Estimation of the Population Size in the Classical Occupancy Problem

In the classical occupancy problem where the random variable X is the number of N elements selected by K individuals when each element is equally likely to be chosen by any of the individuals, it is desired to estimate N. Three estimators given in the literature are compared with three estimators derived in this article, two of which are based on Bayesian methods, utilizing a simulation study. One of the Bayes estimators appears to perform the best along with one proposed in the literature in 1968. The estimators are also compared using data obtained from a cemetery in Ohio.     

Non-estrogen-based treatments for menopausal symptoms

The British Menopause Society Council is committed to provide up-to-date authoritative reviews to aid health professionals to inform and advise women about key issues in postreproductive health. This guidance refers to non-estrogen-based treatments for menopausal symptoms, such as hot flushes, symptoms of urogenital atrophy and lack of sexual desire. Treatment of choice should be based on up to-date information and targeted to individual women's needs. Non-hormonal strategies may be useful for women with estrogen-dependent disease such as breast cancer.     

Developing strategies for deriving small population fertility rates

Many agencies require population estimates and projections by ethnic group. These projections need ethnic-specific, age-specific fertility rates (ASFRs) but their inclusion is challenging since ethnicity is not recorded at birth registration. In this paper maternity data are used in a case study of electoral wards in Bradford, West Yorkshire, to develop fertility rates for small populations for a 1991 based projection. The challenge is to capture local variations in fertility by ethnic group when data are sparse. Small areas were grouped together using cluster analysis to define combinations with similar sociodemographic and fertility experiences so that sparse data could be aggregated to estimate reliable ethnic-specific fertility rates. For comparison, the data were aggregated into the 1991 Office for National Statistics area type classification. Fertility rates by single year of age for all area types were smoothed using the Hadwiger function. For the White ethnic group there were sufficient births to create ethnic-specific, ward-level ASFRs. For other ethnicities grouping of areas was necessary. The accuracy of the ASFRs in predicting births was assessed using mean absolute percentage error. Results show that for some minority groups district-level ethnic-specific fertility rates produced the most accurate birth estimates even though they were based on a larger area. This implies that rates created may be informative about the local area for White ethnic type but not in the same way for smaller ethnic groups. In terms of grouping strategies we recommend that existing classifications are assessed to determine how well variations in rates are stratified before embarking on a custom scheme. Where population sub-groups are small in some areas, it may be more reliable to use rates derived for larger areas and apply these to local populations. Inevitably, the rates used in a projection are a compromise but hopefully will still capture important dimensions of population change.     

On approximating optimal weight “no”-certificates in weighted difference constraint systems

This paper is concerned with the design and analysis of approximation algorithms for the problem of determining the least weight refutation in a weighted difference constraint system. Recall that a difference constraint is a linear constraint of the form \(x_{i}-x_{j} \le b_{ij}\) and a conjunction of such constraints is called a difference constraint system (DCS). In a weighted DCS (WDCS), a positive weight is associated with each constraint. Every infeasible constraint system has a refutation, which attests to its infeasibility. In the case of a DCS, this refutation is a subset of the input constraints, which when added together produces a contradiction of the form \(0 \le -b\), \(b> 0\). It follows that every refutation acts as a “no”-certificate. The length of a refutation is the number of constraints used in the derivation of a contradiction. Associated with a DCS \(\mathbf{D: A\cdot x \le b}\) is its constraint network \(\mathbf{G= \langle V,E, b \rangle }\). It is well-known that \(\mathbf{D}\) is infeasible if and only if \(\mathbf{G}\) contains a simple, negative cost cycle. Previous research has established that every negative cost cycle of length k in \(\mathbf{G}\) corresponds exactly to a refutation of \(\mathbf{D}\) using k constraints. It follows that the shortest refutation of \(\mathbf{D}\) (i.e., the refutation which uses the fewest number of constraints) corresponds to the length of the shortest negative cycle in \(\mathbf{G}\). The constraint network of a WDCS is represented by a constraint network \(\mathbf{G = \langle V, E, b, l \rangle }\), where \(\mathbf{l}:\mathbf{E \rightarrow \mathbb {N}}\) represents a function which associates a positive, integral length with each edge in \(\mathbf{G}\). In the case of a WDCS, the weight of a refutation is defined as the sum of the lengths of the edges corresponding to the refutation. The problem of finding the minimum weight refutation in a WDCS is called the weighted optimal length resolution refutation (WOLRR) problem and is known to be NP-hard. In this paper, we describe a pseudo-polynomial time algorithm for the WOLRR problem and convert it into a fully polynomial time approximation scheme (FPTAS).     

The Ambiguous Role of Welfare Structures in Relation to the Emergence of Activism Among Disabled People: research evidence from Northern Ireland

The boundary between the disability movement and traditional forms of welfare production, whether in the statutory or voluntary sectors is discussed in this article. Drawing on the resource mobilization paradigm in social movement theory, it discusses the role played by existing welfare structures in the formation of disabled people as activists and in the initial stages of mobilization. The article reports on the findings of interviews with activists in the emerging disability movement in Northern Ireland, a region with a very low level of movement activity. It concludes that in such areas, disabled people often lack the resources to mobilize on their own account and are heavily dependent on formal welfare for the necessary networks and opportunities. Although this can be a significant constraint, it is not necessarily so if these opportunities enable the infant movement associations to grow beyond the welfare settings lying behind their emergence. This is more likely to take place if other supportive factors are in place. Many of the required resources are to be found within more traditional voluntary organisations. Few of these organisations play any role in the process of mobilization. But where mobilization is taking place, they are invariably present.     

The value of the aggregate data approach in meta-analysis with time-to-event outcomes

Collecting individual patient data has been described as the 'gold standard' for undertaking meta-analysis. If studies involve time-to-event outcomes, conducting a meta-analysis based on aggregate data can be problematical. Two meta-analyses of randomized controlled trials with time-to-event outcomes are used to illustrate the practicality and value of several proposed methods to obtain summary statistic estimates. In the first example the results suggest that further effort should be made to find unpublished trials. In the second example the use of aggregate data for trials where no individual patient data have been supplied allows the totality of evidence to be assessed and indicates previously unrecognized heterogeneity.     

Similar or Different? Downward Accountability Across Civil Society Organisational Forms

VOLUNTAS: International Journal of Voluntary and Nonprofit Organizations - This research explores accountability to beneficiaries within Civil Society Organisations (CSOs). Conceptualised as...