In the statistical analysis of fMRI data, the parameter of primary interest is the effect of a contrast; of secondary interest is its standard error, and of tertiary interest is the standard error of this standard error, or equivalently, the degrees of freedom (df). In a ReML (Restricted Maximum Likelihood) analysis, we show how spatial smoothing of temporal autocorrelations increases the effective df (but not the smoothness of primary or secondary parameter estimates), so that the amount of smoothing can be chosen in advance to achieve a target df, typically 100. This has already been done at the second level of a hierarchical analysis by smoothing the ratio of random to fixed effects variances (Worsley, K.J., Liao, C., Aston, J.A.D., Petre, V., Duncan, G.H., Morales, F., Evans, A.C., 2002. A general statistical analysis for fMRI data. NeuroImage, 15:1-15); we now show how to do it at the first level, by smoothing autocorrelation parameters. The proposed method is extremely fast and it does not require any image processing. It can be used in conjunction with other regularization methods (Gautama, T., Van Hulle, M.M., in press. Optimal spatial regularisation of autocorrelation estimates in fMRI analysis. NeuroImage.) to avoid unnecessary smoothing beyond 100 df. Our results on a typical 6-min, TR = 3, 1.5-T fMRI data set show that 8.5-mm smoothing is needed to achieve 100 df, and this results in roughly a doubling of detected activations.

译文

:在功能磁共振成像数据的统计分析中,主要关注的参数是对比度的影响;次要利益是其标准误差,三次利益是该标准误差的标准误差,或者等效地是自由度(df)。在ReML(受限最大似然)分析中,我们显示了时间自相关的空间平滑如何增加有效df(而不是主要或辅助参数估计的平滑度),因此可以提前选择平滑量以实现目标df,通常为100。通过平滑随机效应与固定效应方差的比率(Worsley,KJ,Liao,C.,Aston,JAD,Petre,V.,Duncan,GH ,Morales,F.,Evans,AC,2002. fMRI数据的一般统计分析(NeuroImage,15:1-15);我们现在展示如何通过平滑自相关参数在第一级上做到这一点。所提出的方法非常快,并且不需要任何图像处理。它可以与其他正则化方法结合使用(印刷中的Gautama,T.,Van Hulle,M.M.。fMRI分析中自相关估计的最佳空间正则化。NeuroImage),以避免超过100 df的不必要平滑。我们在典型的6分钟,TR = 3、1.5-T fMRI数据集上的结果表明,要达到100 df,需要8.5 mm的平滑处理,这导致检测到的激活次数大约增加了一倍。

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