Vincent F. Melfi

Estimation after adaptive allocation

Abstract In recent years a vast number of adaptive designs have been proposed, often in the context of clinical trials or industrial applications. The adjective adaptive refers to the feature that, in such designs, the current allocation may depend on data already collected. When analyzing such designs, proving consistency and asymptotic normality of estimators is of fundamental importance. For some designs, this has not yet been done. When it has, the proofs have been tailored to the particular design being analyzed, often utilizing martingale arguments. In this paper independence properties of the allocated sequence are proved and then used to provide a simple method for proving consistency and asymptotic normality of estimators for a wide class of designs.

Nonlinear renewal theory for Markov random walks

Let {Sn} be a Markov random walk satisfying the conditions of Kestens Markov renewal theorem. It is shown that if {Zn} is a stochastic process whose finite-dimensional, conditional distributions are asymptotically close to those of {Sn} (in the sense of weak convergence), then the overshoot of {Zn} has the same limiting distribution as that of {Sn}. In the case where {Zn} can be represented as a perturbed Markov random walk, this allows substantial weakening of the slow change condition on the perturbation process; more importantly, no such representation is required. An application to machine breakdown times is given.

Cross-platform learning: children's learning from multiple media

Educational media projects often span several platforms (e.g., games, TV, hands-on materials), under the assumption that multiple platforms elicit greater learning than a single medium. To test this assumption, 672 fourth graders were assigned to use different combinations of math-based Cyberchase media for eight weeks: DVD Only, Web Only, DVD + Web, All Materials, or No Exposure (control). Mathematical problem solving was assessed via hands-on, pretest-posttest tasks, and by tracking software that recorded performance in three Cyberchase online games. Consistent with past research, significantly greater problem solving gains appeared among Cyberchase users than the control group. Pre-post effects were often stronger in the DVD + Web group than in groups that used either medium alone. Moreover, users of multiple media employed significantly more sophisticated mathematical strategies -- and produced more correct responses -- while playing online games. Thus, a unique benefit of cross-platform learning seems to lie in transfer of learning, i.e., applying educational content learned from one medium (e.g., television) to support learning in another medium (e.g., games), resulting in richer engagement and greater posttest gains.

A model for instrumentation system management in concurrent computer systems

An instrumentation system is a measurement-based performance evaluation abstraction. Management of an instrumentation system becomes critical when tracing is enabled on an application program that runs for an excessively long period of time. This paper presents queuing models for two instrumentation system management policies, namely flush-one-when-it-fills (FOF) and flush-all-when-one-fills (FAOF). The performance results obtained analytically are compared to results obtained through trace-driven simulation. An appropriate instrumentation system management policy ensures optimal usage of the available local memory space to avoid excessive flushes of the local buffers or perturbation of the program behavior. The results show that each of the FOF and FAOF policies is suitable for one of these two objectives: the FAOF policy requires a smaller number of flushes but with greater perturbation; the converse is true for the FOF policy. Therefore, a compromise between these two policies may be needed when implementing the instrumentation system management policy.<<ETX>>

Television, Games, and Mathematics: Effects of Children's Interactions with Multiple Media

Research has shown that educational media, such as television series or interactive games, can promote significant learning. However, it is quite common for producers to create several interconnected media, such as a television show and an associated web site, under the assumption that multiple platforms elicit greater learning than a single medium would. The research reported in this paper uses Cyberchase media as the setting in which to investigate the effectiveness of multiple media as a tool for mathematical learning for elementary school children. The study includes both a naturalistic phase, which mirrors childrens typical use of the media, and an experimental phase, which allows for causal inference to be drawn about their learning outcomes.