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Hairong Gu, Woojae Kim, Fang Hou, Zhong-Lin Lu, Mark Pitt, Jay Myung; Hierarchical Bayesian adaptive estimation of the contrast sensitivity function: Part I - effect of sample size. Invest. Ophthalmol. Vis. Sci. 2015;56(7 ):3897.
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© ARVO (1962-2015); The Authors (2016-present)
Lesmes et al (2010) developed a Bayesian adaptive method for accurately and efficiently measuring the contrast sensitivity function (CSF). Kim et al (2013) recently proposed a hierarchical Bayesian extension, dubbed hierarchical adaptive design optimization (HADO), that provides a judicious way to exploit prior information gained from past experiments to achieve even greater efficiency. The purpose of the present study is to evaluate the benefits and validity of HADO in both human and simulated experiments.
We first conducted a 10AFC letter identification experiment with 100 subjects using the quick CSF method of Lesmes et al (2010) and used the data to construct informative priors. We varied the amount of information in the priors by using four different numbers of subjects (5, 12, 30,100) included in the prior construction. We then repeated the experiment with 10 new subjects using the four priors. Performance of the CSF estimation was compared between these different prior conditions, and also against the quick CSF method with a diffuse prior. The same HADO procedure was carried out in Monte Carlo simulations as well to take the effect of sampling error into account.
Figure 1 shows root-mean-squared-error (RMSE) plots of the area-under-the-log-CSF (AULCSF) averaged across all 10 subjects as a function of trial number. The results showed that the informative priors increased the efficiency by lowering the RMSE at a certain number of trials. From the diffuse prior, for comparison, the reduction of RMSE for sample size 5 and 12 averaging over the first 10 trials is about 6.47 dB and the reduction for sample size 30 and 100 is about 10.72 dB. The errors decreased for all priors as the trials accumulated, with the differences among them being indistinguishable at trial 50. Essentially the same (but less noisy) pattern of results was obtained in simulated experiments.
Using well-informed priors in HADO shows higher efficiency in estimating CSF than using the non-informative, diffuse prior in the standard adaptive method. The advantage is considerable even when a small number of subjects are available for constructing the prior. Increasing the sample size brings further but small advantage, which can still be beneficial in clinical settings.
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