Quantifying Uncertainty of the Estimated Visual Acuity Behavioral Function With Hierarchical Bayesian Modeling

Zhao, Yukai; Lesmes, Luis Andres; Dörr, Michael; Lü, Zhong-Lin

doi:10.1167/tvst.10.12.18

Cited by 18 publications

(23 citation statements)

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“…To double-check whether this is reasonable, we computed the covariance of the hyperparameters from their posterior distributions derived from the current HBPTM and did not find any significant covariances. The HBPTM can be extended by replacing the variances σ and δ with covariances ( Zhao, Lesmes, Dorr, & Lu, 2021 ; Zhao, Lesmes, Hou, & Lu, 2021 ).…”

Section: Discussionmentioning

confidence: 99%

Hierarchical Bayesian perceptual template modeling of mechanisms of spatial attention in central and peripheral cuing

Lü

Dosher

2023

Journal of Vision

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The external noise paradigm and perceptual template model (PTM) have successfully been applied to characterize observer properties and mechanisms of observer state changes (e.g. attention and perceptual learning) in several research domains, focusing on individual level analysis. In this study, we developed a new hierarchical Bayesian perceptual template model (HBPTM) to model the trial-by-trial data from all individuals and conditions in a published spatial cuing study within a single structure and compared its performance to that of a Bayesian Inference Procedure (BIP), which separately infers the posterior distributions of the model parameters for each individual subject without the hierarchical structure. The HBPTM allowed us to compute the joint posterior distribution of the hyperparameters and parameters at the population, observer, and experiment levels and make statistical inferences at all these levels. In addition, we ran a large simulation study that varied the number of observers and number of trials in each condition and demonstrated the advantage of the HBPTM over the BIP across all the simulated datasets. Although it is developed in the context of spatial attention, the HBPTM and its extensions can be used to model data from the external noise paradigm in other domains and enable predictions of human performance at both the population and individual levels.

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Section: Discussionmentioning

confidence: 99%

Hierarchical Bayesian perceptual template modeling of mechanisms of spatial attention in central and peripheral cuing

Lü

Dosher

2023

Journal of Vision

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“…One can also compare different data analytic techniques in terms of their ability to reduce uncertainty and generate expected information gain. 49,51…”

Section: Discussionmentioning

confidence: 99%

“…In Simulation 2, we simulated 1386 observers from the population distribution of VA threshold and VA range derived from an existing qVA dataset of 14 eyes tested with Bangerter foils. 18,49 . US 10758120B2): 17,18 p(𝑚|𝑠, 𝑀, 𝜃 𝑉𝐴 ) = 𝑓(𝑚, 𝑀, 𝑑 ′ (𝑠|𝜃 𝑉𝐴 )),…”

Section: Visual Acuity Testsmentioning

confidence: 99%

“…In Simulation 39 and the other of 14 eyes tested with Bangerter foils 18 , using a hierarchical Bayesian model. 49,51 Letter and Grating Contrast Sensitivity Functions. The letter contrast sensitivity function, which specifies contrast sensitivity 𝑆 𝑙𝑒𝑡𝑡𝑒𝑟 (𝑓) for filtered letters of different sizes at center spatial frequency 𝑓, can be described with a log parabola function with three parameters 𝜃 𝐶𝑆𝐹 = (𝜃 𝑃𝐺 𝐶𝑆𝐹 , 𝜃 𝑃𝐹 𝐶𝑆𝐹 , 𝜃 𝐵𝐻 𝐶𝑆𝐹 ):…”

Section: Contrast Sensitivity Testsmentioning

confidence: 99%

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Quantification of Expected Information Gain in Visual Acuity and Contrast Sensitivity Tests

Lü

Zhao

Lesmes

et al. 2023

Preprint

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We introduce expected information gain to quantify measurements and apply it to compare visual acuity (VA) and contrast sensitivity (CS) tests. We simulated observers with parameters covered by the visual acuity and contrast sensitivity tests and observers based on distributions of normal observers tested in three luminance and four Bangerter foil conditions. We first generated the probability distributions of test scores for each individual in each population in the Snellen, ETDRS and qVA visual acuity tests and the Pelli-Robson, CSV-1000 and qCSF contrast sensitivity tests and constructed the probability distributions of all possible test scores of the entire population. We then computed expected information gain by subtracting expected residual entropy from the total entropy of the population. For acuity tests, ETDRS generated more expected information gain than Snellen; scored with VA threshold only or with both VA threshold and VA range, qVA with 15 rows (or 45 optotypes) generated more expected information gain than ETDRS. For contrast sensitivity tests, CSV-1000 generated more expected information gain than Pelli-Robson; scored with AULCSF or with CS at six spatial frequencies, qCSF with 25 trials generated more expected information gain than CSV-1000. The active learning based qVA and qCSF tests can generate more expected information than the traditional paper chart tests. Although we only applied it to compare visual acuity and contrast sensitivity tests, information gain is a general concept that can be used to compare measurements and data analytics in any domain.

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“…1), which describes observer's performance accuracy in the optotype identi cation task as a function of optotype size. 21,22 It can be best described by a sigmoidal function determined by acuity threshold and slope. 23 In this study, we rst measured the acuity psychometric function of ten adults across 12 viewing conditions: monocularly (with the left or right eye) and binocularly with refractive errors corrected or uncorrected, and with the dominant eye and 6 levels of Bangerter Occlusion Foils (i.e., 0.1, 0.2, 0.3, 0.4, 0.6, 0.8).…”

Section: Introductionmentioning

confidence: 99%

Do the Scores from ETDRS and SLVA Charts Agree? An Analysis Based on the Acuity Psychometric Function

Cao¹,

Cheng²,

Lü³

et al. 2022

Preprint

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Objectives. To determine whether scores from the two most widely-used Early Treatment of Diabetic Retinopathy Study (ETDRS) and Standard for Logarithmic Visual Acuity (SLVA) acuity charts are comparable. Methods. Ten normal adults (24.9±1.9 years; 5 females) with normal (0.0 logMAR) or corrected-to-normal visual acuity (VA) participated in this study. The acuity psychometric function, the probability correct response in identifying the orientation of a tumbling E as a function of letter size, was measured using the Psi method. Each participant finished the test under 12 viewing conditions: monocularly (with the left or right eye) and binocularly with refractive errors corrected or uncorrected, and the dominant eye with 6 levels of Bangerter Occlusion Foils (i.e., 0.1, 0.2, 0.3, 0.4, 0.6, 0.8). Simulated tests with the ETDRS and SLVA charts were repeated 1000 times based on the fitted acuity psychometric functions.Results. The VA scores and probability correct from the ETDRS and SLVA charts were slightly but significantly different (mean difference of 0.018 logMAR and 5%, both P < 0.001). The agreement of the VA scores was excellent (0.997 [95% CI, 0.982-0.999]), while the probability correct was fair (0.453 [95% CI, 0.183-0.636]) between these two charts. The precision of the ETDRS chart (0.04 ± 0.00 logMAR) was significantly better (P < 0.001) than that of the SLVA chart (0.07 ± 0.00 logMAR).Conclusions. In clinical, even with different design principles and scoring rules, the ETDRS and SLVA charts produce comparable VA scores for normal adults with no pathological eye disease.

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Quantifying Uncertainty of the Estimated Visual Acuity Behavioral Function With Hierarchical Bayesian Modeling

Cited by 18 publications

References 70 publications

Hierarchical Bayesian perceptual template modeling of mechanisms of spatial attention in central and peripheral cuing

Hierarchical Bayesian perceptual template modeling of mechanisms of spatial attention in central and peripheral cuing

Quantification of Expected Information Gain in Visual Acuity and Contrast Sensitivity Tests

Do the Scores from ETDRS and SLVA Charts Agree? An Analysis Based on the Acuity Psychometric Function

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