Geometric rounding: a dependent randomized rounding scheme

We develop a new dependent randomized rounding method for approximation of a number of optimization problems with integral assignment constraints. The core of the method is a simple, intuitive, and computationally efficient geometric rounding that simultaneously rounds multiple points in a multi-dimensional simplex to its vertices. Using this method we obtain in a systematic way known as well as new results for the hub location, metric labeling, winner determination and consistent labeling problems. A comprehensive comparison to the dependent randomized rounding method developed by Kleinberg and Tardos (J. ACM 49(5):616–639, 2002) and its variants is also conducted. Overall, our geometric rounding provides a simple and effective alternative for rounding various integer optimization problems.     

The role,power and influence of company chairs

This paper develops an analytical framework to depict the heterogeneity that characterises the role of board chair and demonstrate the potential variability in how chairs operate boards and exercise power and influence on strategy, control and resource related tasks at board level. Theories of power and influence, as applied to top management teams and boards of directors, are explicated within the context of contemporary governance practices that are establishing the role of the board chair as distinct to that of the chief executive officer. Specifically, the paper maps sources of power and varying contemporary chair practices, including chair nomenclature (i.e. executive vs. non-executive chairs), chair origin (insider vs. outsider) and chair time (full-time vs. part-time). A number of theoretical chair-power models emerge from this analysis and are subject to empirical analysis using data collected from 160 chairs of 500 FTSE-listed companies. Theoretically and empirically, the paper complements structural approaches to studying boards with attention to behaviour on boards. By linking board structure, board process and the exercise of influence, the study reveals both differences amongst chairs in how they run the board, but also that chairs’ differ in the influence they exert on board-related tasks. Full-time executive chairs exert their greatest influence in strategy and resource dependence tasks whereas part-time, non-executive chairs seem to exert more influence over monitoring and control tasks.     

Demand for health risk reductions: A cross-national comparison between the U.S. and Canada

Using a large stated preference survey conducted across the U.S. and Canada, we assess differences in individual willingness to pay (WTP) for health risk reductions between the two countries. Our utility-theoretic choice model allows for systematically varying marginal utilities for avoided future time in different adverse health states (illness-years, recovered/remission years, and lost life-years). We find significant differences between Canadian and U.S. preferences. WTP also differs systematically with age, gender, education, and marital status, as well as a number of attitudinal and subjective health-perception variables. Age profiles for WTP are markedly different across the two countries. Canadians tend to display flatter age profiles, with peak WTP realized at older ages.     

On the number of separable partitions

Consider partitions of a given set A of n distinct points in general position in ℝ ^d into parts where each pair of parts can be separated by a hyperplane that contains a given set of points E. We consider the problem of counting and generating all such partitions (correcting a classic 1967 result of Harding about the number of such partitions into two parts). Applications of the result to partition problems are presented.     

Are Individuals’ Desired Family Sizes Stable? Evidence from West German Panel Data

Using West German panel data constructed from the 1988 and 1994/1995 wave of the DJI Familiensurvey, we analyze the stability and determinants of individuals’ total desired fertility. We find considerable variation of total desired fertility across respondents and across interviews. In particular, up to 50% of individuals report a different total desired fertility across survey waves. Multivariate analysis confirms the importance of background factors including growing up with both parents, having more siblings, and being Catholic for preference formation. Consistent with the idea that life course experiences provide new information regarding the expected costs and benefits of different family sizes, the influence of background factors on total desired fertility is strong early in life and weakens as subsequent life course experiences, including childbearing, take effect. Accounting for unobserved individual heterogeneity, we estimate that an additional child may increase the total desired fertility of women with children by 0.14 children, less than what conventional estimates from cross-sectional data would have suggested.     

Acceleration of the Multiple-Try Metropolis algorithm using antithetic and stratified sampling

The Multiple-Try Metropolis is a recent extension of the Metropolis algorithm in which the next state of the chain is selected among a set of proposals. We propose a modification of the Multiple-Try Metropolis algorithm which allows for the use of correlated proposals, particularly antithetic and stratified proposals. The method is particularly useful for random walk Metropolis in high dimensional spaces and can be used easily when the proposal distribution is Gaussian. We explore the use of quasi Monte Carlo (QMC) methods to generate highly stratified samples. A series of examples is presented to evaluate the potential of the method.     

Estimation of the means of the bivariate normal using moving extreme ranked set sampling with concomitant variable

The estimation of the means of the bivariate normal distribution, based on a sample obtained using a modification of the moving extreme ranked set sampling technique (MERSS) is considered. The modification involves using a concomitant random variable. Nonparametric-type methods as well as the maximum likelihood estimation are considered. The estimators obtained are compared to their counterparts based on simple random sampling (SRS). It appears that the suggested estimators are more efficient. Also, MERSS with concomitant variable is easier to use in practice than the usual ranked set sampling (RSS) with concomitant variable. The issue of robustness of the procedure is addressed. Real trees data set is used for illustration.     

Assumptions for long-term stochastic population forecasts in 18 European countries

The aim of the ‘Uncertain Population of Europe’(UPE) project was to compute long-term stochastic (probabilistic) population forecasts for 18 European countries. We developed a general methodology for constructing predictive distributions for fertility, mortality and migration. The assumptions underlying stochastic population forecasts can be assessed by analysing errors in past forecasts or model-based estimates of forecast errors, or by expert judgement. All three approaches have been used in the project. This article summarizes and discusses the results of the three approaches. It demonstrates how the—sometimes conflicting—results can be synthesized into a consistent set of assumptions about the expected levels and the uncertainty of total fertility rate, life expectancy at birth of men and women, and net migration for 18 European countries.