Data analysis noise

Bialkowski, S. E., Data Analysis in the Shot Noise Limit 1. Single Parameter Estimation with Poisson and Normal Probability Density Functions, Anal. Chem. 61, 1989, 2479-2483. 

Measurements of electrochemical noise and AC impedance of coated metal substrates are under development (indeed have been used for quite some time). These measurements relate to the corrosion protection afforded by the coating and can, in principle, be made continuously. The complexity of the electrochemical reactions require sophisticated data analysis for extraction of useful information and relationships. 

Uncertainty in Process Discriminants. Because processes operate over a continuum, data analysis generally produces distinguishing features that exist over a continuum. This is further compounded by noise and errors in the sensor measurements. Therefore, the discriminants developed to distinguish various process labels may overlap, resulting in uncertainty between data classes. As a result, it is impossible to define completely distinguishing criteria for the patterns. Thus, uncertainty must be addressed inherently. 

Sections on matrix algebra, analytic geometry, experimental design, instrument and system calibration, noise, derivatives and their use in data analysis, linearity and nonlinearity are described. Collaborative laboratory studies, using ANOVA, testing for systematic error, ranking tests for collaborative studies, and efficient comparison of two analytical methods are included. Discussion on topics such as the limitations in analytical accuracy and brief introductions to the statistics of spectral searches and the chemometrics of imaging spectroscopy are included. 

Figure 3.1 Schematic diagram of an AAS spectrometer. A is the light source (hollow cathode lamp), B is the beam chopper (see Fig. 3.2), C is the burner, D the monochromator, E the photomultiplier detector, and F the computer for data analysis. In the single beam instrument, the beam from the lamp is modulated by the beam chopper (to reduce noise) and passes directly through the flame (solid light path). In a double beam instrument the beam chopper is angled and the rear surface reflective, so that part of the beam is passed along the reference beam path (dashed line), and is then recombined with the sample beam by a half-silvered mirror.

Statistics plays a crucial role in any data analysis, and accordingly, the statistical aspects are mentioned and appropriate equations/code are supplied. E.g. examples are given for the least-squares analysis of data with white noise as well as y2-analyses for data with non-uniformly distributed noise. However, the statistical background for the appropriate choice of the two methods and more importantly, the effects of wrong assumptions about the noise structure are not included. 

There is also a lot of criticism on Taguchi s method, especially with respect to the data analysis part. Some of this criticism focuses on the use of Taguchi s quality criteria the signal-to-noise ratios [15]. A good example of the drawback of these signal-to-noise ratios is given in Chapter 6. 

Some of these differences reflect different philosophical approaches to data analysis. Taguchi s analysis of robust design experiments is frequently conducted in terms of a performance statistic, such as a signal-to-noise ratio, that is calculated for each point of the design array using data obtained from the environmental (noise) array about that point. 

Mateos A, Herrero J, Tamames J, Dopazo J, Supervised neural networks for clustering conditions in DNA array data after reducing noise by clustering gene expression profiles, In Lin SM, Johnson KF, eds., Methods of Microarray Data Analysis II, Boston, Kluwer Academic Publ, pp. 91-103, 2002. 

Unfortunately, direct electrochemical detection of DNA damage in films suffered from poor signal to noise ratios and data analysis that required derivative or other background corrections. Thus we explored catalytic methods of DNA oxidation (cf. Eqs. 3 and 4) to improve signal to noise in SWV detection.[45] At the same time, we began to realize that layer-by-layer growth of films had... 

The traditional way is to measure the impedance curve, Z(co), point-after-point, i.e., by measuring the response to each individual sinusoidal perturbation with a frequency, to. Recently, nonconventional approaches to measure the impedance function, Z(a>), have been developed based on the simultaneous imposition of a set of various sinusoidal harmonics, or noise, or a small-amplitude potential step etc, with subsequent Fourier- and Laplace transform data analysis. The self-consistency of the measured spectra is tested with the use of the Kramers-Kronig transformations [iii, iv] whose violation testifies in favor of a non-steady state character of the studied system (e.g., in corrosion). An alternative development is in the area of impedance spectroscopy for nonstationary systems in which the properties of the system change with time. 

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