11- bayesian networks and causality

Question 1

Bayesian Network defintion

Answer 1

• A graphical model that encodes probabilistic relationships among variables of interest

Question 2

How are Bayesian networks represented?

Answer 2

Direct acyclic graph (DAG)

Question 3

Bayesian network example in medicine

Answer 3

Vars:
- F (whether patient has flu)
- T (fever whether they have it)
- C (Cough)

Probabilities:
- P(T) probability of having fever
- P(T|F) prob of having fever given flu
- P(T|¬F) prob of fever without flu
- P(C|F): of cough given flu
- P(C|¬F) of cough without flu

Question 4

BAyesian student example

Answer 4

Vars:
- Difficulty D
- Ability A
- Grade G

Prob:
- P(D) test being difficult
- P(A) of student being prepared
- P(G|D,A) of getting a grade given the difficulty and ability

DAG:
D->G and A->G

Question 5

What can we do with Bayesian networks

Answer 5

• Joe Bob got a bad grade but good student. Exam hard
• Jane got top marks from uni. talented

These are used to say
- difficult exam, wont choose
- talented, get hired

Are they valid/trustworthy conclusions.

Question 6

With the student performance model, what do we assume?

Answer 6

• Grade G depends on difficulty D and ability A
• D and A are independent of each other i.e P(D|A) = P(D), P(A|D) = P(A)

Question 7

Student example, what do we know?

Answer 7

• Prior probabilites from previous years.

Question 8

Student example, what are we trying to find?

Answer 8

Posterior probabilites
- P(D|G) how difficult is the exame based on grade.
- P(A|G) what is the student’s capability based on grade

Question 9

Student example, how d we find the probabillity that the student has a high ability given a certain mark?

Answer 9

Bayes Theorem.

• P(A|G)=P(G|A)P(A)/P(G)
• Note that the probability increases as P(G) decreases and P(A) increases)

Question 10

In Bayesian net A -> B -> C is equivalent to…

Answer 10

C -> B -> A

Not speculating on whether one thing is causing another to happen

Question 11

Causal network

Answer 11

Like a bayesian network, but the edges represent “causation”

Question 12

Confounders

Answer 12

Variable that indluences both independent variable (exposure) and the dependent variable (outcome.

Can create a spurious association between exposure and outcome, making it difficult to discern the true causal relationship

Question 13

Confounders in exam results

Answer 13

Family support is a confounding factor as it effects both motivation and grade.

Same with Study Habits as it affects both class participation and grade

Question 14

Colliders

Answer 14

Multiple variables go into one

Question 15

Colliders problem in relation to the exam results problem (consider Sleep Quality and Study Habits)

Answer 15

grade is a collider with SQ and SH

• Partition students by grades
• It is possible that students with good grades have both high sleep qual and study habits, and in reverse.
• It might appear that there is a correlation but there is no causal link between the two (SQ and SH)

Question 16

Interventions

Answer 16

Actively manipulating a variable to observe effects on other varibles.

Notation: do operator do(X=x) X is set to a val x by ext. manipulation

Effect: break any incoming edges to X in causal graph and set X to x. Allows us to observe effect ofX on others