Evaluating model misspecification in independent component analysis

<div><p>Independent component analysis (ICA) is a popular blind source separation technique used in many scientific disciplines. Current ICA approaches have focused on developing efficient algorithms under specific ICA models, such as instantaneous or convolutive mixing conditions, intrinsically assuming temporal independence or autocorrelation of the sources. In practice, the true model is not known and different ICA algorithms can produce very different results. Although it is critical to choose an ICA model, there has not been enough research done on evaluating mixing models and assumptions, and how the associated algorithms may perform under different scenarios. In this paper, we investigate the performance of multiple ICA algorithms under various mixing conditions. We also propose a convolutive ICA algorithm for echoic mixing cases. Our simulation studies show that the performance of ICA algorithms is highly dependent on mixing conditions and temporal independence of the sources. Most instantaneous ICA algorithms fail to separate autocorrelated sources, while convolutive ICA algorithms depend highly on the model specification and approximation accuracy of unmixing filters.</p></div

Ten Simple Rules for Effective Statistical Practice.

Several months ago, Phil Bourne, the initiator and frequent author of the wildly successful and incredibly useful “Ten Simple Rules” series, suggested that some statisticians put together a Ten Simple Rules article related to statistics. (One of the rules for writing a PLOS Ten Simple Rules article is to be Phil Bourne [1]. In lieu of that, we hope effusive praise for Phil will suffice.) Implicit in the guidelines for writing Ten Simple Rules [1] is “know your audience.” We developed our list of rules with researchers in mind: researchers having some knowledge of statistics, possibly with one or more statisticians available in their building, or possibly with a healthy do-it-yourself attitude and a handful of statistical packages on their laptops. We drew on our experience in both collaborative research and teaching, and, it must be said, from our frustration at being asked, more than once, to “take a quick look at my student’s thesis/my grant application/my referee’s report: it needs some input on the stats, but it should be pretty straightforward.” There are some outstanding resources available that explain many of these concepts clearly and in much more detail than we have been able to do here: among our favorites are Cox and Donnelly [2], Leek [3], Peng [4], Kass et al. [5], Tukey [6], and Yu [7]. Every article on statistics requires at least one caveat. Here is ours: we refer in this article to “science” as a convenient shorthand for investigations using data to study questions of interest. This includes social science, engineering, digital humanities, finance, and so on. Statisticians are not shy about reminding administrators that statistical science has an impact on nearly every part of almost all organizations.</p

Permutation histograms of t-statistics for two voxels.

<p>Permutation histograms of t-statistics for two voxels.</p

P-value histogram from a group-level test.

<p>P-value histogram from a group-level test.</p

Anatomy of the HRF.

<p>Anatomy of the HRF.</p

Stimulus vectors for an event-related design (top) and a block design (bottom).

<p>The spikes correspond to the onsets of stimuli. There is a sustained period of activity/task in the block design. In both cases, the spacings between events can be unequal.</p

Resting state fMRI image for 1 subject.

<p>The top panel shows one axial slice from the 3D image acquared at each of the 152 time points. denotes a voxel in the brain with coordinates [46, 64, 37]. The plot below shows the intensity of the image at voxel (on the y-axis) at each time point (the x-axis corresponds to time).</p

A slice of the thresholded output map overlaid on a template brain using the image() function.

<p>A slice of the thresholded output map overlaid on a template brain using the image() function.</p

The default brain network obtained via fastICA and overlaid on a template brain.

<p>The default brain network obtained via fastICA and overlaid on a template brain.</p

A slice of the fMRI image plotted by using the image() function in R (left) along with the corresponding smoothed slice (right).

<p>Here the red color corresponds to high intensity values, followed by yellow and white as the values decrease.</p