Geoscience Reference
In-Depth Information
A Bayesian belief network (also called Bayes net) is a graphical representation of
the conditional probability and causality relationships between variables. The
model is described qualitatively by directed acyclic graphs where nodes and edges
represent variables and the dependencies between variables. The nodes where the
edge originates and ends are called the parent and the child, respectively. Bayesian
belief networks allow for probabilistic inference to be performed, indicating that the
probability of each value of a node can be computed when the values of the other
variables are known.
The nodes that can be reached from other nodes are called descendent. In
Bayesian network, each variable is independent of its non-descendent given the state
of its parents. Since the independence among the variables are clearly de
ned, not all
joint probabilities in the Bayesian system need to be calculated, which provides an
ef
cient way to compute the posterior probabilities. Suppose the set of variables in a
BBN is {A
1
,A
2
,
,A
n
} and that parents (A
i
) denotes the set of parents of the node
…
A
i
in the BBN. Then the joint probability distribution for {A
1
,A
2
,
,A
n
} can be
…
calculated from the product of individual probabilities of the nodes:
Y
n
i
¼
1
PA
i
parents
ð
A
i
Þ
P
ð
A
i
; ...;
A
n
Þ¼
ð
j
Þ
ð
1
Þ
In our case, the Bayesian belief network represents the multiple relationships
between different spatial, temporal and other factors, including errors in the tech-
nology itself (input), and the facet of the candidate road segment that we wish to
identify (output). We use a Bayesian belief network to impute automatically the
probability for each road segment in a
filtered road set.
Figure
3
shows the network structure that we use to infer the matched road
segment with respect to GPS traces. A candidate road segment is treated as a
function of the states of the variables included in the BBN.
To what extent a road segment is matched with a location may be partly
determined by the information of the previously matched data. For example,
PDOP
DirectionDiff
Road Matched
(Yes, No)
RoadAzimuth
DistToRoad
AngleDiff
Connectivity
Fig. 3 Model structure for the inference of map matching
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