相关论文: Rigorous confidence intervals for critical probabi…

We extend the method of Balister, Bollob\'as and Walters for determining rigorous confidence intervals for the critical threshold of two dimensional lattices to three (and higher) dimensional lattices. We describe a method for determining a…

We give accurate estimates for the bond percolation critical probabilities on seven Archimedean lattices, for which the critical probabilities are unknown, using an algorithm of Newman and Ziff.

We present a method of general applicability for finding exact or accurate approximations to bond percolation thresholds for a wide class of lattices. To every lattice we sytematically associate a polynomial, the root of which in $[0,1]$ is…

We present Monte Carlo estimates for site and bond percolation thresholds in simple hypercubic lattices with 4 to 13 dimensions. For d<6 they are preliminary, for d >= 6 they are between 20 to 10^4 times more precise than the best previous…

The site percolation thresholds p_c are determined to high precision for eight Archimedean lattices, by the hull-walk gradient-percolation simulation technique, with the results p_c = 0.697043, honeycomb or (6^3), 0.807904 (3,12^{2}),…

We present percolation thresholds calculated numerically with the eigenvalue formulation of the method of critical polynomials; developed in the last few years, it has already proven to be orders of magnitude more accurate than traditional…

We present a general method for predicting bond percolation thresholds and critical surfaces for a broad class of two-dimensional periodic lattices, reproducing many known exact results and providing excellent approximations for several…

Confidence interval performance is typically assessed in terms of two criteria: coverage probability and interval width (or margin of error). In this paper, we assess the performance of four common proportion interval estimators: the Wald,…

In this work we apply a highly efficient Monte Carlo algorithm recently proposed by Newman and Ziff to treat percolation problems. The site and bond percolation are studied on a number of lattices in two and three dimensions. Quite good…

We present an efficient method of calculating exact confidence intervals for the hypergeometric parameter representing the number of "successes," or "special items," in the population. The method inverts minimum-width acceptance intervals…

Suppose the lifetime of a large sample of batteries in routine use is measured. A confidence interval is computed to 394 plus/minus 1.96 times 4.6 days. The standard interpretation is that if we repeatedly draw samples and compute…

Introductory texts on statistics typically only cover the classical "two sigma" confidence interval for the mean value and do not describe methods to obtain confidence intervals for other estimators. The present technical report fills this…

In this paper, I compute the inhomogeneous (multi-probability) bond critical surfaces for the (4,6,12) and (3^4,6) lattices using the linearity approximation described in (Scullard and Ziff, J. Stat. Mech. P03021), implemented as a…

We simulate the bond and site percolation models on a simple-cubic lattice with linear sizes up to L=512, and estimate the percolation thresholds to be $p_c ({\rm bond})=0.248\,811\,82(10)$ and $p_c ({\rm site})=0.311\,607\,7(2)$. By…

We develop and apply two calibration procedures for checking the coverage of approximate Bayesian credible sets including intervals estimated using Monte Carlo methods. The user has an ideal prior and likelihood, but generates a credible…

There are over 55 different ways to construct a confidence respectively credible interval (CI) for the binomial proportion. Methods to compare them are necessary to decide which should be used in practice. The interval score has been…

This paper concerns the construction of confidence intervals in standard seroprevalence surveys. In particular, we discuss methods for constructing confidence intervals for the proportion of individuals in a population infected with a…

The goal of any estimation study is an interval estimation of a the parameter(s) of interest. These estimations are mostly expressed using empirical confidence intervals that are based on sample point estimates of the corresponding…

When computing a confidence interval for a binomial proportion p one must choose between using an exact interval, which has a coverage probability of at least 1-{\alpha} for all values of p, and a shorter approximate interval, which may…

Given an IID sample from a positive distribution, we provide a method for constructing rigorous finite sample lower confidence bounds for the expectation of the distribution. The method is based on constructing rigorous confidence regions…