1. CSCE 582: Bayesian Networks Paper Presentation conducted by Nick Stiffler Ben Fine

2. Bayesian networks: A teacher’s view Russel G Almond Valerie J Shute Jody S. Underwood Juan-Diego Zapata-Rivera

3. ACED A Computer-Based-Assessment-for- Learning system covering the topic of sequences In this Paper it spans three sequence types Arithmetic Geometric Recursive

4. ACED A Prototype that explores Madigan and Almond Algorithms for selection of the next task in an assessment The use of targeted diagnostic feedback Tech solutions to make the assessment accessible to students with visual impairments

5. Geometric Sequence Model Proficiency Levels available to each node Low. Medium High.

6. Bayesian Network (SS) Individual task outcome variables -are entered as findings in task specific nodes where the results are propagated through the proficiency model Posterior Proficiency Model -gives the belief about the proficiency state for a particular student Note: Any functional of the posterior distribution can be used as a sore

7. Terminology S i0, S i1,…,S ik – proficiency variables for student i S i0 – special overall PV (Solve Geo. Problems) X i – Body of evidence P(S ik |X i ) -conditional distribution of S k given the observed outcomes

8. The Four Statistics (at least the ones we look at) Margin Cut Mode EAP

9. Margin The Marginal Distribution of Proficiency P(S ik |X i ) expected numbers of students in each proficiency Σ i P(S ik |X i ) Average proficiency for the class Σ i P(S ik |X i ) class size

10. Cut Identifier for a special state Ex. students ≥ medium are proficient P(S ik ≥ medium |X i ) Average cut score is the expected proportion of “proficient” students in the class

11. Mode The value of m the produces max{P(S ik = m |X i )} Improvements If student is within a threshold should be identified as being on the boundary When the Marginal Distribution is evenly spread out the system should identify students who have the greatest uncertainty To get modal scores count the number of students assigned to each category

12. EAP Expected a Posteriori Assign numbers to states to get an expectation over posterior High : 1 Medium : 0 Low : -1 1*P(S ik = high |X i ) + 0 * P(S ik = med |X i ) -1*P(S ik = low|X i ) Reduces to: P(S ik = high |X i ) - P(S ik = low |X i )

13. EAP (cont.) What it means The EAP would return the average ability level for each class Standard Deviation variability of proficiency

14. Scores coming out of the BN

15. Individual Level Plots

16. Comparing Groups

20. Reliability Observed Score = True Score + Error Signal to noise ration in signal processing Applying the Spearmen – Brown formula

21. Spearmen – Brown formula is the predicted reliability N is the number of "tests" combined is the reliability of the current "test" predicts the reliability of a new test by replicating the current test N times creating a test with N parallel forms of the current exam. Thus N = 2 implies doubling the exam length by adding items with the same properties as those in the current exam.

22. Why BN Works Well Offers significant improvement over number right scoring Bayes network estimates stabilize sub scores by borrowing strength from the overall reliability Differs from other methods b/c it starts with an expert constructed model of how the proficiencies interact Other methods use observed correlations b/t the scores on subtest