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Table 1 The conditional probabilities between for the variables Ai,j and θi,j

From: Error-correcting decoders for communities in networks

A i,j θ i,j P(Ai,j|θi,j) P(θi,j|Ai,j)
1 0 p in \(\frac {p_{in}}{p_{in} + p_{out}}\)
1 1 p out \(\frac {p_{out}}{p_{in} + p_{out}}\)
0 0 1 - pin \(\frac {1-p_{in}}{2-(p_{in} + p_{out})}\)
0 1 1 - pout \(\frac {1-p_{out}}{2-(p_{in} + p_{out})}\)
  1. The last column was calculated using Bayes’ rule with an assumption on the prior of P(θi,j=1)=1/2