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When starting an N -body simulation of an isolated galaxy, it is desirable to select particles from a distribution function to ensure that the model is in equilibrium. Random sampling from a DF is widely used, but results in a set of particles that differs by shot noise from that intended. This paper presents a method to reduce sampling noise that has been developed by the author in a many collaborations over a number of years. The technique has been partly described in past papers, though the ideas have not previously been gathered together, nor have its advantages been clearly demonstrated in past work. Of course, sampling errors can also be reduced by a brute force increase in the number of particles, but methods to achieve the same effect with fewer particles have obvious advantages. Here we not only describe the method, but also present three sets of simulations to illustrate the practical advantages of reducing sampling error. The improvements are not dramatic, but are clearly worth having. [ABSTRACT FROM AUTHOR]

Nested sampling (NS) is a popular algorithm for Bayesian computation. We investigate statistical errors in NS both analytically and numerically. We show two analytic results. First, we show that the leading terms in Skilling's expression using information theory match the leading terms in Keeton's expression from an analysis of moments. This approximate agreement was previously only known numerically and was somewhat mysterious. Second, we show that the uncertainty in single NS runs approximately equals the standard deviation in repeated NS runs. While intuitive, this was previously taken for granted. We close by investigating our results and their assumptions in several numerical examples, including cases in which NS uncertainties increase without bound. [ABSTRACT FROM AUTHOR]

In sample surveys that collect information on skewed variables, it is often desirable to assess the influence of sample units on the sampling error of survey-weighted estimators of finite population parameters. The conditional bias is an attractive measure of influence that accounts for the sampling design and the estimation method. It is defined as the design expectation of the sampling error conditional on a given unit being selected in the sample. The estimation of the conditional bias is relatively straightforward for simple sampling designs and estimators. However, for complex designs or complex estimators, it may be tedious to derive an explicit expression for the conditional bias. In those complex surveys, variance estimation is often achieved through replication methods such as the bootstrap. Bootstrap methods of variance estimation are typically implemented by producing a set of bootstrap weights that is provided to users along with the survey data. In this article, we show how to use these bootstrap weights to obtain an estimator of the conditional bias. Our bootstrap estimator is evaluated in a simulation study and illustrated using data from the Canadian Survey of Household Spending. [ABSTRACT FROM AUTHOR]

Motivation: It is commonly assumed in pattern recognition that cross-validation error estimation is ‘almost unbiased’ as long as the number of folds is not too small. While this is true for random sampling, it is not true with separate sampling, where the populations are independently sampled, which is a common situation in bioinformatics.Results: We demonstrate, via analytical and numerical methods, that classical cross-validation can have strong bias under separate sampling, depending on the difference between the sampling ratios and the true population probabilities. We propose a new separate-sampling cross-validation error estimator, and prove that it satisfies an ‘almost unbiased’ theorem similar to that of random-sampling cross-validation. We present two case studies with previously published data, which show that the results can change drastically if the correct form of cross-validation is used.Availability and implementation: The source code in C++, along with the Supplementary Materials, is available at: http://gsp.tamu.edu/Publications/supplementary/zollanvari13/.Contact: ulisses@ece.tamu.eduSupplementary information: Supplementary data are available at Bioinformatics online. [ABSTRACT FROM AUTHOR]