The proposal of evaluating the uncertainty type A of the stationary random component of measured signal from its regularly sampled observations (auto-correlated) is presented. In the first step the regularly variable components of the signal are indentified and removed from the raw sample data. Then upgraded formulas for standard uncertainty type A of the sample and of the mean value are expres...

A method based on canonical correlation analysis (CCA) for solving the blind source (BSS) problem is presented. In contrast to independent components analysis (ICA), the proposed method utilises the autocorrelation in the source signals. This makes the BSS problem easier to solve than if only the statistical distribution of the sample values is considered. Experiments show that the method is mu...

We derive the statistical limit of the spectral autocorrelation function and of the survival probability for the indirect photodissociation of molecules in the regime of non-overlapping resonances. The results are derived in the framework of random matrix theory, and hold more generally for any chaotic quantum system that is weakly coupled to the continuum. The “correlation hole” that character...

For some time I have wondered why graphical methods for categorical data are so poorly developed and little used compared with methods for quantitative data. For quantitative data, graphical methods are commonplace adjuncts to all aspects of statistical analysis, from the basic display of data in a scatterplot, to diagnostic methods for assessing assumptions and finding transformations, to the ...

Like many numerical methods, solvers for initial value problems (IVPs) on ordinary differential equations estimate an analytically intractable quantity, using the results of tractable computations as inputs. This structure is closely connected to the notion of inference on latent variables in statistics. We describe a class of algorithms that formulate the solution to an IVP as inference on a l...

The detection and characterization of self-organized criticality (SOC), in both real and simulated data, has undergone many significant revisions over the past 25 years. The explosive advances in the many numerical methods available for detecting, discriminating, and ultimately testing, SOC have played a critical role in developing our understanding of how systems experience and exhibit SOC. In...

Dealing with several structures of different complexities, we adopt various strategies to extract information. The general idea is to find appropriate tools to analyze the variation of the corresponding autocorrelation functions. First, for homogeneous media under different conditions, we recover, in a statistical way, a relationship between porosity and the autocorrelation function. Then, for ...

Description Package for assessing the statistical significance of periodic expression based on Fourier analysis and comparison with data generated by different background models License GPL-2 Index 8 ar1analysis Performs AR1 fitting Description Calculation of the autocorrelation coefficients genes and variance of corresponding random variables to fit gene expression time series by AR1 processes...

Most machine learning, data mining and statistical methods rely on the assumption that the analyzed data points are independent and identically distributed (i.i.d.). More specifically, the individual examples included in the training data are assumed to be drawn independently from each other from the same probability distribution. However, cases where this assumption is violated can be easily f...