### Table 2. Monte Carlo Results

"... In PAGE 12: ... In case I, the nucleus can experience arbitrarily high electric elds, while in case II, the stronger elds do not contribute because they have smaller Boltzmann weights. Numerical results are shown in Table2 for di erent values, NMC, of Monte Carlo realizations of ion con gurations. The percent deviations shown are fractional di erences with respect to the mean eld theoretical result of 3.... In PAGE 14: ...alculations for the 7Be electron capture rate in the Sun (see, e.g., Iben, Kalata, amp; Schwartz 1967; Bahcall amp; Moeller 1969; Bahcall 1989). The results of numerical simulations (see Table2 ) show that the standard formula (Bahcall 1989) is accurate to better than 1% .We obtained similar results for R=R = 0:0, 0.... In PAGE 14: ... They conclude that Debye screening describes the electron capture rates to within 2% . Combining the results of Table2... ..."

### Table 1. Table 1. Monte Carlo Inputs

"... In PAGE 9: ...The #0Crst column of Table1 lists the quantities that were dispersed within the lim- its shown in the second column. The #0Cnal column denotes the type of random distri- bution sampled; apos;G apos; for Gaussian and apos;U apos; for uniform.... ..."

### Table 3: CPU time comparison with the Monte Carlo method considering variation in G,C,I

"... In PAGE 6: ... We can see that they match very well. Table3 shows the CPU speedup of HPC method 0.015 0.... ..."

### Table 6 Monte Carlo Results for Ordered Response Model Estimators

2005

"... In PAGE 19: ... The tables present the mean bias and root mean square error (RMSE) for each of the estimators of g175. Table6 presents these for the Ordered Probit estimator, the Lewbel estimator, the SNP estimator with g75 =3, and the PGOP estimator with g77 =1. The corresponding results for SNP(5) and PGOP(3) are given in Table 7.... ..."

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### Table 1: Variance for Monte Carlo Estimate of R 4 0 xdx

"... In PAGE 10: ... Normally only one sample is taken in each S i (with density p i ), and in this case the variance of the estimate is: var #20 N X i=1 g#28x i #29 p i #28x i #29 ! = N X i= 1 var #12 g#28x i #29 p i #28x i #29 #13 (7) The most common example of stratified sampling in graphics is jittering for pixel sampling[11]. As an example of the Monte Carlo solution of an integral I set g#28x#29 to be x over the interval (0, 4): I = Z 4 0 xdx= 8(8) The great impact of the shape of the function p on the variance of the N sample estimate is shown in Table1 . Note that the variance is lessened when the shape of p is similar to the shape of g.... In PAGE 10: ...n Table 1. Note that the variance is lessened when the shape of p is similar to the shape of g.The variance drops to zero if p = g=I,butI is not usually known or we would not have to resort to Monte Carlo. One important principle illustrated in Table1 is that stratified sampling is often far superior to importance sampling. Although the variance for this stratification on I is inversely proportional to the cube of the number of samples, there is no general result for the behavior of variance under stratification.... ..."

### Table 1. Table 1. Monte Carlo Inputs Variable Range Dist

"... In PAGE 9: ...The #0Crst column of Table1 lists the quantities that were dispersed within the lim- its shown in the second column. The #0Cnal column denotes the type of random distri- bution sampled; apos;G apos; for Gaussian and apos;U apos; for uniform.... ..."

### Table 1: Bayesian Bioassay Design by Curve Fitting of Monte Carlo Experiments

1999

"... In PAGE 7: ... To avoid under tting or over tting, we use both graphical methods for model checking and ANOVA as suggested by Cleveland, Grosse, and Shyu (1991) to experiment with speci cation of the surface (linear, degree=1; or quadratic, degree=2) and the neighborhood size (span). Table1 lists the optimal design obtained by the Monte Carlo method and the choice for the loess tting for the = 1 case. For I = 1, the Monte Carlo results are obtained by a xed grid with 500 equally spaced grid points, where the corresponding utility (g) for each grid point is obtained by averaging the preposterior risks with 5 repeated samples.... In PAGE 7: ...5 independent of the sample size. Table1 shows that the Monte Carlo results for the case = 1 ( .496, for n = 1, and... ..."

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### Table 1: Performance of ^ v0 on 100 Monte-Carlo runs.

"... In PAGE 4: ... The AR part of the ARMA(4,4) model used for y[n] was estimated us- ing a modified Yule-Walker algorithm on length 4096 data frames with an overlap factor of 1/2. Table1 presents some typical results for the estimation of the speed v0 from 8 s samples of y(t). The best performance were obtained by using a set of weights f 1; 2g strongly in favor of the pole fit to the detriment of the power fit.... ..."

### Table 1. 6-DOF Monte-Carlo variables.

1997

"... In PAGE 6: ...g., aerodynamics or winds), the uncertainty is es- timated using linear interpolation between the regions given in Table1 . Gaussian distributions are sampled for most parameters.... In PAGE 10: ...ion frequency is approximately 2.5 Hz. Monte-Carlo Simulation During ight of the Mars Microprobe space- craft, a combination of o -nominal e ects is likely to be encountered. Hence, it is impor- tant to statistically assess the e ect of combi- natorial variations in all of the EDI parame- ters listed in Table1 . To accomplish this, two- thousand o -nominal cases were randomly esti- mated and simulated in a Monte-Carlo fashion.... In PAGE 10: ... A 99.7% probability exists that each random pa- rameter will remain within the 3{ uncertainty bounds of Table1 . In addition to a detailed set of impact conditions, the total angle-of-attack was monitored at discrete points along the heat pulse.... ..."

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### Table 1 Monte Carlo comparison of Boolean probit and throbit

2004

"... In PAGE 10: ... In each, Xs are normal draws held fixed in repeated samples, but we manipulate their means and the value of s1 and s2 to control the proportion of failures, successes with ambiguous causes, and successes with discernible causes. Table1 displays the results of the first set of simulations. Xs and ss are configured such that roughly half the sample Table 1 Monte Carlo comparison of Boolean probit and throbit... In PAGE 11: ...eed to go out and uncover information about discernible causes, e.g., from case studies. Note, however, that the simulations whose results are posted in Table1 represent a relatively easy case for both models: Roughly half of the observations have the dependent variable taking on a value of one. In many cases in political science, successes are comparatively rarer, leading to a skewed distribution of the dependent variable.... In PAGE 12: ... To make the results for Boolean probit and throbit comparable, we include in Table 2 only summary statistics for trials in which the former successfully converged.14 Restricting our attention to these experiments, we see similar results to those in Table1 . In general, throbit does at least as well if not better than Boolean probit in terms of bias, and considerably better in terms of relative efficiency.... ..."

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