A play-the-winner-type urn design with reduced variability

We propose a new adaptive allocation rule, the drop-the-loser, that randomizes subjects in the course of a trial comparing treatments with dichotomous outcomes. The rule tends to assign more patients to better treatments with the same limiting proportion as the randomized play-the-winner rule. The new design has significantly less variable allocation proportion than the randomized play-the-winner rule. Decrease in variability translates into a gain in statistical power. For some values of success probabilities the drop-the-loser rule has a double advantage over conventional equal allocation in that it has better power and assigns more subjects to the better treatment. Acknowledgments. I thank Stephen Durham, the associate editor, and the referees for their helpful suggestions.     

An Examination of the Interaction Between Modelling and Its Relationship with Construction Kits: Lessons from the Past and for the Future

Construction kits have played a significant part in nurturing the growth and development of the minds and manipulation-based skills of children (and adults) in formal and non-formal education settings. These kits have origins rooted in the representation of the built world and now have a diversity of form and function, including technical versions with moving parts. This article examines some of the historically based ideas that lie behind the role that kits may have in terms of physical modelling. The article traces the transformation of kits from simple bricks and blocks into more complicated pieces for space-filling and achieving the transfer of forces and motion. This transformation occurred during the Victorian era when the influence of the ideas of educationalists and, perhaps rather strangely, exponents of early aviation, played major roles in determining the diversity of forms of construction kit and modelled possibilities that are now to be seen in classrooms and homes. The article ends with a review of some of the lessons from the past and present that will need to be considered in relation to concrete modelling in schools for the future. This revised version was published online in July 2006 with corrections to the Cover Date.     

Getting the Most Out of a Mandatory Subordinated Debt Requirement

Recent advances in asset pricing—the reduced-form approach to pricing risky debt and derivatives—are used to quantitatively evaluate several proposals for mandatory bank issue of subordinated debt. We find that credit spreads on both fixed- and floating-rate subordinated debt provide relatively clean signals of bank risk and are not unduly influenced by nonrisk factors. Fixed-rate debt with a put is unacceptable, but making the putable debt floating resolves most problems. Our approach also helps to clarify several different notions of “bank risk.”