True statistic

An old statement is very true - statistical treatment is no substitute for good data. 

The reality of HTS is that the true statistical hit rate is often greater than the operational hit rate that can be accommodated by confirmation assays. In such a case, the use of a Top X method carries a number of significant drawbacks, the most significant of which is the creation of artificially high false negative rates through the neglect of actives less potent than the cutoff used. This is often overlooked but is of critical importance. 

In evaluating two testraethods for repeatability or reproducibility, the variances (standard deviation squared) of the two can be com pared by means of the variance ratio or F test. This is a tried and true statistical technique which has many other uses, as well as being a critical part of analysis of variance. 

Once these links and meaningful process control plans are made, operators can for the first time experience true statistical process control beginning with the critical few parameters that control color quality for the final product. 

In order to obtain properly averaged results, either collision parameters for each trajectory must be selected by Monte Carlo methods or, when starting values are systematically chosen, the final results must be integrated over complete statistical distributions. The purpose of a Monte Carlo selection technique is to ensure that the distributions of each parameter within a sample of trajectories approach the true statistical distributions as the size of the sample grows. Some examples of how this can be done for different types of distribution function will be described below. Before starting the integration, it is generally necessary to transform the selected values of the collisional... 

The five a(np) values in Table 10.3 are in close agreement (i.e. 0.595 0.015 nm2), but they are much larger than the value, 0.40 nm2, calculated for a close-packed monolayer of freely rotating neopentane molecules. However, it must be kept in mind that the C(BET) values are very low (i.e. 6-8) and therefore it is unlikely that nm(np) represents the true statistical monolayer capacity. 

Upper bound An plausible upper limit to the true value of a quantity. This is usually not a true statistical confidence limit (IRIS, 1999). 

Theoretical probability identifies the possible outcomes of a statistical experiment, and uses theoretical arguments to predict the probability of each. Many applications in chemistry take this form. In atomic and molecular structure problems, the general principles of quantum mechanics predict the probability functions. In other cases the theoretical predictions are based on assumptions about the chemical or physical behavior of a system. In all cases, the validity of these predictions must be tested by comparison with laboratory measurements of the behavior of the same random variable. A full determination of experimental probability, and the mean values that come from it, must be obtained and compared with the theoretical predictions. A theoretical prediction of probability can never be tested or interpreted with a single measurement. A large number of repeated measurements is necessary to reveal the true statistical behavior. 

Even with equimolar amounts of each ketone true statistical distribution is not observed, see B. P. Mundy, R. Srinivasa, Y. Kim, T. Dolph and R. J. Wamet, J. Org. Chem., 1982, 47,1657. 

A construction makes use of only an insignificant fraction of the Gibbs canonical ensemble and hence is essentially out of equilibrium. This is different from thermodynamic nonequilibrium—it arises because the system is being investigated at time scales much shorter than those required for true statistical equilbrium. Such systems exhibit broken ergodicity [68], as epitomized by a cup of coffee in a closed room to which cream is added and then stirred. The cream and coffee equilibrate within a few seconds (during which vast amounts of microinformation are generated within the whorled patterns) the cup attains room temperature within tens of minutes and days may be required for the water in the cup to saturate the air in the room. 

At point B, the accommodation of additional chains has reached its maximum. The relative crowding of the chains at point B means that the molecules will not be able to attain their true statistical equilibrium conformations instead, a pseudoequilibrium will be attained. In the region between A and B, it is usually found that the thickness of the adsorbed polymer layer increases, since more units of each chain are forced further away from the adsorbent surface (longer loops and tails are formed see Fig. 14.4). 

The true statistical distributions of the variables uSed in criticality calculations are not known exactly. Thus, calculated confidence levels are not precise. For foe same reason, statistical treatments more complex than those above may not give real improvements. 

In this paper we shall establish rather interesting results relating the method of statistical linearization and estimation of parameters for linear systems. In particular we establish that the coefficient estimators for linear models, when the observed data comes from a non-linear structure are, surprisingly, the "true" statistical linearization coefficients. The significance of this result is discussed, along with important questions that are generated. 

The unexpected answer that we establish in this paper is that these parameter estimates will converge to the "true" statistical. linearization coefficients for the white noise excitation case. Even of more conceptual interest is that the specific form of the non-linearity does not have to be known. Thus, in order to construct the linear model, we only require the model order, as well as the observed response data from the true system. 

Instead of the true statistics being applied, the usual practice is to assume the stationary statistics of the linear system (2.2) and calculate A through the expectations,... 

We have shown that the "true" statistical linearization coefficients for the linearized model of a non-linear structure excited by gausslan white noise can be obtained merely from observations on the response vector alone, without requiring any detailed knowledge of the specific form of the non-linearities that govern the structural behavior. 

In order to reduce uncertainty, Bayesian inference is proposed to incorporate the new information with the prior information. After Bayesian updating (i) distributions of E and j/j change (ii) both the variances of E and y decrease significantly (iii) both the coefficients of variance of E and y decrease significantly. So the uncertainty is reduced dramatically, and the random variables are more closer to their true statistical distributions ... 

---