# 1. 5 points. In lecture we mentioned that the directionality

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1. 5 points. In lecture we mentioned that the directionality of edges in Bayesian networks do not necessarily
reflect causality, but having causal edges often lead to simpler network structures (and hence greater inference
efficiency). We will explore this concept further using the burglar alarm example, shown above.
(a) Write out all the independence / conditional independence assumptions implied by the graphical structure
of the original network. (Use B, E, A, J, M as the random variables.)
Hint: There should be 21 in total. Recall that ALBIC is equivalent to BlILA|C (so they only count as
one conditional independence), but ALB|C is different from AlIL BIC, D.
(b) Now consider networks (a) and (b) that involve the same variables. In each of these cases, we consider
variables in a different order, and when introducing the variable, we introduced all the edges necessary to
ensure the original probability distribution can still be represented. For example, in network (a), when
A was introduced, both arrows leading from M and J were necessary, otherwise conditional independence
assumptions not present in the original network would have been introduced (e.g., if M A was not
MILAJ would be introduced). Write out all the independence con
ional independence
present, the
assumptions implied by the graphical structure of network (a)
MaryCalls
MaryCalls
PB)
P(E)
Burglary
Earthquake
001
002
JohnCalls
JohnCalls
E
РА)
Earthquake
95
Alarm
Alarm
94
29
001
Burglary
Burglary
A PM
A PU
Earthquake
Alarm
MaryCalls
JohnCalls
90
70
01
05
(b)
(a)
Figure 1: From left to right, we will refer to the above Bayesian networks as the original network, network (a)
and network (b)