Analyzing supersaturated designs with entropic measures

A supersaturated design is a design for which there are fewer runs than effects to be estimated. In this paper, we propose a method for screening out the important factors from a large set of potentially active variables, based on an information theoretical approach. Three entropy measures: Rényi entropy, Tsallis entropy and Havrda–Charvát entropy, have been associated with the measure of information gain, in order to identify the significant factors using data and assuming generalized linear models. The investigation of the proposed method performance and the comparison of each entropic measure application have been accomplished through simulation experiments. A noteworthy advantage of this paper is the use of generalized linear models for analyzing data from supersaturated designs, a fact that, to the best of our knowledge, has not yet been studied.     

Statement of Withdrawal: Statistical analysis of an endemic disease from a capture–recapture experiment

There are a number of statistical techniques for analysing epidemic outbreaks. However, many diseases are endemic within populations and the analysis of such diseases are complicated by changing population demography. Motivated by the spread of cowpox among rodent populations, a combined mathematical model for population and disease dynamics is introduced. An MCMC algorithm is then constructed to make statistical inference for the model based on data being obtained from a capture–recapture experiment. The statistical analysis is used to identify the key elements in the spread of the cowpox virus.     

Classical estimation of hazard rate and mean residual life functions of Pareto distribution

Abstract

In this paper we find the maximum likelihood estimates (MLEs) of hazard rate and mean residual life functions (MRLF) of Pareto distribution, their asymptotic non degenerate distribution, exact distribution and moments. We also discuss the uniformly minimum variance unbiased estimate (UMVUE) of hazard rate function and MRLF. Finally, two numerical examples with simulated data and real data set, are presented to illustrate the proposed estimates.     

New Data,Strategies, and Insights for Listeria monocytogenes Dose‐Response Models: Summary of an Interagency Workshop, 2011

Listeria monocytogenes is a leading cause of hospitalization, fetal loss, and death due to foodborne illnesses in the United States. A quantitative assessment of the relative risk of listeriosis associated with the consumption of 23 selected categories of ready‐to‐eat foods, published by the U.S. Department of Health and Human Services and the U.S. Department of Agriculture in 2003, has been instrumental in identifying the food products and practices that pose the greatest listeriosis risk and has guided the evaluation of potential intervention strategies. Dose‐response models, which quantify the relationship between an exposure dose and the probability of adverse health outcomes, were essential components of the risk assessment. However, because of data gaps and limitations in the available data and modeling approaches, considerable uncertainty existed. Since publication of the risk assessment, new data have become available for modeling L. monocytogenes dose‐response. At the same time, recent advances in the understanding of L. monocytogenes pathophysiology and strain diversity have warranted a critical reevaluation of the published dose‐response models. To discuss strategies for modeling L. monocytogenes dose‐response, the Interagency Risk Assessment Consortium (IRAC) and the Joint Institute for Food Safety and Applied Nutrition (JIFSAN) held a scientific workshop in 2011 (details available at http://foodrisk.org/irac/events/ ). The main findings of the workshop and the most current and relevant data identified during the workshop are summarized and presented in the context of L. monocytogenes dose‐response. This article also discusses new insights on dose‐response modeling for L. monocytogenes and research opportunities to meet future needs.     

Sums of powers of binomial coefficients

An asymptotic series for sums of powers of binomial coefficients is derived, the general term being defined and usable with a computer symbolic language. Sums of squares of coefficients in the symmetric case are shown to have a link with classical moment problems, but this property breaks down for cubes and higher powers. Problems of remainders for the asymptotic series are mentioned. Using the reflection formula for I'(.), a continuous form for a binomial function is set up, and this becomes oscillatory outstde the usual range. A new contmued fraction emerges for the logarithm of an adjusted sum of binomial squares. The note is a contribution to the problem of the interpretation of asymptotic series and processes for their convergence acceleration.     

Bayesian analysis of a multiple-recapture model

In the Bayesian analysis of a multiple-recapture census, different diffuse prior distributions can lead to markedly different inferences about the population size N. Through consideration of the Fisher information matrix it is shown that the number of captures in each sample typically provides little information about N. This suggests that if there is no prior information about capture probabilities, then knowledge of just the sample sizes and not the number of recaptures should leave the distribution of Nunchanged. A prior model that has this property is identified and the posterior distribution is examined. In particular, asymptotic estimates of the posterior mean and variance are derived. Differences between Bayesian and classical point and interval estimators are illustrated through examples.     

Asymptotocally nonparametric tests with censored paired data

A class of asymptotically nonparametric test with contains a test proposed by Wei(1980), is considered for testing the equality of two continuous distribution funcitons when paired observations are subject to arbitrary right censorship. It is shown that under the null hypothesis each test statistic converges in distribution to the standard normal random variable. Furthermore. the Monte Carlo simulation results indicate that some tests in this class are more powerful than Wei's test. A generalization to incomplete censored paired data is also included.