markov processes. For many performance criteria of interest, including the asymptotic variance, the task of finding efficient couplings can be phrased in terms of problems related to optimal transport theory. We investigate general structural properties, proving a singularity theorem that has both geometric and probabilistic interpretations. Moreover, we show that those problems can often be solved approximately and support our findings with numerical experiments. For the particular objective of estimating the variance of a Bayesian posterior, our analysis suggests using novel techniques in the spirit of antithetic variates. Addressing the convergence to equilibrium of coupled processes we furthermore derive a modified Poincare inequality.},
  language  = {en}
}
@misc{Tschisgale2020,
  type      = {Master Thesis},
  author    = {Tschisgale, Paul},
  title     = {Introduction to the Glauber dynamics for the Curie-Weiss Potts model},
  doi       = {10.25932/publishup-48676},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-486769},
  school      = {Universit{\"a}t Potsdam},
  pages     = {104},
  year      = {2020},
  abstract  = {This thesis aims at presenting in an organized fashion the required basics to understand the Glauber dynamics as a way of simulating configurations according to the Gibbs distribution of the Curie-Weiss Potts model. Therefore, essential aspects of discrete-time Markov chains on a finite state space are examined, especially their convergence behavior and related mixing times. Furthermore, special emphasis is placed on a consistent and comprehensive presentation of the Curie-Weiss Potts model and its analysis. Finally, the Glauber dynamics is studied in general and applied afterwards in an exemplary way to the Curie-Weiss model as well as the Curie-Weiss Potts model. The associated considerations are supplemented with two computer simulations aiming to show the cutoff phenomenon and the temperature dependence of the convergence behavior.},
  language  = {en}
}
@article{SeeligRabeMalemShinitskietal.2020,
  author    = {Seelig, Stefan A. and Rabe, Maximilian Michael and Malem-Shinitski, Noa and Risse, Sarah and Reich, Sebastian and Engbert, Ralf},
  title     = {Bayesian parameter estimation for the SWIFT model of eye-movement control during reading},
  series = {Journal of mathematical psychology},
  volume    = {95},
  journal   = {Journal of mathematical psychology},
  publisher = {Elsevier},
  address   = {San Diego},
  issn      = {0022-2496},
  doi       = {10.1016/j.jmp.2019.102313},
  pages     = {32},
  year      = {2020},
  abstract  = {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.},
  language  = {en}
}
@phdthesis{Seelig2021,
  author    = {Seelig, Stefan},
  title     = {Parafoveal processing of lexical information during reading},
  doi       = {10.25932/publishup-50874},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-508743},
  school      = {Universit{\"a}t Potsdam},
  pages     = {xi, 113},
  year      = {2021},
  abstract  = {During sentence reading the eyes quickly jump from word to word to sample visual information with the high acuity of the fovea. Lexical properties of the currently fixated word are known to affect the duration of the fixation, reflecting an interaction of word processing with oculomotor planning. While low level properties of words in the parafovea can likewise affect the current fixation duration, results concerning the influence of lexical properties have been ambiguous (Drieghe, Rayner, \& Pollatsek, 2008; Kliegl, Nuthmann, \& Engbert, 2006). Experimental investigations of such lexical parafoveal-on-foveal effects using the boundary paradigm have instead shown, that lexical properties of parafoveal previews affect fixation durations on the upcoming target words (Risse \& Kliegl, 2014). However, the results were potentially confounded with effects of preview validity. The notion of parafoveal processing of lexical information challenges extant models of eye movements during reading. Models containing serial word processing assumptions have trouble explaining such effects, as they usually couple successful word processing to saccade planning, resulting in skipping of the parafoveal word. Although models with parallel word processing are less restricted, in the SWIFT model (Engbert, Longtin, \& Kliegl, 2002) only processing of the foveal word can directly influence the saccade latency. Here we combine the results of a boundary experiment (Chapter 2) with a predictive modeling approach using the SWIFT model, where we explore mechanisms of parafoveal inhibition in a simulation study (Chapter 4). We construct a likelihood function for the SWIFT model (Chapter 3) and utilize the experimental data in a Bayesian approach to parameter estimation (Chapter 3 \& 4). The experimental results show a substantial effect of parafoveal preview frequency on fixation durations on the target word, which can be clearly distinguished from the effect of preview validity. Using the eye movement data from the participants, we demonstrate the feasibility of the Bayesian approach even for a small set of estimated parameters, by comparing summary statistics of experimental and simulated data. Finally, we can show that the SWIFT model can account for the lexical preview effects, when a mechanism for parafoveal inhibition is added. The effects of preview validity were modeled best, when processing dependent saccade cancellation was added for invalid trials. In the simulation study only the control condition of the experiment was used for parameter estimation, allowing for cross validation. Simultaneously the number of free parameters was increased. High correlations of summary statistics demonstrate the capabilities of the parameter estimation approach. Taken together, the results advocate for a better integration of experimental data into computational modeling via parameter estimation.},
  language  = {en}
}