Noise statistical tools

In order to generalize the noise 200 samples of the noises are taken and analyzed with a statistical tool. The amplitudes obtained are modeled by a Weibull Probability Density Function (PDF), as it is suggested for similar noises on ADSL analysis [15,16]. 

In this paper the PLS method was introduced as a new tool in calculating statistical receptor models. It was compared with the two most popular methods currently applied to aerosol data Chemical Mass Balance Model and Target Transformation Factor Analysis. The characteristics of the PLS solution were discussed and its advantages over the other methods were pointed out. PLS is especially useful, when both the predictor and response variables are measured with noise and there is high correlation in both blocks. It has been proved in several other chemical applications, that its performance is equal to or better than multiple, stepwise, principal component and ridge regression. Our goal was to create a basis for its environmental chemical application. 

Thus, multilinear models were introduced, and then a wide series of tools, such as nonlinear models, including artificial neural networks, fuzzy logic, Bayesian models, and expert systems. A number of reviews deal with the different techniques [4-6]. Mathematical techniques have also been used to keep into account the high number (up to several thousands) of chemical descriptors and fragments that can be used for modeling purposes, with the problem of increase in noise and lack of statistical robustness. Also in this case, linear and nonlinear methods have been used, such as principal component analysis (PCA) and genetic algorithms (GA) [6]. 

Accordingly, noise spectra are a strong diagnostic tool to trace the sources of noise, and to study the limitations stemming from different sources (source stability, atom reservoir stability, detector used, etc.). For instance, it will be important to see if the noise of the detector is predominant, as this type of noise can be described by Poisson statistics where ... 

An essential component of calculations is to calibrate new methods, and to use the results of calculations to predict or rationalize the outcome of experiments. Both of these types of investigation compare two types of data and the interest is in characterizing how well one set of data can represent or predict the other. Unfortunately, one or both sets of data usually contain noise , and it may be difficult to decide whether a poor correlation is due to noisy data or to a fundamental lack of connection. Statistics is a tool for quantifying such relationships. We will start with some philosophical considerations and move into elementary statistical measures, before embarking on more advanced tools. 

Statistical techniques are powerful tools, which can be used in the search for minor constituents in planetary spectra. Correlation analysis is particularly applicable to the detection of gases with many, generally weak spectral features. Correlation analysis is best applied when the signatures of a suspected constituent are of the same magnitude or possibly even less than the noise level of the instrument. Under such conditions visual inspection of a spectral region where known lines of a particular gas should appear may not be conclusive. The advantage of correlation analysis is that many spectral positions can be searched simultaneously. 

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