Validazione statistica che, nelle ipotesi considerate, il numero dei conteggi ISS ottenuti via MD segue una distribuzione di Poisson

A stochastic scheme, namely, PLM-Lap, has recently been propounded, which relies on the profile likelihood (PL) constructed with a Laplace distribution for estimating muscle activation onsets (MAOs) in surface electromyographic (sEMG) data. The MAO detection accuracy and robustness of the PLM-Lap have been empirically shown to be better than those of several state-of-the-art approaches. The algorithm designates the data point index associated with the maximum of the PL function as an onset occurrence by regarding every sEMG data point as a candidate onset and hence exhaustively evaluating the objective function. This article concerns an expedient and faster approach premised on the discrete Fibonacci search (DFS) to locate the maximum of the discrete PL function. The experimental results support that both the exhaustive and DFS procedures are equivalent in a statistical sense, whereas the latter offers impressive computational savings by a factor of approximately 90. Owing to the speed-up, the accuracy of MAO estimation may further be enhanced by modeling the sEMG data with a set of PL functions, each one built using a suitable probability distribution, and picking the estimate from the best model. Three statistical criteria, i.e., Kolmogorov-Smirnov, Lilliefors, and Anderson-Darling test, for choosing the probability distribution are recommended. A freely downloadable MATLAB package, namely PROLIFIC, meant for sEMG onset detection is available on MATLAB File Exchange from the following link: https://www.mathworks.com/matlabcentral/fileexchange/76495-prolific-profile-likelihoodbased-on-fibonacci-search.

The Bayesian information criterion (BIC), the Akaike information criterion (AIC), and some other indicators derived from them are widely used for model selection. In their original form, they contain the likelihood of the data given the models. Unfortunately, in many applications, it is practically impossible to calculate the likelihood, and, therefore, the criteria have been reformulated in terms of descriptive statistics of the residual distribution: the variance and the mean-squared error of the residuals. These alternative versions are strictly valid only in the presence of additive noise of Gaussian distribution, not a completely satisfactory assumption in many applications in science and engineering. Moreover, the variance and the mean-squared error are quite crude statistics of the residual distributions. More sophisticated statistical indicators, capable of better quantifying how close the residual distribution is to the noise, can be profitably used. In particular, specific goodness of fit tests have been included in the expressions of the traditional criteria and have proved to be very effective in improving their discriminating capability. These improved performances have been demonstrated with a systematic series of simulations using synthetic data for various classes of functions and different noise statistics.

Modelling raindrop size distribution (DSD) is a fundamental issue to connect remote sensing observations with reliable precipitation products for hydrological applications. To date, various standard probability distributions have been proposed to build DSD models. Relevant questions to ask indeed are how often and how good such models fit empirical data, given that the advances in both data availability and technology used to estimate DSDs have allowed many of the deficiencies of early analyses to be mitigated. Therefore, we present a comprehensive follow-up of a previous study on the comparison of statistical fitting of three common DSD models against 2D-Video Distrometer (2DVD) data, which are unique in that the size of individual drops is determined accurately. By maximum likelihood method, we fit models based on lognormal, gamma and Weibull distributions to more than 42.000 1-minute drop-by-drop data taken from the field campaigns of the NASA Ground Validation program of the Global Precipitation Measurement (GPM) mission. In order to check the adequacy between the models and the measured data, we investigate the goodness of fit of each distribution using the Kolmogorov-Smirnov test. Then, we apply a specific model selection technique to evaluate the relative quality of each model. Results show that the gamma distribution has the lowest KS rejection rate, while the Weibull distribution is the most frequently rejected. Ranking for each minute the statistical models that pass the KS test, it can be argued that the probability distributions whose tails are exponentially bounded, i.e. light-tailed distributions, seem to be adequate to model the natural variability of DSDs. However, in line with our previous study, we also found that frequency distributions of empirical DSDs could be heavy-tailed in a number of cases, which may result in severe uncertainty in estimating statistical moments and bulk variables.

The aim of this article is to perform a statistical analysis of reactive oxygen species (ROS) cytometric data. It is demonstrated that the classical parametric and nonparametric statistical tests are not suitable to examine these data; the Kolmogorov-Smirnov test and the modification proposed by Lampariello are shown to be too sensitive with respect to the experimental bias (due to procedure or to the instrument) and variability in the ROS production within the repeated samples. Several approaches are examined and discussed. Modifications of the Lampariello's procedure are proposed to include the variability within samples. The validity of the proposed approach is verified by analyzing repeated measurements of ROS formation in cultured human lymphocytes untreated or treated with ferrous sulfate. The proposed approach is successful in considering the "intersample" variability in the ROS data analysis and keeps a good level of validity. Nevertheless, this procedure is not user-friendly and needs to be handled by an expert operator.