Interval estimation of a small proportion via inverse sampling

On the basis of a negative binomial sampling scheme, we consider a uniformly most accurate upper confidence limit for a small but unknown proportion, such as the proportion of defectives in a manufacturing process. The optimal stopping rule, with reference to the twin criteria of the expected length of the confidence interval and the expected sample size, is investigated. The proposed confidence interval has also been compared with several others that have received attention in the recent literature.     

ESTIMATION OF THE NUMBER OF PEOPLE IN A DEMONSTRATION

It is of interest to estimate the size of a crowd in a demonstration. We propose a practical method to obtain an estimate of the size of the crowd and its standard error. This method has been implemented in practice and, compared with other counting methods, is found to be more efficient, more timely and have less scope for bias. The method described in this paper was motivated by the annual 1 July demonstrations in Hong Kong, and data from the 2006 demonstration are used as an example of the proposed method.     

Exact Tests of Significance in Higher Dimensional Tables

We describe methods used to provide an exact test of significance of the hypothesis that all factors are mutually independent of each other in 2³ and 2⁴ contingency tables. Several numerical examples demonstrate the advantages of exact tests over approximate significance levels. We give bounds on the number of tables needed to perform this exact significance test. In four or more dimensions the number of tables in this enumeration becomes astronomical with even modest sample sizes. Inverting the characteristic function of the exact distribution has proved useful in these situations.     

A Note on Bayesian Analyses of Capture–Recapture Data with Perfect Recaptures

The present article deals with the problem of misspecifying the disturbance-covariance matrix as scalar, when it is locally non scalar. We consider a family of shrinkage estimators based on OLS estimator and compare its asymptotic properties with the properties of OLS estimator. We proposed a similar family of estimators based on FGLS and compared its asymptotic properties with the shrinkage estimator based on OLS under a Pitman's drift process. The effect of misspecifying the disturbances covariance matrix was analyzed with the help of a numerical simulation.     

Statistical Inference of Type-II Progressively Hybrid Censored Data with Weibull Lifetimes

In this article, we discuss the maximum likelihood estimators and approximate maximum likelihood estimators of the parameters of the Weibull distribution with two different progressively hybrid censoring schemes. We also present the associated expressions of the expected total test time and the expected effective sample size which will be useful for experimental planning purpose. Finally, the efficiency of the point estimation of the parameters based on the two progressive hybrid censoring schemes are compared and the merits of each censoring scheme are discussed.     

A Poisson geometric process approach for predicting drop-out and committed first-time blood donors

A Poisson geometric process (PGP) model is proposed to study individual blood donation patterns for a blood donor retention program. Extended from the geometric process (GP) model of Lam [16 Y. Lam, Geometric process and replacement problem, Acta Math. Appl. Sin. 4 (1988), pp. 366–377. doi: 10.1007/BF02007241[Crossref] , [Google Scholar]], the PGP model captures the rather pronounced trend patterns across clusters of donors via the ratio parameters in a mixture setting. Within the state-space modeling framework, it allows for overdispersion by equating the mean of the Poisson data distribution to a latent GP. Alternatively, by simply setting, the mean of the Poisson distribution to be the mean of a GP, it has equidispersion. With the group-specific mean and ratio functions, the mixture PGP model facilitates classification of donors into committed, drop-out and one-time groups. Based on only two years of observations, the PGP model nicely predicts donors’ future donations to foster timely recruitment decision. The model is implemented using a Bayesian approach via the user-friendly software WinBUGS.     

‘I make use of my precious experience,and help others. It's a kind of blessing.’ Does public sharing of past experiences help in the rehabilitation of former offenders or drug abusers?

The Community Education Service (CES) of The Society of Rehabilitation and Crime Prevention (SRACP) has pioneered the adoption of life education in crime prevention education in Hong Kong since 1977. Under this programme, former offenders and drug abusers are recruited to share their experiences with community audiences. Through such sharing, it is hoped that the former offenders and drug abusers will gain a deeper insight into the consequences of committing crime or abusing drugs, have the courage to admit their failings and find the way to lead a more fulfilling and law-abiding life.

In the past, different organizations have employed former offenders and drug abusers in educational programmes, particularly in relation to the prevention of juvenile delinquency. A number of studies demonstrate the educational effectiveness of sharing past deviant behaviours with audiences. Moreover, the mission of SRACP is to help the reintegration into society of former offenders and drug abusers. Consequently, employing former offenders and drug abusers to share their experiences serves another important function; to facilitate the transformation of their past histories into valuable assets and help with their own rehabilitation during the process of serving others, as suggested by ‘helper therapy’ and ‘professional ex-s’ (Brown 1991). A successful rehabilitation means success in reducing recidivism.

This paper examines whether sharing one's real-life experiences with others can influence the rehabilitation process, and provides recommendations for improving service delivery to benefit both audience and the speakers themselves. Fifteen individuals who were formerly either offenders or drug abusers, aged between 18 and 45 years, and who had led a ‘clean’ life for the previous six months, took part in in-depth interviews in order to investigate their perceptions of the function of real-life experience sharing in their own rehabilitation. Concepts of labelling theory (Becker 1963) and self-fulfilling prophecy (Wilkins 1976) provided the framework for these interviews.

The study concludes that respondents are normally able to help themselves to resist crime and drugs, given that the internal and external factors affecting sharing are well addressed. The results identify practical implications and directions for future involvement of former offenders and drug abusers in community-based crime prevention education programmes.     

Marginal Likelihood Estimation with the Cross-Entropy Method

We consider an adaptive importance sampling approach to estimating the marginal likelihood, a quantity that is fundamental in Bayesian model comparison and Bayesian model averaging. This approach is motivated by the difficulty of obtaining an accurate estimate through existing algorithms that use Markov chain Monte Carlo (MCMC) draws, where the draws are typically costly to obtain and highly correlated in high-dimensional settings. In contrast, we use the cross-entropy (CE) method, a versatile adaptive Monte Carlo algorithm originally developed for rare-event simulation. The main advantage of the importance sampling approach is that random samples can be obtained from some convenient density with little additional costs. As we are generating independent draws instead of correlated MCMC draws, the increase in simulation effort is much smaller should one wish to reduce the numerical standard error of the estimator. Moreover, the importance density derived via the CE method is grounded in information theory, and therefore, is in a well-defined sense optimal. We demonstrate the utility of the proposed approach by two empirical applications involving women's labor market participation and U.S. macroeconomic time series. In both applications, the proposed CE method compares favorably to existing estimators.     

Facilitating the Calculation of the Efficient Score Using Symbolic Computing

The score statistic continues to be a fundamental tool for statistical inference. In the analysis of data from high-throughput genomic assays, inference on the basis of the score usually enjoys greater stability, considerably higher computational efficiency, and lends itself more readily to the use of resampling methods than the asymptotically equivalent Wald or likelihood ratio tests. The score function often depends on a set of unknown nuisance parameters which have to be replaced by estimators, but can be improved by calculating the efficient score, which accounts for the variability induced by estimating these parameters. Manual derivation of the efficient score is tedious and error-prone, so we illustrate using computer algebra to facilitate this derivation. We demonstrate this process within the context of a standard example from genetic association analyses, though the techniques shown here could be applied to any derivation, and have a place in the toolbox of any modern statistician. We further show how the resulting symbolic expressions can be readily ported to compiled languages, to develop fast numerical algorithms for high-throughput genomic analysis. We conclude by considering extensions of this approach. The code featured in this report is available online as part of the supplementary material.     

幼儿园种植课程提升幼儿关键经验的思考

关键经验是幼儿在发展过程中必不可少的,通过与课程主动互动不断生成的,通过多种形式获得的经验。关键经验具有目标性、生成性、连续性、选择性、主动性的特点。梳理幼儿园种植课程的关键经验类型,并以关键经验视域反思种植课程存在问题,建议采取的应对策略：1）明确关键经验目标性,进行种植课程整体规划;2）重视关键经验生成性与连续性,丰富种植课程内容;3）关注关键经验选择性,调整种植课程结构;4）强调关键经验主动性,鼓励幼儿多种形式参与。