In a Kalman filter model, discuss how you would compute the joint posterior distribution Pr ( w 1

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In a Kalman filter model, discuss how you would compute the joint posterior distribution

Pr ( w 1 …T | x 1 …T ) over all of the unknown world states. What form will this posterior distribution

take? In the Kalman filter we choose to compute the max-marginals solution instead. Why is this?