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] = {p[t|Mi(k+1), z, Dk] . p[Mi(k+1)| z, Dk]}
p[t | z, Dk] = {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 Ci(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