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Mark Pitt, Hairong Gu, Fang Hou, Woojae Kim, Zhong-Lin Lu, Jay Myung; Hierarchical Bayesian adaptive estimation of the contrast sensitivity function: Part II -- effect of type of prior. Invest. Ophthalmol. Vis. Sci. 2015;56(7 ):3898.
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© ARVO (1962-2015); The Authors (2016-present)
The contrast sensitivity function (CSF) characterizes spatial vision in both normal and clinical populations. The quick CSF method (Lesmes, et al, 2010) measures CSF precisely in only a few trials. Kim et al. (2014) introduced a hierarchical Bayesian framework in which adaptive estimation of the CSF can be further accelerated and improved by using prior knowledge (e.g., parameter estimates) from previously tested participants. The current experiment explored how the specification of priors influences adaptive estimation by comparing conditions in which the priors varied from correctly specified to incorrectly specified.
Priors were created from parameter estimates from a study in which the CSF of 100 observers with normal vision were measured using the quick CSF procedure in a 10AFC letter identification task under three viewing conditions: no filter (Normal), weak neutral density filter (ND1, 78.8% attenuation) and strong neutral density filter (ND2, 97.2% attenuation). In the current study, 10 participants were tested with quick CS in the Normal viewing condition three times, each using a different prior: Normal (correctly specified), ND2 (misspecified) and a mixture prior consisting of equal parts Normal, ND1, and ND2. Diffuse priors (no prior knowledge) were used in a control condition.
The root mean squared error (RMSE) of the Area Under the log CSF (AULCSF) was calculated across trials for each participant in all conditions using the estimated true AULCSF, obtained after 100 trials in an additional diffuse condition. Aggregate data over the first ten trials showed that, when compared to results in the diffuse condition, estimation error in the ND2 (misspecified) condition decreased by 0.41dB. The Normal (correctly specified) prior condition yielded the greatest improvement (7.80 dB) over the diffuse condition. Surprisingly, the mixture prior showed a significant benefit (4.24 dB drop). Estimates improved for all conditions as trials accumulated, with differences among them being almost indistinguishable by trial 50.
Prior knowledge can influence the accuracy and efficiency of adaptive CSF measurement. A correctly specified prior can greatly improve estimation, but a misspecified prior is comparable to a diffuse prior. When the prior is unknown, a mixture prior is a smart choice, providing significant benefit without cost.
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