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Understanding Bayesian Networks: Causal Reasoning in Student Performance and Grades

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This document explores the application of Bayesian networks in modeling the relationships between student intelligence, grades, SAT performance, and perceived difficulty of classes. Through evidential reasoning and intercausal analysis, it demonstrates how these factors interplay to affect a student's academic outcomes. Key probabilistic concepts are illustrated, revealing insights into how letter grades and test performance influence perceptions of class difficulty and intelligence. The findings emphasize the complexity of student performance and its implications for educational assessment.

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Understanding Bayesian Networks: Causal Reasoning in Student Performance and Grades

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  1. Representation Probabilistic Graphical Models Bayesian Networks Reasoning Patterns

  2. d0 d1 i0 i1 0.6 0.4 0.7 0.3 g1 g2 g3 i0,d0 0.3 0.4 0.3 i0,d1 0.05 0.25 0.7 s0 s1 i1,d0 0.9 0.08 0.02 i0 0.95 0.05 i1,d1 0.5 0.3 0.2 i1 0.2 0.8 l0 l1 g1 0.1 0.9 g2 0.4 0.6 g3 0.99 0.01 The Student Network Difficulty Intelligence Grade SAT Letter

  3. Causal Reasoning Intelligence Intelligence Difficulty Difficulty Grade SAT P(l1) ≈ 0.5 Letter P(l1 | i0) ≈ 0.39 P(l1 | i0 , d0) ≈ 0.51

  4. g1 g2 g3 i0,d0 0.3 0.4 0.3 i0,d1 0.05 0.25 0.7 i1,d0 0.9 0.08 0.02 i1,d1 0.5 0.3 0.2 Evidential Reasoning P(d1) = 0.4 P(i1) = 0.3 P(d1 | g3) ≈ P(i1 | g3) ≈ 0.63 0.08 Difficulty Intelligence Student gets a C  Grade SAT Letter

  5. Intercausal Reasoning P(d1) = 0.4 P(i1) = 0.3 P(d1 | g3) ≈ 0.63 P(i1 | g3) ≈ 0.08 P(i1 | g3, d1) ≈ 0.11 Difficulty Intelligence Class is hard! Grade SAT Student gets a C  Letter

  6. Intercausal Reasoning Explained X1 X2 Y OR

  7. Intercausal Reasoning II P(i1) = 0.3 P(i1 | g2) ≈ 0.175 P(i1 | g2, d1) ≈ 0.34 Difficulty Difficulty Intelligence Class is hard! Grade SAT g2 Student gets a B  Letter

  8. Student Aces the SAT • What happens to the posterior probability that the class is hard? Difficulty Intelligence Grade SAT Student aces the SAT  Letter Student gets a C 

  9. Student Aces the SAT P(d1) = 0.4 P(i1) = 0.3 P(d1 | g3) ≈ 0.63 P(i1 | g3) ≈ 0.08 P(d1 | g3, s1) ≈ 0.76 P(i1 | g3, s1) ≈ 0.58 Difficulty Intelligence Grade SAT Student aces the SAT  Letter Student gets a C 

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