Editorial

Helmut Anheier is Assistant Professor of Sociology at Rutgers University, New Brunswick, New Jersey; Research Associate, Institute for Policy Studies, Johns Hopkins University, Baltimore, Maryland, USA.     

A Bayesian method of sample size determination with practical applications

Summary.  The problem motivating the paper is the determination of sample size in clinical trials under normal likelihoods and at the substantive testing stage of a financial audit where normality is not an appropriate assumption. A combination of analytical and simulation-based techniques within the Bayesian framework is proposed. The framework accommodates two different prior distributions: one is the general purpose fitting prior distribution that is used in Bayesian analysis and the other is the expert subjective prior distribution, the sampling prior which is believed to generate the parameter values which in turn generate the data. We obtain many theoretical results and one key result is that typical non-informative prior distributions lead to very small sample sizes. In contrast, a very informative prior distribution may either lead to a very small or a very large sample size depending on the location of the centre of the prior distribution and the hypothesized value of the parameter. The methods that are developed are quite general and can be applied to other sample size determination problems. Some numerical illustrations which bring out many other aspects of the optimum sample size are given.     

Pooling multivariate data under W, LR and LM tests

Two independent random samples are drawn from two multivariate normal populations with mean vectors μ1 and μ2 and a common variance-covariance matrix Σ. Ahmed and Saleh (1990) considered preliminary test maximum likelihood estimator (PMLTE) for estimating μ1 based on the Hotelling's T _N ², when it is suspected that μ1=μ2. In this paper, the PTMLE based on the Wald (W), Likelihood Ratio (LR) and Lagrangian Multiplier (LM) tests are considered. Using the quadratic risk function, the conditions of superiority of the proposed estimator for departure parameter are derived. A max-min rule for the size of the preliminary test of significance is presented. It is demonstrated that the PTMLE based on W test produces the highest minimum guaranteed efficiencies compared to UMLE among the three test procedures.     

The Secrets of Scheherazade: Toward a Functional Analysis of Imaginative Literature

A functional analysis of selected aspects of imaginative literature is presented. Reading imaginative literature is described as a process in which the reader makes indirect contact with the contingencies operating on the behavior of story characters. A functional story grammar is proposed in which the reader''s experience with a story is interpreted in terms of escape contingencies in which the author initially introduces an establishing operation consisting of a source of tension, which is resolved in some way by the outcome of the story. Although escape contingencies represent the functional basis for the structure of stories, they are to be understood in a context of many other reinforcers for reading fiction. Other contingencies that maintain reading are discussed. Functional analyses of imaginative literature have much to offer, both in improving literary education and in understanding the behavioral processes that occur on the part of the reader.     

The non-profit sector in East Germany: before and after unification

The paper describes how the non-profit sector in East Germany has passed through several distinct phases in recent years. It shows how the role of the non-profit sector under the system of party dominance and centralised economic and social planning signified a major contradiction of East German society: the artificial under-development of civic society in eastern Europe's most successful economy. During the first phase of the transition period in late 1989, the expression and manifestation of political views was predominant. With the disintegration of the socialist party-state, the needs for social service provision increased. West German organisations have increasingly become the dominant factor in East German non-profit sector affairs. The paper argues that the East German non-profit sector will emerge as a slightly poorer and more secular version of its West German counterpart.     

Are there more almost separable partitions than separable partitions?

A partition of a set of n points in d-dimensional space into p parts is called an (almost) separable partition if the convex hulls formed by the parts are (almost) pairwise disjoint. These two partition classes are the most encountered ones in clustering and other partition problems for high-dimensional points and their usefulness depends critically on the issue whether their numbers are small. The problem of bounding separable partitions has been well studied in the literature (Alon and Onn in Discrete Appl. Math. 91:39–51, 1999; Barnes et al. in Math. Program. 54:69–86, 1992; Harding in Proc. Edinb. Math. Soc. 15:285–289, 1967; Hwang et al. in SIAM J. Optim. 10:70–81, 1999; Hwang and Rothblum in J. Comb. Optim. 21:423–433, 2011a). In this paper, we prove that for d≤2 or p≤2, the maximum number of almost separable partitions is equal to the maximum number of separable partitions.