Tail asymptotics for the maximum of perturbed random walk

Consider a random walk $S=(S_n:n\geq 0)$ that is ``perturbed'' by a stationary sequence $(\xi_n:n\geq 0)$ to produce the process $(S_n+\xi_n:n\geq0)$. This paper is concerned with computing the distribution of the all-time maximum $M_{\infty}=\max \{S_k+\xi_k:k\geq0\}$ of perturbed random walk with a negative drift. Such a maximum arises in several different applications settings, including production systems, communications networks and insurance risk. Our main results describe asymptotics for $\mathbb{P}(M_{\infty}>x)$ as $x\to\infty$. The tail asymptotics depend greatly on whether the $\xi_n$'s are light-tailed or heavy-tailed. In the light-tailed setting, the tail asymptotic is closely related to the Cram\'{e}r--Lundberg asymptotic for standard random walk.Comment: Published at http://dx.doi.org/10.1214/105051606000000268 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

A Foundation Failure in Philadelphia

The foundation failure of the 22 story, steel framed, federal courthouse in Philadelphia occurred because of an inadequate geotechnical assessment of a complex geological condition. The founding elevations for caissons were improperly determined on materials that could not sustain the design load. This condition was further complicated by the presence of groundwater and poor concrete construction practices. These conditions resulted in an extensive and costly remedial measures which included a grouting program and the replacement of 14 faulty caissons

When Things Go Wrong in the Clinic: How to Prevent and Respond to Serious Student Misconduct

This article documents the types of misconduct that students commit, explores why serious misconduct occurs, examines whether such conduct can be anticipated and reduced by prescreening and monitoring potentially problematic students, and suggests how misconduct might be addressed once it occurs. The authors\u27 analysis thus encompasses both legal obligations and pedagogical considerations, and it takes account of the differing perspectives of clinical professors, law school administrators, and bar examiners. The authors operate from a student centered perspective that emphasizes the support and development of law students. This article is prescriptive, therefore, in the extent to which it emphasizes preventive actions and constructive responses. The purpose of this article is not to prescribe how a clinical professor should deal with any particular instance of misconduct, but rather to empower clinical professors to deal thoughtfully with such situations by providing them with helpful information and an analytic framework

Using educational analytics to improve test performance

Learning analytics are being used in many educational applications in order to help students and Faculty. In our work we use predictive analytics, using student behaviour to predict the likely performance of end of semester final grades with a system we call PredictED. The main contribution of our approach is that our intervention automatically emailed students on a regular basis, with our prediction for the outcome of their exam performance. We targeted first year, first semester University students who often struggle with making the transition into University life where they are given much more responsibility for things like attending class, completing assignments, etc. The form of student behaviour that we used is students’ levels and types of engagement with the University’s Virtual Learning Environment (VLE), Moodle. We mined the Moodle access log files for a range of parameters based on temporal as well as content access, and use machine learning techniques to predict likely pass/fail, on a weekly basis throughout the semester using logs and outcomes from previous years as training material. We chose ten first-year modules with reasonably high failure rates, large enrolments and stability of module content across the years to implement an early warning system on. From these modules 1,558 students were registered for one of these modules. They were offered the chance to opt into receiving weekly email alerts warning them about their likely outcome. Of these 75% or 1,181 students opted into this service. Pre-intervention there were no differences between participants and non-participants on a number of measures related to previous academic record. However, post- intervention the first-attempt final grade performance yielded nearly 3% improvement (58.4% to 61.2%) on average for those who opted in. This tells us that providing weekly guidance and personalised feedback to vulnerable first year students, automatically generated from monitoring of their online behaviour, has a significant positive effect on their exam performance

When Things Go Wrong in the Clinic: How to Prevent and Respond to Serious Student Misconduct

This article documents the types of misconduct that students commit, explores why serious misconduct occurs, examines whether such conduct can be anticipated and reduced by prescreening and monitoring potentially problematic students, and suggests how misconduct might be addressed once it occurs. The authors\u27 analysis thus encompasses both legal obligations and pedagogical considerations, and it takes account of the differing perspectives of clinical professors, law school administrators, and bar examiners. The authors operate from a student centered perspective that emphasizes the support and development of law students. This article is prescriptive, therefore, in the extent to which it emphasizes preventive actions and constructive responses. The purpose of this article is not to prescribe how a clinical professor should deal with any particular instance of misconduct, but rather to empower clinical professors to deal thoughtfully with such situations by providing them with helpful information and an analytic framework

Student data: data is knowledge – putting the knowledge back in the students’ hands

Learning Management Systems are integral technologies within higher education institutions. These tools automatically amass large amounts of log data relating to student activities. The field of learning analytics uses data from learning management systems (LMSs) and student information systems to track student progress and predict future performance in order to enhance learning environments (Siemens, 2011). The aim of this paper is to describe a project where we utilized a system developed in Dublin City University to use information about student engagement with our LMS, Moodle, to create a model predicting pass or failure in certain modules. The project is divided into three distinct phases. An initial investigation was completed analyzing Moodle activity for the last six years. The purpose of this exercise was to determine automatically if “trends” could be identified linking Moodle engagement with student attainment. This was done by training a machine learning classifier to map student online behaviour, against outcomes. Once the classifier was trained, several modules were identified as suitable for building a predictor of student exam success.Ten modules were identified for semester 1 with a further seven identified for semester 2. The second phase involved analyzing current students’ engagement with these modules and sending students information about the predictions of their attainment for the module, based on their Moodle engagement. At this stage concerns were raised within the university that the data that we share with the students could actually have the opposite effect to what we are after, i.e. the student may look at the data and think that there is no point in putting in more effort as ‘I’m too far behind already’. Dietz-Uhler and Hurn refer to this as “instead of being a constructive tool, feedback becomes a prophet of failure” (Dietz-Uhler, 2013). This contention was addressed by conducting an online survey with students in an effort to explore their experiences of being provided with feedback regarding their engagement with the LMS. The third and final phase of this project was the development of a dashboard for lecturers to enable monitoring of their students’ engagement with their module on Moodle. This enables lecturers to have an overview of how students are engaging with their course on Moodle and quickly identify students who are not engaging with the LMS and who are potentially at risk of failure or non-completion. There are numerous examples of the use of learning analytics in higher education. This study focuses on the provision of data obtained through learning analytics to the student and qualitative analysis that was conducted in relation to this data. This research adds to the existing research into learning analytics being used for student retention