Mixtures of peaked power Batschelet distributions for circular data with application to saccade directions

Mulder, Kees; Klugkist, Irene; Renswoude, Daan van; Visser, Ingmar

doi:10.1016/j.jmp.2019.102309

Cited by 6 publications

(8 citation statements)

References 48 publications

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“…Potential model misspecification could also arise from modeling the horizontal bias. It has been shown that von Mises distribution is not necessarily optimal for describing the distribution of the saccade angles, due to the fact that the real distributions of saccade angles are typically more peaked than what von Mises distribution allows (Mulder et al, 2020). We used the von Mises distribution because it is relatively well known and can be fitted easily in Stan, whereas alternative distributions—such as the power Batchelet distribution as proposed by Mulder et al (2020)—would make the implementation much more complicated.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…It has been shown that von Mises distribution is not necessarily optimal for describing the distribution of the saccade angles, due to the fact that the real distributions of saccade angles are typically more peaked than what von Mises distribution allows (Mulder et al, 2020). We used the von Mises distribution because it is relatively well known and can be fitted easily in Stan, whereas alternative distributions—such as the power Batchelet distribution as proposed by Mulder et al (2020)—would make the implementation much more complicated. A second potential misspecification of the horizontal bias could be that the current implementation assumes that at any point in time, it is equally likely to make a saccade to the left direction as to right direction.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Section: Extensions and Future Directionsmentioning

confidence: 99%

“…We used the von Mises distribution because it is relatively well known and can be fitted easily in Stan, whereas alternative distributions -such as the power Batchelet distribution as proposed by Mulder et al (2020) -would make the implementation much more complicated. A second potential misspecification of the horizontal bias could be that the current implementation assumes that at any point in time, it is equally likely to make a saccade to the left direction as to right direction.…”

Section: Extensions and Future Directionsmentioning

confidence: 99%

See 3 more Smart Citations

WALD-EM: Wald accumulation for locations and durations of eye movements.

Kucharský¹,

Renswoude²,

Raijmakers³

et al. 2021

Psychological Review

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Describing, analyzing and explaining patterns in eye movement behavior is crucial for understanding visual perception. Further, eye movements are increasingly used in informing cognitive process models. In this article, we start by reviewing basic characteristics and desiderata for models of eye movements. Specifically, we argue that there is a need for models combining spatial and temporal aspects of eye-tracking data (i.e., fixation durations and fixation locations), that formal models derived from concrete theoretical assumptions are needed to inform our empirical research, and custom statistical models are useful for detecting specific empirical phenomena that are to be explained by said theory.In this article, we develop a conceptual model of eye movements, or specifically, fixation durations and fixation locations, and from it derive a formal statistical model -meeting our goal of crafting a model useful in both the theoretical and empirical research cycle. We demonstrate the use of the model on an example of infant natural scene viewing, to show that the model is able to explain different features of the eye movement data, and to showcase how to identify that the model needs to be adapted if it does not agree with the data. We conclude with discussion of potential future avenues for formal eye movement models.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Section: Conclusion and Discussionmentioning

confidence: 99%

Section: Extensions and Future Directionsmentioning

confidence: 99%

Section: Extensions and Future Directionsmentioning

confidence: 99%

See 2 more Smart Citations

WALD-EM: Wald accumulation for locations and durations of eye movements.

Kucharský¹,

Renswoude²,

Raijmakers³

et al. 2021

Psychological Review

Self Cite

View full text Add to dashboard Cite

show abstract

“…More generally, Holzmann et al (2004) established conditions for the identifiability of mixtures of location-scale extensions of wrapped circular models including the wrapped symmetric α-stable, wrapped normal, and WC distributions. Mixtures with circular triangular (McVinish and Mengersen 2008), skew-rotationally symmetric (Miyata et al 2020), and power Batschelet (Mulder et al 2020b) components have also been considered.…”

Section: Circular Modelsmentioning

confidence: 99%

Recent advances in directional statistics

Pewsey

García‐Portugués

2021

TEST

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Mainstream statistical methodology is generally applicable to data observed in Euclidean space. There are, however, numerous contexts of considerable scientific interest in which the natural supports for the data under consideration are Riemannian manifolds like the unit circle, torus, sphere, and their extensions. Typically, such data can be represented using one or more directions, and directional statistics is the branch of statistics that deals with their analysis. In this paper, we provide a review of the many recent developments in the field since the publication of Mardia and Jupp (Wiley 1999), still the most comprehensive text on directional statistics. Many of those developments have been stimulated by interesting applications in fields as diverse as astronomy, medicine, genetics, neurology, space situational awareness, acoustics, image analysis, text mining, environmetrics, and machine learning. We begin by considering developments for the exploratory analysis of directional data before progressing to distributional models, general approaches to inference, hypothesis testing, regression, nonparametric curve estimation, methods for dimension reduction, classification and clustering, and the modelling of time series, spatial and spatio-temporal data. AnWe are most grateful to three anonymous referees and, in alphabetical order, to

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Virtual reality (VR) as a testing bench for consumer optical solutions: a machine learning approach (GBR) to visual comfort under simulated progressive addition lenses (PALs) distortions

García García,

Sauer,

Watson

et al. 2024

Virtual Reality

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For decades, manufacturers have attempted to reduce or eliminate the optical aberrations that appear on the progressive addition lens’ surfaces during manufacturing. Besides every effort made, some of these distortions are inevitable given how lenses are fabricated, where in fact, astigmatism appears on the surface and cannot be entirely removed, or where non-uniform magnification becomes inherent to the power change across the lens. Some presbyopes may refer to certain discomfort when wearing these lenses for the first time, and a subset of them might never adapt. Developing, prototyping, testing and purveying those lenses into the market come at a cost, which is usually reflected in the retail price. This study aims to test the feasibility of virtual reality (VR) for testing customers’ satisfaction with these lenses, even before getting them onto production. VR offers a controlled environment where different parameters affecting progressive lens comforts, such as distortions, image displacement or optical blurring, can be inspected separately. In this study, the focus was set on the distortions and image displacement, not taking blur into account. Behavioural changes (head and eye movements) were recorded using the built-in eye tracker. We found participants were significantly more displeased in the presence of highly distorted lens simulations. In addition, a gradient boosting regressor was fitted to the data, so predictors of discomfort could be unveiled, and ratings could be predicted without performing additional measurements.

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Mixtures of peaked power Batschelet distributions for circular data with application to saccade directions

Cited by 6 publications

References 48 publications

WALD-EM: Wald accumulation for locations and durations of eye movements.

WALD-EM: Wald accumulation for locations and durations of eye movements.

Recent advances in directional statistics

Virtual reality (VR) as a testing bench for consumer optical solutions: a machine learning approach (GBR) to visual comfort under simulated progressive addition lenses (PALs) distortions

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