Markov models for sequences of microsaccades
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1
University of Potsdam, Department of Mathematics, Germany
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2
University of Potsdam, Department of Psychology, Germany
While fixating our eyes perform small, erratic eye movements. These so called fixational eye movements (FEM) are classified in tremor, drift, and microsaccades. However, this classification seems incomplete if we account for the possible different shapes and sequences of microsaccades observed during fixation. Over the last decades, the term saccadic intrusion (SI) has been introduced as a fourth type of FEM (Abadi et al. (2000), Vision Research, 40:2813-2829; Abadi & Gowen (2004), Vision Research, 44:2675-2690). The most prominent SI is a monophasic square wave intrusion that is also often referred to as square-wave jerk. This type of SI is a sequence of two saccades separated by a short time interval. Projected on the horizontal direction of movement, the first saccade drives the eye away from the initial position and the second corrective movement returns the eyes back. Whether SIs represent an independent new component of FEM is an ongoing discussion.
In this work, we use a novel method to investigate the statistical dependence of sequences of microsaccades. Our method exploits a recently developed wavelet-based microsaccade detection algorithm and a symbolic dynamics approach (Bettenbühl et al. (2010), Journal of Eye Movement Research, 3(5):1, 1-14). In contrast to previous studies, we neglect temporal proximity of saccadic events during fixation. Consequently, we describe the sequences of microsaccade directions as realizations of a stationary discrete Markov process. Using Bayesian inference, we estimate the order of the Markov chain (i.e., the length of the memory in the sequence of microsaccade directions) with an exact measure, the Bayes factor. Monte Carlo simulations confirmed that our method reliably estimates the order of a Markov process from its realizations.
Our investigation suggests that the observed sequences of microsaccade directions are best described by a first-order Markov process. This finding indicates that at each position in the sequence a microsaccade direction depends only on the previous one. Consistent with such a dynamical model, the most common type of SIs, the square-wave jerk, and single microsaccades appear to be events generated by the same process. Our rigorous statistical treatment lends support to the earlier interpretation “that fixational saccades and SIs are generated by the same neural circuit” (Otero-Millan et al. (2010), Journal of Neuroscience, 31(12), p. 4379).
Keywords:
Bayesian inference,
fixational eye movements,
Markov chain,
mathematical modeling,
microsaccades,
stochastic process
Conference:
BC11 : Computational Neuroscience & Neurotechnology Bernstein Conference & Neurex Annual Meeting 2011, Freiburg, Germany, 4 Oct - 6 Oct, 2011.
Presentation Type:
Poster
Topic:
motor control (please use "motor control" as keyword)
Citation:
Bettenbühl
M,
Rusconi
M,
Engbert
R and
Holschneider
M
(2011). Markov models for sequences of microsaccades.
Front. Comput. Neurosci.
Conference Abstract:
BC11 : Computational Neuroscience & Neurotechnology Bernstein Conference & Neurex Annual Meeting 2011.
doi: 10.3389/conf.fncom.2011.53.00160
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Received:
22 Aug 2011;
Published Online:
04 Oct 2011.
*
Correspondence:
Mr. Mario Bettenbühl, University of Potsdam, Department of Mathematics, Potsdam, Brandenburg, 14476, Germany, mario.bettenbuehl@uni-potsdam.de