Effective sample size

With the Monte Carlo method, the sample is taken to be a cubic lattice consisting of 70 x 70 x 70 sites with intersite distance of 0.6 nm. By applying a periodic boundary condition, an effective sample size up to 8000 sites (equivalent to 4.8-p.m long) can be generated in the field direction (37,39). Carrier transport is simulated by a random walk in the test system under the action of a bias field. The simulation results successfully explain many of the experimental findings, notably the field and temperature dependence of hole mobilities (37,39). 

A model has been developed for determining a cost-effective sample size (n) when estimating cost (8). 

We may also determine the effective sample size (/z) in accordance with... 

O. Berntsson, L-G. Danielsson and S. Folestad, Estimation of effective sample size when analyzing powders with diffuse reflectance near-infrared spectrometry. Anal Chim. Acta, 364, 243-251 (1998). 

Quantifying overall sampling quality the effective sample size 41... 

The fundamental perspective of this review is that simulation results are not absolute, but rather are intrinsically accompanied by statistical uncertainty [4-8]. Although this view is not novel, it is at odds with informal statements that a simulation is "converged." Beyond quantification of uncertainty for specific observables, we also advocate quantification of overall sampling quality in terms of the "effective sample size" [8] of an equilibrium ensemble [9,10]. 

Thus, given an ensemble generated by a particular (non-ideal) simulation, possibly consisting of a great many "snapshots," the key conceptual question is To how many i.i.d. configurations is the ensemble equivalent in statistical quality The answer is the effective sample size [1,9,10] which will quantify the statistical uncertainty in every slow observable of interest — and many "fast" observables also, due to coupling, as described earlier. 

If indeed the basic goal of equilibrium sampling is to estimate state populations, then these populations can act as the fundamental observables amenable to the types of analyses already described. In practical terms, following 10, a binomial description of any given state permits the effective sample size to be estimated from the populations of the state recorded in independent simulations — or from effectively independent segments of a sufficiently long trajectory. This approach will be described shortly in a publication. 

Overall sampling quality — quantitative analysis. For dynamical trajectories, the "structural decorrelation time" analysis [10] can estimate the slowest timescale affecting significant configuration-space populations and hence yield the effective sample size. For non-dynamical simulations, a variance analysis based on multiple runs is called for [1]. Analyzing the variance in populations of approximate physical states appears to be promising as a benchmark metric. 

Lyman, E., Zuckerman, D.M. On the structural convergence of biomolecular simulations by determination of the effective sample size. J. Phys. Chem. B 2007, 111, 12876-82. 

Bemtsson O, Burger T, Folestad S, Danielsson LG, Kuhn J, Fricke J. 1999. Effective sample size in diffuse reflectance near-IR spectrometry. Anal. Chem. 71(3) 617-623. 

The effective sample size ranges for the six mills, which we considered in this study, are summarized in Table Vlll. As can be seen, these units in concert can cover essentially the entire range of sample sizes from a few milligrams of a.i. up to 50 kg. This capability should cover sample needs for most research and field development programs. The stated sample size ranges shown in Table Vlll are based on the smallest practical sample size for each unit of a 5% flowable, and the largest sample possible of a 30 or 50% flowable. 

Downsizing, whereby the majority class from the training set is sampled to produce a balanced training set of actives and inactives, was found to worsen the predictive accuracy as it reduces the effective sample size considerably when... 

Effective Sample Size of a Parametric Prior. Univ. Texas Working Paper Series 36. 

In building a gel based machine, it will probably be equally desirable that the gel can swell and deswell over a range without dramatic changes in the properties of the surface region. This requirement imposes a coupling of effective sample size, diffusion rate and response time on any gel device. The self-diffusion coefficient of water is... 

If diffuse reflection spectrometry is to be used for quality control purposes, it is essential to know the actual investigated sample volume, which is equivalent to the radiation penetration depth or the effective sample size meff- In a publication by Berntsson et al. [73], the effective sample size of pharmaceutical powders was investigated by the three-flux approximation presented above that they called the equation of radiative transfer (ERT) method, and an empirical method they called the variable layer thickness (VLT) method. In this publication, the effective sample size meg is defined as the mass per area of the sample at which its diffuse reflectance has reached 98% of the diffuse reflectance of a corresponding optically thick sample. 

FIGURE 3.14 Effective sample size and penetration depth of microcrystalline cellulose powder according to the ERT method (solid line) and the VLT method (dashed line). (Reproduced from O. Berntsson, T. Burger, S. Folestad, L.-G. Danielsson, J. Kuhn, and J. Fricke, Ana/. Chem., 71 617-623 (1999) by permission of American Chemical Society Copyright 1999.)... 

This method is compared to a totally independent procedure, the VLT method, where diffuse reflection spectra are collected at several controlled powder thicknesses. Assuming that the backing is either completely transparent or completely opaque, the diffuse reflectance of the powder layers increases with increasing sample thickness until the reflectance of an optically thick sample (Roo) is reached. For each measured wavelength, an exponential function is fitted to the experimental data (plots of log(l /R) vs. sample thickness, where R is the measured reflectance). Using the 98% limit, the effective sample size can be obtained from the exponential fit (see [75] for a detailed discussion of the VLT method). 

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