begin{equation}
small{
Delta (h)_{T+S} =
prod_{j=1}^{N} left[frac {P(x^j,y^j|theta_{paired})}
{P(x^j,y^j|theta_{unpaired})}right]left[frac{P(bp)_{x^j,y^j}
P(bp_{x^j,y^j}|pbp_{x^{j-1},y^{j+1}}) P(dl_{x^j})
P(dl_{x^j}|pdl_{x^{j-1}})P(dr_{y^j})P(dr_{y^j}|pdr_{y^{j+1}})}{P(sl)
P(dl|sl) P(sr) P(dr|sr)}right]}
end{equation}