6.8 Consider the model yt = xt + vt, where vt is Gaussian white noise with variance σ2 v, xt are independent Gaussian random variables with mean zero and var(xt) = rtσ2x with xt independent of vt, and r1, . . . , rn are known constants. Show that applying the EM algorithm to the problem of estimating σ2x and σ2 v leads to updates (represented by hats)

where, based on the current estimates (represented by tildes),

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n rt t=1 and 2 n - ) + ], n t=1