演画像データ分析に対する古典的及びベイズ的アプローチ

The validity of F statistics for classical inference on imagingdata depends on the sphericity assumption. This assumption statesthat the difference between two measurement sets(e. g. those for two levels of a particular variable)has equal variance for all pairs of such sets. In practice this assumption can be violated in several different ways, for example, by differences in variance induced by different experimental conditions, and/or by serial correlations within imaging timeseries.<BR>A considerable literature exists in applied statistics that describes and compares various techniques for dealing with sphericity violation in the context of repeated measurements. The analysis techniques exploited by the Statistical Parametrical Mapping(SPM)package in released versions and those under development also employ a range of strategies for dealing with the variance structure of imaging data, but these have never been explicitly compared with more conventional approaches. In this work we will show how SPM'99compensates only for sphericity violations associated with serial correlations. It employs a correction to the degrees of freedom that is mathematically identical to that employed by the Greenhouse-Geisser univariate F-test. This correction is applied after a filtering stage which swamps the intrinsic auto-correlation with an imposed structure. It is the non-sphericity of this imposed structure which is then approximated using the degrees of freedom correction.<BR>More recent approaches that we have developed use a Parametric Empirical Bayesian(PEB)technique to estimate whichever variance components are of interest. This is equivalent to iterative Restricted Maximum Likelihood(ReML). In functional magnetic resonance imaging(fMRI)time series, for example, these would correspond to the variance of the white noise component as well as the variance of, for example, an AR<BR>(1)component. In a mixed effects analysis they would correspond to the within-subject variance(possibly different for each subject)and the between-subject variance. More generally, when the population of subjects consists of different groups, we may have different residual variance in each group. PEB partitions the overall degrees of freedom(e. g. total number of fMRI scans)in such a way as to ensure that the variance component estimates are unbiased. This takes place using a version of an Expectation-Maximisation(EM)procedure where the model coefficients and variance estimates are re-estimated iteratively.<BR>This theoretical discussion will be complemented by some illustrative data analysis, showing how sphericity violations vary in magnitude across voxels in actual imaging data.