对比敏感度函数的非参贝叶斯估计

发布时间：2018-03-11 19:41

本文选题：心理物理学函数　切入点：高斯过程　出处：《中国科学技术大学》2016年博士论文　论文类型：学位论文

【摘要】：无论是在基础研究还是临床应用上,对比敏感度函数在预测被试者视觉功能上都有重要且不可替代的作用。研究发现对比敏感度函数可以解释为一个二维的心理物理学函数,进而可以采用比传统方法更高效的二维自适应贝叶斯方法进行估计。本研究中,我们首先研究如何采用二维贝叶斯估计通过行为学数据估计对比敏感度函数,这些数据由常见试验方法如阶梯法、普赛(Ψ)法、以及二维贝叶斯自适应方法。我们进行了大量的仿真(simulation)实验,并通过心理物理学实验验证实验结果。我们研究发现二维贝叶斯估计相比于心理物理学研究中常用的一维贝叶斯估计有更高的估计效率——可以在仅仅四分之一的采样数就能达到相同的估计精度。进一步地,我们比较了不同采样方法下,二维贝叶斯估计的效率。我们发现估计的效率及精确度相似,这提示传统的阶梯法、普赛法和现代的二维自适应方法的采样效率是类似的,而前人研究中的二维自适应方法的更高的估计效率主要来自于二维贝叶斯估计方法的使用,而不是更好的采样方法。心理物理学函数(Psychometric function,PF)描述了被试的反应如何随知觉刺激强度而变化,是心理物理学研究中的基本测量数据。一般地,该函数通过特定的数学模型如韦伯(Weibull)或逻辑斯特(Logistic)对实验数据拟合得到,这被称为有参(Model-based)方法。有参方法在模型正确定义时有很好的估计效率,但当模型错误时估计的效率和精度将明显降低。我们进一步提出了一种非参贝叶斯估计(model-free Bayesian inference)方法——高斯过程分类(Gaussian Processes Classification),来从行为学数据中估计心理物理学函数。这一非参方法仅仅假设了函数的连续性和平滑性,不做任何关于函数形状的假设。我们采用蒙特-卡洛(Monte-Carlo)仿真模拟该非参方法、传统的有参的最大似然法(maximum likelihood,ML)以及另一非参心理物理学方法——局部线性拟合法(local linear fitting,LLF),对一理想心理物理学函数进行估计。我们通过统计分析研究了通过该非参方法对心理物理学函数两个关键参数——阈值(threshold)和斜率(slope)——的估计精度,发现高斯过程分类方法在估计心理物理学函数时常常比其余两种方法精度和效率更高。我们最后将高斯过程分类扩展到对一种二维心理物理学函数——对比敏感度函数的估计与拟合中。通过蒙特卡洛仿真,我们大量的统计分析了高斯过程分类在估计对比敏感度的关键性质峰值增益(peak gain)、对数对比敏感度函数下面积(area under log contrast sentivity function,AULCSF)以及局部损伤(local deficits)时的精度和效率,并与传统二维最大似然法及一维估计方法进行比较,发现在估计正常人的CSF时,最大似然法精度略好于高斯过程分类,但估计有局部损伤的CSF时,最大似然法精度明显变差,而高斯过程分类依然保持着不错的估计精度。考虑到实际实验条件的复杂性以及高斯过程分类的可靠性和适应性,我们建议在测量对比敏感度时应用高斯过程分类方法。
[Abstract]:Whether it is in the basic research and clinical application, contrast sensitivity function was tested in the prediction of visual function has an important and irreplaceable role. The study found that contrast sensitivity function can be interpreted as a two-dimensional psychophysical function, which can be used for two-dimensional adaptive Bias method is more efficient than the traditional method of estimation. In this study, we first study how to use the two-dimensional Bias estimated by behavioral data to estimate the contrast sensitivity function, these data by common test methods such as gradient method, pusai (PSI) method, and two adaptive Vee Bias method. We have done a lot of simulation experiments (simulation), and verified by the experimental results of psychophysical experiments. We found that the two-dimensional Bias estimation compared to one-dimensional Bias in psychophysical studies commonly used estimation has higher estimation efficiency- Can achieve the same estimation accuracy in only 1/4 of the number of sampling can. Further, we compare the different sampling methods, the efficiency of two dimensional Bayesian estimation. We found that the efficiency and accuracy of estimation is similar, suggesting that the step of the traditional methods, the sampling efficiency of adaptive methods and modern Pusaifa is similar, but the higher the estimation efficiency of adaptive methods in previous studies mainly from two-dimensional Bayes estimation method is used, and the sampling method is not better. The psychophysical function (Psychometric function, PF) describes the subject's response to sensory stimuli with intensity changes, is the basic data in psychophysical studies. In general, this function through mathematics such as Webb model specific (Weibull) or (Logistic) logic of fitting the experimental data, this is called ginseng (Model- Based) method. Parametric method in model estimation when the correct definition of efficiency is very good, but when the efficiency and accuracy of estimation error of the model will be significantly reduced. We further propose a nonparametric Bayesian estimation method (model-free Bayesian inference) - Gauss (Gaussian Processes Classification) classification process, from behavioral psychophysics function estimation data. This method assumes that the only non parametric function continuity and smoothness, don't do anything about the shape of the function hypothesis. We use Monte Carlo (Monte-Carlo) simulation of the non parametric method, the traditional maximum likelihood parameters (maximum likelihood, ML) and other non participation psychophysical methods -- local linear fitting (local linear, fitting, LLF), to an ideal psychophysical function was estimated by statistical analysis. We studied the non parametric Methods two key parameters of psychophysical function threshold (threshold) and slope (slope) - estimation accuracy classification method in the estimation process found Gauss psychophysical function than the other two methods have higher precision and efficiency. Finally, we will process the expansion of the Gauss classification of a two-dimensional function estimation and fitting of psychophysics the contrast sensitivity function. Through Monte Carlo simulation, we analyzed a large number of Gauss classification in the estimation of key properties of gain peak contrast sensitivity (peak gain), the logarithm of the contrast sensitivity function (area under log contrast area under sentivity function, AULCSF) and local damage (local deficits) the accuracy and efficiency of the then, the method is compared with the maximum likelihood method and the traditional one-dimensional two-dimensional estimation, found in the estimation of normal CSF, accuracy of maximum likelihood method Slightly better than the Gauss classification, but it is estimated that local damage CSF, accuracy of maximum likelihood method was worse, but Gauss still maintained the estimation accuracy of classification is good. Considering the actual experimental conditions and the complexity of Gauss classification reliability and adaptability, we suggest in the measurement of contrast sensitivity when using the Gauss process classification method.

【学位授予单位】：中国科学技术大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O212.8

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