Homework 10: Estimating with DAGs
36-402, Advanced Data Analysis
Due at the start of class, Tuesday, 19 April 2011
This homework will illustrate some of the advantages of using a known DAG
structure. You will need to read the lectures on graphical models carefully in
order to do it.
Figure 1 is an elaboration of the graph used in lectures. All problems refer
to it, unless otherwise specified.
The file fake-smoke.csv contains some (synthetic) data, for use in problem
5.
1. Parents and children (10 points)
(a) (5 points) For each variable in the model, list its parents; or, if it has
no parents, say so.
(b) (5 points) For each variable in the model, list its children. (Some
variables have no children.)
2. Joint distributions and factorization (10 points) Using the graph, list the
smallest collection of marginal and conditional distributions which must
be estimated in order to get the joint distribution of all variables.
3. Associations (20 points) Should there be a positive association, a negative
association, or no association between the following variables? Explain
with reference to the graph. (2 points each)
(a) Yellowing of teeth and cancer?
(b) Yellowing of teeth and cancer, controlling for smoking?
(c) Yellowing of teeth and cancer, controlling for occupational prestige?
(d) Yellowing of teeth and cancer, controlling for smoking and exposure
to asbestos?
(e) Smoking and cancer, controlling for the amount of tar in the lungs?
(f) Asbestos and cancer, controlling for cellular damage?
(g) Smoking and cancer, controlling for asbestos?
(h) Smoking and asbestos, controlling for cellular damage?
(i) Tar in lungs and cancer, controlling for asbestos, smoking, and yel-
lowing of teeth?
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