Untruthful answering in repeated randomized response procedures

A simple and clear procedure is given that allows to some degree the estimation and testing of the probability of an untruthful answer in addition to estimating the population proportion by using Warner's (1965) randomized response technique twice.     

不同总体量和样本量时如何计算比例的置信区间

在总体或者总体子集不大情况下的抽样调查中,往往不易得出合理的关于比例的区间估计。这一类问题在抽样调查实践中已经严重到非说不可的地步。文章讨论了在样本量不大或者(和)在总体不大时估计比例的置信区间时往往忽略的问题,并给出了在不同情况下如何计算置信区间的方法。     

Variance estimation for measures of change in probability sampling

Variance estimation of changes requires estimates of variances and covariances that would be relatively straightforward to make if the sample remained the same from one wave to the next, but this is rarely the case in practice as successive waves are usually different overlapping samples. The author proposes a design‐based estimator for covariance matrices that is adapted to this situation. Under certain conditions, he shows that his approach yields non‐negative definite estimates for covariance matrices and therefore positive variance estimates for a large class of measures of change.     

On How to Deal with Deep Uncertainties in a Risk Assessment and Management Context

Recently, several authors have presented interesting contributions on how to meet deep or severe uncertainties in a risk analysis setting. In this article, we provide some reflections on some of the foundational pillars that this work is based on, including the meaning of concepts such as deep uncertainty, known probabilities, and correct models, the aim being to contribute to a strengthening of the scientific platform of the work, as well as providing new insights on how to best implement management policies meeting these uncertainties. We also provide perspectives on the boundaries and limitations of analytical approaches for supporting decision making in cases of deep uncertainties. A main conclusion of the article is that deep uncertainties call for managerial review and judgment that sees beyond the analytical frameworks studied in risk assessment and risk management contexts, including those now often suggested to be used, such as robust optimization techniques. This managerial review and judgment should be seen as a basic element of the risk management.     

A class of simple approximate sequential tests for adaptive comparison of two treatments

We consider the problem of sequentially deciding which of two treatments is superior, A class of simple approximate sequential tests is proposed. These have the probabilities of correct selection approximately independent of the sampling rule and depending on unknown parameters only through the function of interest, such as the difference or ratio of mean responses. The tests are obtained by using a normal approximation, and this is employed to derive approximate expressions for the probabilities of correct selection and the expected sample sizes. A class of data-dependent sampling rules is proposed for minimizing any weighted average of the expected sample sizes on the two treatments, with the weights being allowed to depend on unknown parameters. The tests are studied in the particular cases of exponentially.     

Robust bayesian analysis given a lower bound on the probability of a set

Suppose that just the lower bound of the probability of a measurable subset K in the parameter space Ω is a priori known, when inferences are to be made about measurable subsets A in Ω. Instead of eliciting a unique prior distribution, consider the class Г of all the distributions compatible with such bound. Under mild regularity conditions about the likelihood function, the range of the posterior probability of any A is found, as the prior distribution varies in Г. Such ranges are analysed according to the robust Bayesian viewpoint. Furthermore, some characterising properties of the extended likelihood sets are proved. The prior distributions in Г are then considered as a neighbour class of an elicited prior, comparing likelihood sets and HPD in terms of robustness.     

Sampling Some Truncated Distributions Via Rejection Algorithms

In this article, we develop rejection sampling algorithms to sample from some truncated and tail distributions. Such samplers are needed in many Markov chain Monte Carlo methods, often in connection with Bayesian inference. In addition to univariate normal, gamma, and beta distributions, we consider multivariate normal distributions truncated to certain sets.     

On a generalization of Poisson sampling

In real-time sampling, the units of a population pass a sampler one by one. Alternatively the sampler may successively visit the units of the population. Each unit passes only once and at that time it is decided whether or not it should be included in the sample. The goal is to take a sample and efficiently estimate a population parameter. The list sequential sampling method presented here is called correlated Poisson sampling. The method is an alternative to Poisson sampling, where the units are sampled independently with given inclusion probabilities. Correlated Poisson sampling uses weights to create correlations between the inclusion indicators. In that way it is possible to reduce the variation of the sample size and to make the samples more evenly spread over the population. Simulation shows that correlated Poisson sampling improves the efficiency in many cases.     

Turing’s anticipation of empirical bayes in connection with the cryptanalysis of the naval enigma *

The Enigma was a cryptographic (enciphering) machine used by the German military during WWII. The German navy changed part of the Enigma keys every other day. One of the important cryptanalytic attacks against the naval usage was called Banburismus, a sequentiai Bayesian procedure (anticipating sequential analysis) which was used from the sorine of 1941 until the middle of 1943. It was invented mainlv bv A. M. Turina and was perhaps the first important sequential Bayesian IE is unnecessab to describe it here. Before Banburismus could be started on a given day it was necessary to identifv which of nine ‘biaram’ (or ‘diaraph’) tables was in use on that day. In Turing’s approach to this identification hk had io istimate the probabilities of certain ‘trigraphs’. rrhese trigraphs were used. as described below. for determinine the initial wheel settings of messages). For estimatidg the probabilities, Turing inventedin important special case o the nonparametric (nonhypermetric) Empirid Bayes method independently of Herbert Robbins. The techniaue is the sumxisine form of Emdrical Baves in which a physical prior is assumed to eist but no apbroxiGate functional fonn is assumed for it.