Bayesian analysis of elapsed times in continuous‐time Markov chains

The authors consider Bayesian analysis for continuous‐time Markov chain models based on a conditional reference prior. For such models, inference of the elapsed time between chain observations depends heavily on the rate of decay of the prior as the elapsed time increases. Moreover, improper priors on the elapsed time may lead to improper posterior distributions. In addition, an infinitesimal rate matrix also characterizes this class of models. Experts often have good prior knowledge about the parameters of this matrix. The authors show that the use of a proper prior for the rate matrix parameters together with the conditional reference prior for the elapsed time yields a proper posterior distribution. The authors also demonstrate that, when compared to analyses based on priors previously proposed in the literature, a Bayesian analysis on the elapsed time based on the conditional reference prior possesses better frequentist properties. The type of prior thus represents a better default prior choice for estimation software.     

Optimal scaling of Metropolis algorithms: Heading toward general target distributions

The authors provide an overview of optimal scaling results for the Metropolis algorithm with Gaussian proposal distribution. They address in more depth the case of high‐dimensional target distributions formed of independent, but not identically distributed components. They attempt to give an intuitive explanation as to why the well‐known optimal acceptance rate of 0.234 is not always suitable. They show how to find the asymptotically optimal acceptance rate when needed, and they explain why it is sometimes necessary to turn to inhomogeneous proposal distributions. Their results are illustrated with a simple example.     

An evaluation of the childhood family structure measures from the sixth wave of the British Household Panel Survey

Summary.  The paper performs an evaluation of the data that were collected in the sixth wave of the British Household Panel Survey (BHPS) on childhood family structure. After comparing such data with a large number of studies by using external sources, we find that the BHPS data overestimate the proportion of people who report an experience of life in a non-intact family during childhood by about 10%. Although an explanation based on recall error that deteriorates with the age of the BHPS respondents is possible, the overestimation is likely to be accounted for by non-ignorable attrition that may affect most of the comparison studies based on longitudinal data. Conversely, comparisons with other independent measurements from the BHPS itself reveal that the wave 6 data underestimate the proportion of young people who have lived at least part of their childhood in a non-intact family by about 8%. The probability of disagreement between these two sets of measures is strongly associated with poor interview characteristics, which may affect the comparison measure more than the wave 6 measure. Despite such differences, there is therefore a substantial degree of similarity between the family structure information that was collected in the sixth wave of the BHPS and the host of highly diverse records against which it has been compared.     

How bad can a voting location be

Two questions concerning the location of a single facility by a voting process are investigated for transportation networks:

- What is the maximum number of customers located on the network preferring some rival point over a voting solution?

- How does the average distance of the customers to the facility increase when a voting location instead of a Weber location is chosen for the facility?

Complete answers are given for general networks and for certain planar networks, viz., the so-called generalized cacti.     

Leveraging middle managers’ brokerage for corporate entrepreneurship: The role of multilevel social capital configurations

Building on recent efforts to bring a socio-political perspective to social capital research, we develop and test a multilevel framework that explains why middle managers who occupy brokerage positions differ in their ability and willingness to engage in entrepreneurial behavior. More specifically, we provide a contextualized understanding of the links among middle managers' brokerage, their political-support ties, and their personal initiative. Results derived from data on 383 middle managers and 72 top managers in 34 business units indicate that political-support ties with top managers strengthen the relationship between middle managers’ brokerage and personal initiative. However, this positive effect depends on the social capital resources available in the focal business unit. It is attenuated in business units with a supportive and trusting social context and amplified in business units with high levels of internal connectedness. By uncovering these incompatibilities and complementarities, our study demonstrates the value of accounting for different social capital configurations and the interplay of their inherent social capital resources when examining the effects of brokerage on corporate entrepreneurship.