7. Using the binary REM sleep data from Carlin and Polson (1992) (see Exercise 8 7.odc), apply a dynamic logistic model with scale mixing on the variance of the states, and with degrees of freedom assigned the prior used by Knorr-Held (1999). Thus

with appropriate priors for the initial value θ1 and with an equally weighted discrete prior on ν = 2k , for k = −1,−0.9,−0.8, . . . , 6.9, 7. Consider the form of the density for the one-step-ahead state θ121 at T = 120.

y~Bern(), logit(,) = 0, ~ 0N(0-1, V/2) ~ Ga(0.5v, 0.5v), t> 1,