Statistical efficiency

Calculating the statistical efficiency, a. A plot of tj,a A)i,la A) against tj, shows a steep rise before j off. Here the property A corresponds to the pressure calculated from the molecular dynamics simulation of... 

The goal of the four principles of experimental design is statistical efficiency and the economizing of resources.The single most important initial step in achieving such an outcome is to clearly define the objective of the study get a clear statement of what questions are being asked. 

The median is not affected by outlying data, but the statistical efficiency is not good. This means that the rehability of the estimation of a dataset s population mean from a small sample of data is lower than for the other methods. 

All other things being equal, having equal numbers of subjects in the two treatment groups provides the maximum amount of information (the greatest power) with regard to the relative efficacy of the treatments. There may, however, be issues that override statistical efficiency ... 

Note the difference in the transformation properties of statistical (efficiency) tensors as compared to angular functions (compare equ. (8.82) with equs. (8.80)). 

DP E F f f. Ha He AG Degree of polymerization Activation energy, enhancement factor for gas-liquid mass transfer with reaction, electrochemical cell potential Faraday constant, F statistic Efficiency of initiation in polymerization Ca/CaQ or na/nao, fraction of A remaining unconverted Hatta number Henry constant for absorption of gas in liquid Free energy change kj/kgmol Btu/lb-mol... 

Typical systems contain between several hundred and a few thousand water molecules. The number of ions is much smaller. In practice, it is determined by two contradicting requirements, namely (i) the need to achieve small concentrations, as they are typical for most experiments, and (ii) the statistical efficiency of the simulation, which requires the average over as many ions as possible. As a compromise, electrolyte concentrations are usually in the range between 0.5 and 3mol/l. As more powerful computers become available and thus the simulation of larger systems becomes possible, systems at lower concentrations can be investigated. Typical time scales for Molecular Dynamics simulations reach up to about 2 nanoseconds at present. 

Despite impressive progress, there are other directions in which optimization of alchemical pathways can still be improved. For example, research in optimizing alchemical pathways has focused on minimizing the variance of TI, yet in most cases, WHAM/BAR is a more efficient method. While the uncertainties of various pathways using TI and WHAM/BAR are strongly related, they are not identical, so further research will be needed to clarify the best pathway for BAR. Additionally, some alchemical intermediates may suffer from long correlation times, and what might be the minimum variance pathway in theory may not be the minimum variance pathway in practice when the statistical efficiency is included. 

Hanemann, W.M., Loomis, J.B., and Kanrrinen, B.J., 1991, Statistical efficiency of dorrble-bounded dichotomous choice contingent yaiaatioTL, American Journal of Agricultural Economics, 73 1255—1263. 

The "whiteness" of the residuals can be analyzed by plotting their cumulative periodogram and observing closeness to the ideal ramp line. Another common diagnostic technique is to determine the statistical efficiency of adding one or two parameters (and terms) to the model. This will check if the minimal parametric model chosen is truly parsimonious. The statistical F-test based on the extra-sum-of-squares principle is useful for this efficiency test. 

Human umbilical cord tissue is relatively readily available in most locations, and the ability to fragment it into multiple similar carriers allows for replicates and statistical efficiency in experimental design. Ethical clearance and informed consent for its use in experimentation are required. 

The effect of the correlation between successive configmations on a given property is conventionally expressed as a statistical efficiency [64] or by a closely related autocorrelation time of that property [64,66]. The precision of different properties is affected differently by the correlation and... 

As mentioned, the translation displacement parameter A affects the statistical efficiency of simulated properties, and it is normally selected differently for different types of particles. For our asymmetric electrolyte, denote the macroion and small-ion displacement parameters by Au and Ai, respectively. Due to the extensive accumulation of counterions near macroions, the approach with single-particle trial moves leads to a very restricted total macroion displacement and hence to poor statistics [ 103]. When a hard-core overlap is encountered, i.e., r[Pg.152]

In this section we review briefly the principles of both static and dynamic Monte Carlo methods, with emphasis on the issues that determine the statistical efficiency of an algorithm. 

Table 3.39 compares the detailed self-consistent principle with the factor and averaged versions of the residual QSAR modeling of Eq. (3.141). If Eq. (3.141) is amended with the residual correlation factor or its complement to yield the observed-to-QSAR activity proportionality or if the averaged activity in Eq. (3.146) is replaced with expressions of Eqs. (3.147) A =5.285636) and (3.148) (yf = 5.20711), then the results are systematically the same or very close to those reported in Table 3.38. In other words, whenever the model resembles the direct molecular variables dependency, the direct QSAR statistical efficiency will be systematically reached.

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