Prediction statistics

S. Sun, Reduced representation model of protein structure prediction statistical potential and genetic algorithms. Protein Sci. 2 (1993), 762-785. 

S. Sun, Reduced representation approach to protein tertiary structure prediction statistical potential and simulated annealing, J. Theor. Biol. 172 (1995), 13-32. 

The new samples constitute what is called the validation set and, of course, the more validation samples you have, the more representative the conclusions will be. The RMSEP (root mean square error of prediction) statistic measures how well the model predicts new samples. It is calculated as... 

Fluctuations in analytical results can be predicted statistically as soon as a laboratory works at a constant level of high quality (Hartley, 1990), which implies in the first place that limits of determination and detection should be constant and well known. In the situation of absence of systematic fluctuations, normal statistics (e.g. regression analysis, t- and F-tests, analysis of variance) can be applied to study the results wherever necessary (Shewhart, 1931). Whenever a laboratory is in statistical control, the results are not necessarily accurate they are, however, reproducible. The ways to verify accuracy will be described in the next paragraphs. 

Belles and Fair (55) compared flood-point predictions from the Eckert correlation to published experimental data for random packings. Their massive data bank consisted mainly of data for first-generation packings, but also included some data for second-generation packings. For the data compared, Bolles and Fair showed that Eckert s correlation gave reasonable flood-point prediction. Statistically, they showed that if a safety factor of 1.3 was applied to the correlation flood-point predictions, the designer will have 95 percent confidence that the column will not flood. 

Likewise tests of whether the data of a survey or an experiment fit some particular curve is of no scientific or economic consequence... With enough data no curve will fit the results of an experiment. The question that one faces in using any curve or any relationship is this how robust are the conclusions Would some other curve make safer predictions Statistical significance of B/A thus conveys no knowledge, no basis for action. 

Grover SA, Lowensteyn I, Esrey KL et al. (1995). Do doctors accurately assess coronary risk in their patients Preliminary results of the coronary health assessment study. British Medical Journal 310 975-978 Hackett ML, Anderson CS (2005). Predictors of depression after stroke a systematic review of observational studies. Stroke 36 2296-2301 Harrell FE Jr., Lee KL, Califf RM et al. (1984). Regression modelling strategies for improved prognostic prediction. Statistics in Medicine 3 143-152... 

For the purposes of comparing assay, content uniformity, and dissolution data, simple statistics such as sample mean value (SMV) and relative standard deviation (%RSD) derived from experience of performing the tests over long periods of time can be used as acceptance criteria. Alternatively, more sophisticated statistics such as the z-test, F-test or t-test as shown in Table 16-4 can be applied [17-19,25]. In the case of evaluating CU data, it can be concluded that results from two labs are equivalent based on applying the simple statistics of the difference between the SMV from Lab A and Lab B (Table 16-4) not to be more than 2.0%. In the other examples where the more sophisticated statistics such as z-test, F-test, or t-test are applied (Table 16-4), results from two labs are considered to be equivalent because the calculated statistics in each case (z-calculated values of 0.32/0.64, F-calculated value of 0.14, or T-calculated values of 0.30/0.60) are less than the predicted statistics (z-critical value of 1.64, F-critical values of 3.18, or T-critical value of 1.73) [19,25]. 

It is not practical to conduct free-radical polymerizations under conditions where there is an equilibrium between polymerization and depolymerization processes. The polymer synthesis is effectively irreversible in normal radical polymerizations. The course of the reaction is then determined kinetically, and the molecular weight distribution cannot be predicted statistically as was done for equilibrium step-growth polymerizations described in Chapters. 

Walsh, D.E. Zaccori, N. Predictive statistical process controls—a neural network approach to maximizing tablet yield. Pharm. Tech. Eur. 2001, 13 (9), 46-53. 

Thus, despite some disagreement on the CO internal state distributions, which will undoubtedly be settled by further experiments, the major observations of our group. Rice et al. and Weston and co-workers is that with collision energies approximately twice the HOCO well depth, CO has modest internal energy, i.e., substantially less than would be predicted statistically. This agrees with the targe observed propensity for energy disposal into CM translation [33, 39], and the OH rotational state distributions which are colder than statistical [32, 33]. 

Regression analysis includes not only the estimation of model regression parameters, but also the calculation of goodness of fit and -> goodness of prediction statistics, regression diagnostics, residual analysis, and influence analysis [Atkinson, 1985]. 

The goodness of prediction statistic measures how well a model can be used to estimate future (test) data, e.g. how well a regression model (or a classification model)... 

This constraint is included in the maximization (or minimization) of some goodness of prediction statistic and prevents models with collinearity but without predictive power, i.e. chance correlation, from being taken into account. 

In this case it is seen that the probability that the predicted statistic 9) is greater than the observed statistic T(y) is conditional on the data y. If we assume that the posterior distribution of the parameters in conjunction with the model are a sufficient statistic for the data, then we can write... 

Table IV. Prediction statistics for all wine color measures.

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