## 1 Introduction
For example, students enrolled in for-credit courses might be interested in course grades whereas others enrolled in MOOCs for the sole purpose of enjoyment of learning might be better served by information about satisfaction or perceived learning. Yet others taking professional certification preparation courses might benefit from learning the probability of being employed within three months of completion of the course. An effective information delivery system would be _automated_, _accurate_, and _impactful_. _Automation_ is particularly important in large-enrollment online courses. In MOOCs with many thousands of students, instructor feedback to each student, even with teaching assistants, is unrealistic [26, 27]. Peer review has been suggested as one way to fill the gap [28]. A mechanized cheerleader like the one envisioned here could be another tool for addressing the student-instructor interaction void. Even when instructors can't realistically provide one-on-one feedback to all, the imagined system could allow instructors to engage in triage by identifying those students most in need of intervention. _Accuracy_ means that messages are tailored to each student so that feedback is as individualized and precise as possible. This means foregoing the use of statistical aggregates. Suppose, for example, that a message is to convey the probability that a student with a grade of C on an exam will pass a course. One way to estimate that probability is to calculate, for all previous students with C exam scores, the ratio of those who passed the course relative to the total--a statistical aggregate that fails to recognize individual variation. A more accurate message system would consider the exam score but also whether the student is part-time or full-time, her learning style, undergraduate grade point average, or any other number of predictors of success. This is accomplished using statistical predictive models; with them, it is conceivable that every student who earned a grade of C on the exam would receive different probabilities of passing the course because the prediction mechanism incorporates personal characteristics that more accurately reflects each student's situation. An _impactful_ message system draws students' attentions in ways that positively affects outcomes. Information that intimidates or demoralizes can have unintended consequences. Information that arrives too late for students to adjust behavior is unproductive. Messages that arrive too frequently may be ignored. Careful thought must be given to how, what, how often, and when information is to be delivered if improved outcomes are to be achieved. Most LMSs have rudimentary messaging capabilities and there are now several publicly-available student signaling or early-warning routines [23]. The system envisioned in this article differs variously from existing products in these ways. * Some LMSs have \"what if\" algorithms that allow students to assess the level of performance needed to achieve a certain course grade. Those \"what if\" routines are based solely on the algebra of the final grade calculation; _i.e._, they are deterministic. We propose a messaging system that is _probabilistic_; it produces predictions using statistical methods that model uncertainty. * The proposed system can be designed to produce _longitudinal_ information so that students can track their progress over time and, importantly, see for themselves how their behavior impacts outcomes. * Our methodology incorporates as much _numerical_ information as possible about _individual_ student characteristics. * The envisioned system can be designed to be either _reactive_ or _proactive_ or both, allowing developers to design a system as complex as needed for the learning environment at hand. Our description of that system unfolds in this way. The probabilistic nature of the proposed system is rooted in statistical predictive models; a brief introduction to predictive models is provided in the next section.