Artificial data

One can feed SINGLE with artificial data that are numbers which contain a common element number(n) = con + n element. If the program is effecient it should find this element. If the artifical reaction times are given by the term art(n)= 120 + n 20.1 (with n=3 to 11), then one gets the chronophoresis below. The program finds the artificial elementary time plus the half of it. 

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When the dynamic system is described by a set of stiff ODEs and observations during the fast transients are not available, generation of artificial data by interpolation at times close to the origin may be very risky. If however, we ob-... 

The ability of the sequential design to discriminate among the rival models should be examined as a function of the standard error in the measurements (oe). For this reason, artificial data were generated by integrating the governing ODEs for Model 1 with "true" parameter values kt=0.31, k2=0.18, k3=0.55 and k4=0.03 and by adding noise to the noise free data. The error terms are taken from independent normal distributions with zero mean and constant standard deviation (oE). 

Figure 68-1 (a) Artificial data representing a linear relationship between the two variables. This data represents a linear, one-variable calibration, (b) The same artificial data extended in a linear manner. The extrapolated calibration line (broken line) can predict the data beyond the range of the original calibration set with equivalent accuracy, as long as the data itself is linear. 

The result of the optimization can also be represented as a table. In Table 5.2, an illustrative example with batch-related information is shown (artificial data). 

The programs are written modular. The reader can replace the artificial data, generated by a function, with real data from the lab. There is extensive use of graphical output. While the plots are minimal they efficiently illustrate the results of the analyses. In order to keep the programs concise, no effort was made to build comfortable user-interfaces. 

FIGURE 1.2 Artificial data for two sample classes A (denoted by circles, i = 8) and B (denoted by crosses, n2 — 6), and two variables x and x2 (m — 2). Each single variable is useless for a separation of the two classes, both together perform well. 

Two-Dimensional Artificial Data for 10 Objects from Two Classes... 

FIGURE 3.5 Scree plot for an artificial data set with eight variables, v, variance of PCA scores (percent of total variance) v climul. cumulative variance of PCA scores. 

Artificial Data Set with Three -Variables and One y-Variable, Showing the Advantage of Multiple Regression in Comparison to Univariate Regression... 

For the artificial data sets dtrain and dtest used in Section 5.2.1 (Figure 5.7), LR can be applied for a binary classification as follows. The results (group assignments of the test set objects) have been included in the R code as comments Figure 5.8 (right) visualizes the wrong assignments. 

FIGURE 6.8 Results of the 1-means algorithm for varying number of clusters, 1, for an artificial data set consisting of three spherical groups. The different symbols correspond to the cluster results. 

The sample histogram in Figure 2.1 provides a visual summary of the distribution of total cholesterol in a group of 100 patients at baseline (artificial data). The x-axis is divided up into intervals of width 0.5 mmol/1 and the y-axis counts the number of individuals with values within those intervals. 

In a placebo controlled trial in cholesterol lowering we have the following (artificial) data (Table 2.3). 

As an example, suppose in an oncology study we wish to explore whether time to disease recurrence from entry (months) into the study depends upon the size of the primary tumour measured at baseline (diameter in cm). The scatter plot in Figure 6.1 represents (artificial) data on 20 subjects. 

For a more quantitative analysis of the errors involved, artificial data will be addressed first. To see the effects of truncation and restoration of a single spectral line, we shall first consider a monochromatic electromagnetic... 

For the artificial data of Figure 6.4a, the corresponding diagnostic plot is shown in Figure 6.4b. It exposes the robust residuals / clts vs. the robust... 

Analysis. Two separate patterns should be discernible in the artificial data set sherds, clays, and hypothetical mixtures from Chinautla-Sacojito should be separable from raw materials and products from Durazno and fine-and medium-paste subgroups should be recognizable within the major groups. The first pattern involves shape variation, that is, differing mean vectors and differing variance-covariance structures that arise through nat-... 

Jolliffe, IT. (1972). Discarding Variables in a Principal Component Analysis. I. Artificial Data. Applied Statistics, 21,160-173. 

Melville, P. and Mooney, R.J. (2005) Creating diversity in ensembles using artificial data. Journal of Information Fusion (Special Issue on Diversity in Multiple Classifier Systems), 6,... 

Real data Observed data as different from artificial data. 

Jolliffe, I.T. (1972) Discarding variables in a principal component analysis. I. Artificial data. Appl. Stat., 21, 160-173. 

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