Hi Guys,

I am really at a loss. Iam trying to use the total probabilty therom to decompose a conditional probability distribution. I don't know masses about probabilty, but I am trying to program a method documented in a research paper.

p[t | z, Dk] = Total probabilty therom-summation.bmp{p[t|Mi(k+1), z, Dk] . p[Mi(k+1)| z, Dk]}

p[t | z, Dk] = Click image for larger version. 

Name:	summation.bmp 
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ID:	9730{Ci(k+1) . p[t|Mi(k+1), z, Dk]}

so Ci(k+1) = p[Mi(k+1) | z, Dk]

Mi(k+1) = the event that at time k+1, the mapping of network i is the correct mapping

p[Mi(k+1) | z, Dk] = probabilty of event Mi(k+1)

So it holds true that Click image for larger version. 

Name:	summation.bmp 
Views:	11 
Size:	4.8 KB 
ID:	9730Ci(k+1) = 1

In the paper the equation for calculating p[t|Mi(k+1), z, Dk] is specified. The paper also says that " p[t | z, Dk] can be suboptimally decomposed in terms of I estimated PDFs by using the Total Probabilty theorem. "

I need to establish how to calculate p[Mi(k+1) | z, Dk] using the above information. I have researched the total probabilty theorem but with no success.

Many THanks

Laura