![]() The common strategy is to construct a plausible explanatory model for the observed data, estimate the parameters of this model, and compute a suitable statistic for hypothesis testing on some or all of these parameters. Despite the variety, most of the strategies for statistical analysis can be formulated as a general linear model ( glm) ( Christensen, 2002 Scheffé, 1959 Searle, 1971). The field of neuroimaging has continuously expanded to encompass an ever growing variety of experimental methods, each of them producing images that have different physical and biological properties, as well as different information content. Detailed examples of common neuroimaging applications are provided, as well as a complete algorithm – the “randomise” algorithm – for permutation inference with the glm. We also demonstrate how the inference on glm parameters, originally intended for independent data, can be used in certain special but useful cases in which independence is violated. We present a generic framework for permutation inference for complex general linear models ( glms) when the errors are exchangeable and/or have a symmetric distribution, and show that, even in the presence of nuisance effects, these permutation inferences are powerful while providing excellent control of false positives in a wide range of common and relevant imaging research scenarios. In this paper we report on results on approximate permutation methods that are more flexible with respect to the experimental design and nuisance variables, and conduct detailed simulations to identify the best method for settings that are typical for imaging research scenarios. With the availability of fast and inexpensive computing, their main limitation would be some lack of flexibility to work with arbitrary experimental designs. Tested: Matlab 6.5, 7.7, 7.8, 32bit, WinXP,Ĭompiler: LCC 2.4/3.8, BCC 5.5, Open Watcom 1.8, MSVC 2008.Ĭompatibility to 64 bit, Linux and Mac is assumed.Permutation methods can provide exact control of false positives and allow the use of non-standard statistics, making only weak assumptions about the data. Run the unit-test TestShuffle to test validity and speed (see screenshot). The KISS random numbers are much better than the RAND() of the C-standard libs. This implementation is faster due to calling a compiled MEX file and it has a smaller memory footprint. Some use Knuth's method also, some call RANDPERM. NOTES: There are several other shuffle functions in the FEX. I = Shuffle(8, 'index') % UINT8()Ĭhoose 10 different rows from a 1000 x 100 matrix: A rejection method is used: Create an index vector until a derangement is gained. ![]() Index: elements of shuffled vector in the smallest possible integer type.Įquivalent to the index method, but all Index ~= i. This is equivalent to Matlab's RANDPERM, but much faster, if N is large and NOut is small. Create a shuffle index: Index = Shuffle(N, 'index', NOut) Y: Array of same type and size as X with shuffled elements.Ģ. Optional, default: 1st non-singleton dimension. X: DOUBLE, SINGLE, CHAR, LOGICAL, (U)INT64/32/16/8 array.ĭim: Dimension to operate on. While RANDPERM needs 2*LENGTH(X)*8 bytes as temporary memory, SHUFFLE needs just a fixed small number of bytes.ġ. Knuth's shuffle algorithm (also called Fisher-Yates) and the cute KISS random number generator (G. This function is equivalent to X(RANDPERM(LENGTH(X)), but 50% to 85% faster. Shuffle - Random permutation of array elements
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