Solutions - Bayesian Networks in R: With Applications in Systems Biology - page 123

1.2 Consider the graphs shown in Fig. 1.1 .
(a) Obtain the skeleton of the partially directed and directed graphs.
(b) Enumerate the acyclic graphs that can be obtained by orienting the undi-
rected arcs of the partially directed graph.
(c) List the arcs that can be reversed (i.e., turned in the opposite direction),
one at a time, without introducing cycles in the directed graph.
(a) The skeletons of the partially directed and directed graphs are, respectively:

a

A

E

D

A

B C

B

C

D E

(b) Only six acyclic orientations of the partially directed graph are possible:

b

E E E

D D D

A A A

B B B

C C C

c

E E E

D D D

A A A

B B B

C C C

(c) All arcs of the directed graph can be reversed without introducing cycles.
1.3 The (famous) iris data set reports the measurements in centimeters of
the sepal length and width and the petal length and width for 50 flowers from
each of 3 species of iris (“setosa,” “versicolor,” and “virginica”).
(a) Load the iris data set (it is included in the data set package, which is
part of the base R distribution and does not need to be loaded explicitly)
and read its manual page.
(b) Investigate the structure of the data set.
(c) Compare the sepal length among the three species by plotting histograms
side by side.
(d) Repeat the previous point using boxplots.
(a) > data(iris)
> ?iris