Statistical inference for eye movement sequences using spatial and spatio-temporal point processes

Abstract

Eye tracking is a widely used method for recording eye movements, which are important indicators of ongoing cognitive processes during the viewing of a target stimulus. Despite the variety of applications, the analyses of eye movement data have been lacking of methods that could take both the spatial and temporal information into account. So far, most of the analyses are based on strongly aggregated measures, because eye movement data are considered to be complex due to their richness and large variation between and within the individuals. Therefore, the eye movement methodology needs new statistical tools in order to take full advantage of the data. This dissertation is among the first studies to employ point process statistics for eye movement data in order to understand its spatial nature together with the temporal dynamics. Here, we consider eye movements as a realisation of a spatio-temporal point process. The emphasis is in statistical inference on eye movements using existing point process statistics along with the new methods and models introduced in this work. Our aim is to get understanding of eye movements as a temporally evolving process in space. This objective is achieved in four steps: First, we apply the second-order characteristics of point processes to describe features of the process. Second, we develop new functional summary statistics in order to evaluate the temporal nature of the eye movements. Third, we use likelihood-based modelling to assess the uncertainty related to these data summaries. Fourth, the developed models are used both for group comparisons and for distinguishing components in an eye movement sequence. The empirical results of this dissertation give new information on visual processing of paintings. We find evidence that the viewing process of one subject changes during the inspection of the painting being an indication of learning. The behaviour of this learning effect, however, varies between the individuals. We also study differences between novices and non-novices in art viewing by comparing where they look at and for how long the gaze typically stops. The latter distinguishes the two groups, whereas the former reveals minor differences that are not statistically significant. Altogether, we hope that our results encourage researchers to pay more attention to temporal dynamics in eye movement data, as well as to the inevitable variation in the individual level. The spatio-temporal analysis of eye movements presented here is novel and covers a wide range of methods from functional summary statistics to the likelihood-based modelling. The methods and tools presented are applicable to other eye movement data collected in a freeviewing condition, but we believe that the developed models, being rather simple but flexible, could also be useful for the analysis of spatio-temporal sequences outside the field.