Figure 1.
Illustration of microsaccade shape properties reported microsaccade sequence patterns.
(a) illustrates a typical microsaccade shape occurring during fixational eye movements with the designated microsaccade properties. (b) shows microsaccade sequence patterns, composed of one, two or three subsequent microsaccadic events, so-called saccadic intrusions (SI). From left: single saccadic pulse (SSP), double saccadic pulse (DSP), square-wave jerks (SWJ), biphasic square wave intrusion (BSWI). All patterns have been hand-picked from the horizontal trajectories of fixational eye movements. The separating time intervals are not representative for all participants.
Table 1.
Microsaccade properties and estimated Markov order.
Figure 2.
Horizontal FEM trajectory with detected microsaccades and illustration of the sequence of microsaccade directions.
(a) Trajectory of a 20 FEM trial with (upper panel) detected microsaccades and (lower panel) directions of microsaccades. (b) Sequence of microsaccade directions represented as discrete time series of binary states. For the analysis of microsaccade direction sequences, we neglect the temporal proximity existent in the sequence of microsaccades.
Figure 3.
Markov order estimation for sequences of simulated different order Markov chains.
Using a parameterization as zeroth-order Markov chain as null hypothesis, we compared in the Bayes factor the evidences against first-, second-, and third-order parameterization of Markov chain. We simulated sequences of: (a) uncorrelated random processes, (b) first-order Markov chain, and (c) second-order Markov chains, each of two symbols. In (a) we obtained support for zeroth-order parameterization, in (b) evidence against the null for all orders but highest with a first-order parameterization and (c) accordingly for a second-order parameterization. This validated the estimator to be correct.
Figure 4.
Markov order estimation for microsaccade sequences of nineteen participants in a fixation task experiment.
Using the zeroth-order parameterization of the Markov chain model as null hypothesis, we calculated the Bayes factor to separate that order which best described the sequences of microsaccade directions. (a) The thirteen participants show evidence of different strengths against the null hypothesis. Through parsimony, a first-order parameterization of the Markov chain would be estimated as best descriptor. (b) For six participants, support for zeroth- (left column) or second-order (right column) is estimated.
Figure 5.
Each box represents the transition matrix for each participants.
Participants are ordered as in Figure 4. The values are color-coded to facilitate reading. Only the transition matrix for a first order Markov chain is reported.