Bernal S D_2010.pdf - University of Plymouth

3.3. DEFlNmON AND MATHEMATICAL FORMULATION
Note thai node W also sends a message back to the evidence node S, but in this case the resulting
belief is equal to the initial evidence and is not affeclcd by the message, i.e. Bel{s) — A{s) =
(0,1). This is because the type of evidence was hard evidence. If instead, soft evidence was
used (e.g. X(s) = (0.1.0.9)), the top-down message ns{w) would be able lo modify the belief
in S. This can he understood if we consider that soft evidence contains a certain degree of
uncertainly, and is therefore susceptible lo being modulated (confirmed or contradicted) by
other information in the network, while hard evidence is assumed lo be irrefutable fact.
3.3.3.8 Example of belief propagalion with diagnostic evidence and causal evidence (ex­
plaining away)
In this scenario there is both bottom-up and top-down evidence. When evidence is propagated
from a parent lo a child node, from known causes to unknown effects, this is called causal
reasoning or top-down prediction. The main purpose of this scenario is lo illustrate the explain­
ing away effect. For clarity, we omit the detailed numerical calculations for the beliefs and
messages, as the reader can easily follow the example using Figure 3.7, which shows all the
relevant resulting values. These have been obtained using the same Equations ((3.27)-(3.31))
and procedure described in Ihc previous example.
In this example, the prior probability of Gales is set equal lo hard evidence asserting the true
state of the variable. Consequently, top-down evidence from the high-level cause Gales is com­
bined with boiiom-up evidence from the low-level effect Surfing. This is sometimes referred to
as data fusion. The resulting belief in Waves is higher than in the previous scenario (0,87 vs.
0.722). This makes sense, as the variable Waves is now receiving positive evidence not only
from the child node Surfing, but also from the parent node Gales, providing further support for
the belief Waves=true.
This in lum also leads to an update in the belief of Fishing, indicating its value is now even
lower than for Uie previous scenario (0.365 vs. 0.439). This is a direct consequence of the
probability of Waves being higher due to the new evidence introduced in the variable Gales. In
other words, knowing that Ihc moon i.s in a stale which is likely to generate big waves reduces
ihe chances of fishing activity.
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