Bayesian Probabilities and the Histories Algebra

We attempt a justification of a generalisation of the consistent histories programme using a notion of probability that is valid for all complete sets of history propositions. This consists of introducing Cox's axioms of probability theory and showing that our candidate notion of probability obeys them. We also give a generalisation of Bayes' theorem and comment upon how Bayesianism should be useful for the quantum gravity/cosmology programmes.Comment: 10 pages, accepted by Int. J. Theo. Phys. Feb 200

Optimising ITS behaviour with Bayesian networks and decision theory

We propose and demonstrate a methodology for building tractable normative intelligent tutoring systems (ITSs). A normative ITS uses a Bayesian network for long-term student modelling and decision theory to select the next tutorial action. Because normative theories are a general framework for rational behaviour, they can be used to both define and apply learning theories in a rational, and therefore optimal, way. This contrasts to the more traditional approach of using an ad-hoc scheme to implement the learning theory. A key step of the methodology is the induction and the continual adaptation of the Bayesian network student model from student performance data, a step that is distinct from other recent Bayesian net approaches in which the network structure and probabilities are either chosen beforehand by an expert, or by efficiency considerations. The methodology is demonstrated by a description and evaluation of CAPIT, a normative constraint-based tutor for English capitalisation and punctuation. Our evaluation results show that a class using the full normative version of CAPIT learned the domain rules at a faster rate than the class that used a non-normative version of the same system

MODELS AND METHODS FOR IMPLEMENTING PEDAGOGICAL INTERVENTIONS IN MODEL-TRACING COGNITIVE TUTORS

This paper presents some models and methods for generating pedagogical interventions in model-tracing cognitive tutors. They use Bayesian networks for assessment and making decisions, this feature allows managing uncertainty reasoning based on a formal foundation. This technique combines the rigorous probabilistic formalisms with a graphical representation and efficient inference mechanisms. It is explained how Bayesian networks are employed as an inference engine to assess the degree of learning of the relevant knowledge components in the learning domain and determine the proper pedagogical interventions for performing a productive learning proces

Affective learning: improving engagement and enhancing learning with affect-aware feedback

This paper describes the design and ecologically valid evaluation of a learner model that lies at the heart of an intelligent learning environment called iTalk2Learn. A core objective of the learner model is to adapt formative feedback based on students’ affective states. Types of adaptation include what type of formative feedback should be provided and how it should be presented. Two Bayesian networks trained with data gathered in a series of Wizard-of-Oz studies are used for the adaptation process. This paper reports results from a quasi-experimental evaluation, in authentic classroom settings, which compared a version of iTalk2Learn that adapted feedback based on students’ affective states as they were talking aloud with the system (the affect condition) with one that provided feedback based only on the students’ performance (the non-affect condition). Our results suggest that affect-aware support contributes to reducing boredom and off-task behavior, and may have an effect on learning. We discuss the internal and ecological validity of the study, in light of pedagogical considerations that informed the design of the two conditions. Overall, the results of the study have implications both for the design of educational technology and for classroom approaches to teaching, because they highlight the important role that affect-aware modelling plays in the adaptive delivery of formative feedback to support learning