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In the context of fundamental flow studies, experimental databases are expected to provide uncertainty margins on the measured quantities. With the rapid increase in available computational power and the development of high-resolution fluid simulation techniques, Direct Numerical Simulation and Large Eddy Simulation are increasingly used in synergy with experiments to provide a complementary view. Moreover, they can access statistical moments of the flow variables for the development, calibration, and validation of turbulence models. In this context, the quantification of statistical errors is also essential for numerical studies. Reliable estimation of these errors poses two challenges. The first challenge is the very large amount of data: the simulation can provide a large number of quantities of interest (typically about 180 quantities) over the entire domain (typically 100 million to 10 billion of degrees of freedom per equation). Ideally, one would like to quantify the error for each quantity at any point in the flow field. However, storing a long-term sequence of signals from many quantities over the entire domain for a posteriori evaluation is prohibitively expensive. The second challenge is the short time step required to resolve turbulent flows with DNS and LES. As a direct consequence, consecutive samples within the time series are highly correlated. To overcome both challenges, a novel economical co-processing approach to estimate statistical errors is proposed, based on a recursive formula and the rolling storage of short-time signals. [ABSTRACT FROM AUTHOR]

The nonparametric bootstrap has been used in cluster analysis for various purposes. One of those purposes is to account for sampling variability. This can be achieved by obtaining a bootstrap approximation of the sampling distribution function of the estimator of interest and then clustering those distribution functions. Although the consistency of the nonparametric bootstrap in estimating transformations of the sample mean has been known for decades, little is known about how it carries over to clustering. Here, we investigated this problem with a simulation study. We considered single-linkage agglomerative hierarchical clustering and a three-type branching process for parametrized transformations of random vectors of relative frequencies of possible types of the index case of each process. In total, there were nine factors and 216 simulation scenarios in a fully-factorial design. The ability of the bootstrap-based clustering to recover the ground truth clusterings was quantified by the adjusted transfer distance between partitions. The results showed that in the best 18 scenarios, the average value of the distance was less than 20 percent of the maximum possible distance value. We noticed that the results most notably depended on the number of retained clusters, the distribution for sampling the prevalence of types, and the sample size appearing in the denominators of relative frequency types. The comparison of the bootstrap-based clustering results with so-called uninformed random partitioning results showed that in the vast majority of scenarios considered, the bootstrap-based approach led, on average, to remarkably lower classification errors than the random partitioning. [ABSTRACT FROM AUTHOR]

The problem of testing random number generators is considered and a new method for comparing the power of different statistical tests is proposed. It is based on the definitions of random sequence developed in the framework of algorithmic information theory and allows comparing the power of different tests in some cases when the available methods of mathematical statistics do not distinguish between tests. In particular, it is shown that tests based on data compression methods using dictionaries should be included in test batteries. [ABSTRACT FROM AUTHOR]