The growth in the use of computationally intensive statistical procedures, especially with Big Data, has necessitated the usage of parallel computation on diverse platforms such as multicore, GPU, clusters and clouds. However, slowdown due to interprocess communication costs typically limits such methods to "embarrassingly parallel" (EP) algorithms, especially on non-shared memory platforms. This paper develops a broadly-applicable method for converting many non-EP algorithms into statistically equivalent EP ones. The method is shown to yield excellent levels of speedup for a variety of statistical computations. It also overcomes certain problems of memory limitations.
@cite_0 developed a bootstrap approach related to CA, based on applying the bootstrap method to a number of small random subsamples of the original data. Since any bootstrap method requires the user to choose the values of hyperparameters''---size and numbers of subsamples---the authors proposed an adaptive method to choose these parameters. They derived some asymptotic results, but also noted that their method will fail in settings in which the ordinary bootstrap fails. On the other hand, they indicated how their method can be used for time series data, something other CA methods have not yet been extended to.
@cite_0
2002917158
It is a common practice to use resampling methods such as the bootstrap for calculating the p-value for each test when performing large scale multiple testing. The precision of the bootstrap p-values and that of the false discovery rate (FDR) relies on the number of bootstraps used for testing each hypothesis. Clearly, the larger the number of bootstraps the better the precision. However, the required number of bootstraps can be computationally burdensome, and it multiplies the number of tests to be performed. Further adding to the computational challenge is that in some applications the calculation of the test statistic itself may require considerable computation time. As technology improves one can expect the dimension of the problem to increase as well. For instance, during the early days of microarray technology, the number of probes on a cDNA chip was less than 10,000. Now the Affymetrix chips come with over 50,000 probes per chip. Motivated by this important need, we developed a simple adaptive bootstrap methodology for large scale multiple testing, which reduces the total number of bootstrap calculations while ensuring the control of the FDR. The proposed algorithm results in a substantial reduction in the number of bootstrap samples. Based on a simulation study we found that, relative to the number of bootstraps required for the Benjamini-Hochberg (BH) procedure, the standard FDR methodology which was the proposed methodology achieved a very substantial reduction in the number of bootstraps. In some cases the new algorithm required as little as 1 6th the number of bootstraps as the conventional BH procedure. Thus, if the conventional BH procedure used 1,000 bootstraps, then the proposed method required only 160 bootstraps. This methodology has been implemented for time-course dose-response data in our software, ORIOGEN, which is available from the authors upon request.