Computational statistical method

For many reasons, not least the influence of the quality movement and the widespread availability of personal computers, statistical methods are now much more widely appreciated and more frequently applied to the results of rubber tests. Also, a practical reason for not now needing a statistics chapter is the existence of the comprehensive British Standard Application of Statistics to Rubber Testing1 which at the time of writing is being considered for adoption as an ISO standard. It contains references to standards on statistical methods and also has a small bibliography. 

With the development of electronic computers, statistical methods began to thrive and take an ever more important role in empirical researches and system optimization. 

The data processing makes it possible to determine the number of bubbles and their distribution by size from the length of their chords, calculated by the computer. Statistical methods, developed by Weibel [58] and Kawakmi et al. [59] are employed to transform the distribution by chords to distribution by bubble diameter. 

The development of the probabilistic design approach, as already touched on, includes elements of probability theory and statistics. The introductory statistical methods discussed in Appendix I provide a useful background for some of the more advanced topics covered next. Wherever possible, the application of the statistical methods is done so through the use of realistic examples, and in some cases with the aid of computer software. 

Having completed the risk analyses, computed the uncertainties, and identified critical systems by importance measures (which also identifies valuable systems improvements having low costs), the PSA results must be presented. An executive summary compares the risk of operations that were analyzed with the risks of similar operations. It identifies and explains the main contributors to the risk to people untrained in PSA and statistical methods. Figure 6.3-5 shows two pie-charts that show the risk contributions of various initiators for PWRs and BWRs. A chart similar to one of these would be an effective way of showing the risk contributions in simplified form. 

For the equihbrium properties and for the kinetics under quasi-equilibrium conditions for the adsorbate, the transfer matrix technique is a convenient and accurate method to obtain not only the chemical potentials, as a function of coverage and temperature, but all other thermodynamic information, e.g., multiparticle correlators. We emphasize the economy of the computational effort required for the application of the technique. In particular, because it is based on an analytic method it does not suffer from the limitations of time and accuracy inherent in statistical methods such as Monte Carlo simulations. The task of variation of Hamiltonian parameters in the process of fitting a set of experimental data (thermodynamic and... 

Statistical methods are used to measure the density variation as the tool rotates, the stand-off can be estimated and the density corrected. A density caliper can be computed that works for cavings of 2 in. (5 cm) or less when the tool rotates at a speed ranging from 6 to 150 rpm. 

These steps may be completed separately or together, statistical methods can be employed and the computational labour reduced through the use of high speed computers. 

Statistical methods can also be utilized to form probability models or to estimate the likelihood of particular descriptors forming the known classes. Chemical Computing Group Inc. has recently developed a new technology. 

Cununing GL, Rollett JS, Rosotti FJC, Whewell RJ (1972) Statistical methods for the computation of stability constants, I. Straight-line fitting of points with correlated errors. J Chem Soc Dalton Trans 23 2652-2658... 

The major disadvantage of the integral method is the difficulty in computing an estimate of the standard error in the estimation of the specific rates. Obviously, all linear least squares estimation routines provide automatically the standard error of estimate and other statistical information. However, the computed statistics are based on the assumption that there is no error present in the independent variable. 

Quantitative XRF analysis has developed from specific to universal methods. At the time of poor computational facilities, methods were limited to the determination of few elements in well-defined concentration ranges by statistical treatment of experimental data from reference material (linear or second order curves), or by compensation methods (dilution, internal standards, etc.). Later, semi-empirical influence coefficient methods were introduced. Universality came about by the development of fundamental parameter approaches for the correction of total matrix effects... 

Bakshi, B. R., and Utojo, U., Unification of neural and statistical methods that combine inputs by linear projection, Comput Chem. Eng. 22(12), 1859-1878 (1998). 

The goal of EDA is to reveal structures, peculiarities and relationships in data. So, EDA can be seen as a kind of detective work of the data analyst. As a result, methods of data preprocessing, outlier selection and statistical data analysis can be chosen. EDA is especially suitable for interactive proceeding with computers (Buja et al. [1996]). Although graphical methods cannot substitute statistical methods, they can play an essential role in the recognition of relationships. An informative example has been shown by Anscombe [1973] (see also Danzer et al. [2001], p 99) regarding bivariate relationships. 

Return now to the assertions of the Introduction. The explanation of assertion (1) was pointed out previously. Assertion (2), that the PDT is a practical computational tool, was the subject of Sect. 9.2.3. See especially the discussion "the general computational tricks work for the PDT also, emphasizing the general statistical methods of stratification and importance weighting, and their correspondence to the natural theoretical analyses of the PDT partition function. 

This set of articles presents the computational details and actual values for each of the statistical methods shown for collaborative tests. These methods include the use of precision and estimated accuracy comparisons, ANOVA tests, Student s t-testing, The Rank Test for Method Comparison, and the Efficient Comparison of Methods tests. From using these statistical tests the following conclusions can be derived ... 

There are two other methods in which computers can be used to give information about defects in solids, often setting out from atomistic simulations or quantum mechanical foundations. Statistical methods, which can be applied to the generation of random walks, of relevance to diffusion of defects in solids or over surfaces, are well suited to a small computer. Similarly, the generation of patterns, such as the aggregation of atoms by diffusion, or superlattice arrays of defects, or defects formed by radiation damage, can be depicted visually, which leads to a better understanding of atomic processes. 

The early structure-activity studies [69, 70] were limited in the number of compounds studied but showed that reasonable correlations could be drawn between the structure of compounds and their biological activity without a complete understanding of the underlying mechanisms involved. Chou and Jurs [71] expanded the approach to structure-activity relationships by applying computer-assisted mathematical and statistical methods to a large set of N-nitroso compounds. These methods... 

Computational methods have been applied to determine the connections in systems that are not well-defined by canonical pathways. This is either done by semi-automated and/or curated literature causal modeling [1] or by statistical methods based on large-scale data from expression or proteomic studies (a mostly theoretical approach is given by reference [2] and a more applied approach is in reference [3]). Many methods, including clustering, Bayesian analysis and principal component analysis have been used to find relationships and "fingerprints" in gene expression data [4]. 

De Lean, A., Hancock, A. A. and Lefkowitz, R. J. (1982). Validation and statistical analysis of a computer modeling method for quantitative analysis of radioligand binding data for mixtures of pharmacological receptor subtypes, Mol. Pharmacol., 21, 5-16. 

The rapid development of computer engineering initiated a simultaneous development and wide application of statistical methods of modeling of PS properties and processes occurring in them. It is... 

The LIMS computer is located on the site, and several terminals may be provided for entry of data from notebooks and instrument readouts and for the retrieval of information. Bar coding for sample tracking and access codes for laboratory personnel are part of the system. Instruments may be interfaced directly with the LIMS computer to allow direct data entry without help from the analyst. The LIMS may also incorporate statistical methods and procedures, including statistical control and control chart maintenance. See Workplace Scene 6.4. 

The validity of the results is a central issue, and it is confirmed by comparing traditional methods with their robust counterparts. Robust statistical methods are less common in chemometrics, although they are easy to access and compute quickly. Thus, several robust methods are included. 

R is freely available under the GNU General Public License. It offers high computational speed, a useful help system, a huge variety of statistical methods, and the possibility of extension by own developed methods. R requires basic knowledge in programming and statistics. 

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