On the estimation of the most probable number in a serial dilution experiment

The purpose of this paper is to present some alternative estimates for the 'most probable number' of bacteria in a serial dilution experiment. These estimates are directed to be less biased than the ordinary maximum likelihood estimate. A numerical example illustrates the extent to which the variance and the mean square error of these estimates are generally less than those corresponding to the maximum likelihood estimate.     

The Progress of Financial Market Integration in East Asia

The study investigates the progress of financial market integration in selected East Asian countries after the 1997 financial crisis. Adopting Johansen (Econometrica 59:1551–1580, 1991) multivariate cointegration on the region’s credit and stock markets, the study finds only partial cointegration in both markets which imply a low level of integration. However, for regional stock markets, the result suggests that the level of integration has been improving after the crisis.     

Asymptotic joint distribution of sample quantiles and sample mean with applications

Based on a sample from an absolutely continuous distribution F with density f, and with the aid of the Bahadur (Ann. Math. Statist. 37( 1966 ), 577-580) representation of sample quantiles, the asymptotic joint distribution of three statistics, the sample p^th and q^th quantiles (0 < p < q < l) and the sample mean, is obtained. Using the Cramer-Wold device, asymptotic distributions of functions of the three statistics can be derived. In particular, the asymptotic joint distribution of the ratio of sample p^th quantile to sample mean and the ratio of sample q^th quantile to sample mean is presented. Finally, consistent estimators are proposed for the variances and covariances of these limiting distributions.     

A new class of mixture models for differential gene expression in DNA microarray data

One of the fundamental issues in analyzing microarray data is to determine which genes are expressed and which ones are not for a given group of subjects. In datasets where many genes are expressed and many are not expressed (i.e., underexpressed), a bimodal distribution for the gene expression levels often results, where one mode of the distribution represents the expressed genes and the other mode represents the underexpressed genes. To model this bimodality, we propose a new class of mixture models that utilize a random threshold value for accommodating bimodality in the gene expression distribution. Theoretical properties of the proposed model are carefully examined. We use this new model to examine the problem of differential gene expression between two groups of subjects, develop prior distributions, and derive a new criterion for determining which genes are differentially expressed between the two groups. Prior elicitation is carried out using empirical Bayes methodology in order to estimate the threshold value as well as elicit the hyperparameters for the two component mixture model. The new gene selection criterion is demonstrated via several simulations to have excellent false positive rate and false negative rate properties. A gastric cancer dataset is used to motivate and illustrate the proposed methodology.     

A Bayesian compartmental model for the evaluation of 1,3-butadiene metabolism

Summary. We propose a Bayesian model for physiologically based pharmacokinetics of 1,3-butadiene (BD). BD is classified as a suspected human carcinogen and exposure to it is common, especially through cigarette smoke as well as in urban settings. The main aim of the methodology and analysis that are presented here is to quantify variability in the rates of BD metabolism by human subjects. A three-compartmental model is described, together with informative prior distributions for the population parameters, all of which represent real physiological variables. The model is described in detail along with the meanings and interpretations of the associated parameters. A four-compartment model is also given for comparison. Markov chain Monte Carlo methods are described for fitting the model proposed. The model is fitted to toxicokinetic data obtained from 133 healthy subjects (males and females) from the four major racial groups in the USA, with ages ranging from 19 to 62 years. Subjects were exposed to 2 parts per million of BD for 20 min through a face mask by using a computer-controlled exposure and respiratory monitoring system. Stratification by ethnic group results in major changes in the physiological parameters. Sex and age were also tested but not found to have a significant effect.     

Improved quality control charts for monitoring the process mean,using double-ranked set sampling methods

Statistical control charts are widely used in the manufacturing industry. The Shewhart-type control charts are developed to improve the monitoring process mean by using the double quartile-ranked set sampling, quartile double-ranked set sampling, and double extreme-ranked set sampling methods. In terms of the average run length, the performance of the proposed control charts are compared with the existing control charts based on simple random sampling, ranked set sampling and extreme-ranked set sampling methods. An application of real data is also considered to investigate the performance of the suggested process mean control charts. The findings of the study revealed that the newly suggested control charts are superior to the existing counterparts.