Comments on a Monte Carlo approach to the analysis of functional neuroimaging data.

Functional neuroimaging is probably always going to be methodologically pluralistic. There are several reasons for this. For example, brain functions or processes can be characterized at different levels and scales, and it may be the case that there is no fundamental processing level but that different phenomena are optimally described at different scales or levels. Methods developed and validated at specific spatiotemporal scales and for certain parameter ranges (e.g., degrees of freedom, amount of filtering) may not be applicable at other spatiotemporal scales or parameter ranges. Furthermore, the rapid development in fMRI and MEG/EEG illustrates the need for descriptive, exploratory, and inferential methods. Descriptive and exploratory methods are useful in characterizing the nature of the signal that is present in the data, while inferential methods are used to test hypotheses and to determine confidence intervals. Basically, there are three inferential approaches to the analysis of functional imaging data: theoretical parametric (e.g., Friston et al., 1995; Worsley et al., 1992, 1996) approaches, nonparametric approaches (e.g., Holmes et al., 1996), and Monte Carlo or simulation approaches (e.g., Forman et al., 1995; Poline and Mazoyer, 1993). These approaches differ in the assumptions made about the properties of data and the approximations used in their statistical analyses. What is of importance is not the number of assumptions or the characteristics of the approximations made, but how well these assumptions and approximations are fulfilled by empirical data and the robustness of the method if the assumptions are not fully met. This notion emphasizes the importance of empirical validation and explicit characterization of the inherent limitations of a given method. Progress in and the credibility of a scientific field are critically dependent on the long-term consistency and convergence of empirical results. Discussion and critical evaluation of the methods used in a given scientific field are of vital importance in this process. An example of such a critical evaluation and discussion is summarized below. Recently, functional neuroimaging studies have been published in Nature (Geyer et al., 1996), Science (Kinomura et al., 1996), and the Proceedings of the National Academy of Sciences of the USA (Roland et al., 1998) using a cluster analysis method described by Roland et al. (1993). This method has been criticized by Frackowiak et al. (1996) and subsequently defended by Roland and Gulyas (1996). In this issue of NeuroImage, Roland and colleagues (Ledberg et al., 1998) return to some of the issues previously raised. Ledberg et al. (1998) describe a revised version of the Roland et al. (1993) method acknowledging the critique of Frackowiak et al. (1996). This illustrates the importance of proper empirical validation of any proposed method before it is accepted and applied to experimental data. The constructive result of this critical evaluation is the significant improvement of the method (Ledberg et al., 1998). The reason for the closer examination of the Roland et al. (1993) method and the consequent discussion in the European Journal of Neuroscience was diverging results and interpretations of data relating to the functional neuroanatomy of vision, in particular color perception (Frackowiak et al., 1996). Two general topics are at issue. The first relates to the functional anatomy of vision, which is not discussed in Ledberg et al. (1998) and will not be discussed here. The second issue relates to methodology and is independent of the first, whereas conclusions about the functional anatomy of vision are most certainly dependent on the method used. A Monte Carlo approach to the analysis of PET data using cluster size as the test statistic was proposed by Poline and Mazoyer (1993). A similar approach has been applied to the analysis of fMRI data (Forman et al., 1995). In general, Monte Carlo approaches are critically dependent on adequately characterizing the image noise, using sufficient numbers of simulated realizations (since the tails of the observed probability NEUROIMAGE 8, 108–112 (1998) ARTICLE NO. NI980375