The effect of small sample on optimal designs for logistic regression models

Asymptotic methods are commonly used in statistical inference for unknown parameters in binary data models. These methods are based on large sample theory, a condition which may be in conflict with small sample size and hence leads to poor results in the optimal designs theory. In this paper, we apply the second order expansions of the maximum likelihood estimator and derive a matrix formula for the mean square error (MSE) to obtain more precise optimal designs based on the MSE. Numerical results indicate the new optimal designs are more efficient than the optimal designs based on the information matrix.     

刑事证明标准的经济分析

提高证明标准,边际收益递减,边际成本递增。但证明标准不是越高越好,也不是越低越好,最佳证明标准应当由社会净收益最大化来决定。当证明标准的边际社会收益等于边际社会成本时,社会净收益实现了最大化,证明标准达到了最佳程度。对于不同性质的案件、刑事诉讼中不同阶段的诉讼行为来说,证明标准的边际收益是不同的,应当采取不同的证明标准。提高证明标准对于公、检、法等部门具有不同的边际收益和成本。部门收益和成本与社会收益和成本之间存在差异会导致部门行为的扭曲,损害社会利益。所以,必须采取措施促使部门和社会之间收益与成本趋于一致,从而实现社会利益的最大化。     

概念·构成·尺度:中国化马克思主义吸引力的认识论域

中国化马克思主义吸引力是指由中国化马克思主义理论呈现出的科学性、价值性而产生的一种能够使人民群众认同并自觉地遵循和实践的力量。从概念、构成、尺度切入,是我们深入理解中国化马克思主义吸引力的三个重要视域。     

上海米号业嘉谷堂房产纠纷解析——兼论中日战争对上海粮食行业的影响

抗战期间,上海市米号业同业公会会所——嘉谷堂被难民占住。抗战结束以后,为了收回会所,公会方面与十余家占住户打了多年的官司,直至新中国建立后的1954年才最终获得解决。抗战胜利以后,上海粮食业本就饱受恶性通胀和政府管制之苦,处境艰难,而旧址被占,更使其业务的开展受到严重的空间制约。从这个意义上说,中日战争不仅打乱了上海粮食行业的发展之路,也给它在战后恢复正常的运作秩序埋下了隐患。     

A variable-neighbourhood search algorithm for finding optimal run orders in the presence of serial correlation

The responses obtained from response surface designs that are run sequentially often exhibit serial correlation or time trends. The order in which the runs of the design are performed then has an impact on the precision of the parameter estimators. This article proposes the use of a variable-neighbourhood search algorithm to compute run orders that guarantee a precise estimation of the effects of the experimental factors. The importance of using good run orders is demonstrated by seeking D-optimal run orders for a central composite design in the presence of an AR(1) autocorrelation pattern.     

VARIATIONAL BAYESIAN ANALYSIS FOR HIDDEN MARKOV MODELS

The variational approach to Bayesian inference enables simultaneous estimation of model parameters and model complexity. An interesting feature of this approach is that it also leads to an automatic choice of model complexity. Empirical results from the analysis of hidden Markov models with Gaussian observation densities illustrate this. If the variational algorithm is initialized with a large number of hidden states, redundant states are eliminated as the method converges to a solution, thereby leading to a selection of the number of hidden states. In addition, through the use of a variational approximation, the deviance information criterion for Bayesian model selection can be extended to the hidden Markov model framework. Calculation of the deviance information criterion provides a further tool for model selection, which can be used in conjunction with the variational approach.     

Accelerated test system strength models based on Birnbaum–Saunders distribution: a complete Bayesian analysis and comparison

Several models for studies related to tensile strength of materials are proposed in the literature where the size or length component has been taken to be an important factor for studying the specimens’ failure behaviour. An important model, developed on the basis of cumulative damage approach, is the three-parameter extension of the Birnbaum–Saunders fatigue model that incorporates size of the specimen as an additional variable. This model is a strong competitor of the commonly used Weibull model and stands better than the traditional models, which do not incorporate the size effect. The paper considers two such cumulative damage models, checks their compatibility with a real dataset, compares them with some of the recent toolkits, and finally recommends a model, which appears an appropriate one. Throughout the study is Bayesian based on Markov chain Monte Carlo simulation.     

Optimum designs for parameter estimation in a mixture experiment with two correlated responses

In this paper, we investigate a mixture problem with two responses, which are functions of the mixing proportions, and are correlated with known dispersion matrix. We obtain D- and A-optimal designs for estimating the parameters of the response functions, when none or some of the regression coefficients of the two functions are the same. It is shown that when no prior knowledge about the regression coefficients is available, the D-optimal design is independent of the dispersion matrix, while the A-optimal design depends on it, provided the response functions are of different degree. On the other hand, when some of the regression coefficients are known to be the same for both the functions, the D-optimal design depends on the dispersion matrix when the two response functions are not of the same degree.     

Generalized minimum aberration mixed-level orthogonal arrays: A general approach based on sequential integer quadratically constrained quadratic programming

Orthogonal fractional factorial designs and in particular orthogonal arrays (OAs) are frequently used in many fields of application, including medicine, engineering, and agriculture. In this article, we present a methodology and an algorithm to find an OA, of given size and strength, which satisfies the generalized minimum aberration criterion. The methodology is based on the joint use of polynomial counting functions, complex coding of levels, and algorithms for quadratic optimization and puts no restriction on the number of levels of each factor.     

The performance of model averaged tail area confidence intervals

We investigate the exact coverage and expected length properties of the model averaged tail area (MATA) confidence interval proposed by Turek and Fletcher, CSDA, 2012, in the context of two nested, normal linear regression models. The simpler model is obtained by applying a single linear constraint on the regression parameter vector of the full model. For given length of response vector and nominal coverage of the MATA confidence interval, we consider all possible models of this type and all possible true parameter values, together with a wide class of design matrices and parameters of interest. Our results show that, while not ideal, MATA confidence intervals perform surprisingly well in our regression scenario, provided that we use the minimum weight within the class of weights that we consider on the simpler model.