Utilising D vines in a Bayesian belief network
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Scope
This method explains how to use D vines in creating rank correlations in a Bayesian belief network.
Definition
Kurowiecka and Cooke explain the method [1].
Let's take a BBN with five nodes
----1: . How is the BBN simulated? It is easy to get to page 136 half way (point 4). However, how is the vine formed from this? Why does the book say that the sampling order MUST be D4=(4,3,2,1) but D5=D(5,4,2,3,1)? --Jouni 11:25, 1 June 2009 (EEST) (type: truth; paradigms: science: comment)
- ----#:: . you cannot always find a regular vine whose nodes correspond to the arcs of a bbn. You have to do it "piecewise". You first extract a sampling order from the bbn. In thee ordering, each node is conditionally independent of its ancestors given its parents. Each variable can be sampled using a D vine. However, the D vine for variable n+1 is not a simple extendion of the D vine for vbl n. One needs to look at examples to see this. Roger, added by --Jouni 10:36, 2 June 2009 (EEST) (type: truth; paradigms: science: comment)
----2: . What does the Figure 6.10 actually mean at page 171? --Jouni 11:25, 1 June 2009 (EEST) (type: truth; paradigms: science: comment)
----3: . When we have the vine and the rank correlations that are required, how do we actually proceed? I can see why we need r21, r31, r43, r54, r52|4 based on the bbn, but I cannot see how to actually compute it? (Example 5.2 at page 137.) --Jouni 11:25, 1 June 2009 (EEST) (type: truth; paradigms: science: comment)
----4: . Do I understand correctly that the vine D4 is used to calculate r42, which is needed in D5 but that is not directly assessed? (Example 5.2 again?) --Jouni 11:25, 1 June 2009 (EEST) (type: truth; paradigms: science: comment)
----5: . How critical is the choice of copula? What are the criteria for choosing a copula? Can you cause a large bias by choosing a wrong copula? --Jouni 11:25, 1 June 2009 (EEST) (type: truth; paradigms: science: comment)
- ----#:: . you can build a bbn with arbitrary copulae, as long as zero correlation implies independence. However, if you want to update your bbn on observations, you are pretty much restricted to the normal copula. Roger, added by --Jouni 10:36, 2 June 2009 (EEST) (type: truth; paradigms: science: comment)
- ↑ Kurowiecka and Cooka: Uncertainty analysis. John Wiley and sons, 2006.
