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I have this hidden markov model/network with four unknown variables $y_{1:4}$ with the discrete domain $(0,1)$ and four known observations $y^{obs}_{1:4}$ and a potential function $\phi(x_i,x_j)$.

$$ \phi(x_i,x_j)= \begin{cases} 5,& \text{if } x_i=x_j\\ 2, & \text{otherwise} \end{cases} $$

Here's a visualization of the network

Markov network

At last I have this statistical information $$p(y^{obs}_i = 1 | y_i = 1) = 0.95$$ $$p(y^{obs}_i = 0 | y_i = 0) = 0.99$$

I now need to compute $p(y_1 = 1 | y^{obs}_1=1,y^{obs}_2=0,y^{obs}_3=0,y^{obs}_4=0$). I however have not a single clue on how to do this. I'm completely new to HMM's and online formula's don't even come close this this sort of problem.

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