Consider the logistic DLM given by (see Storvik 2002)

yt t

Bin(r logit( + t))

N( t 1w)

Simulate T = 300 observations from this model with = 09, w = 1 and = =05

(a) Assume that and are known. Implement a SMC algorithm for sequential ltering and parameter learning of and w assuming a Gaussian prior on and an inverse-gamma prior on w

(b) Assume that and are also unknown. Rewrite the model as yt t

Bin(r logit( t))

N( + ( t 1 )w)

where t = + tandw= w ImplementaSMCalgorithmforon line ltering and parameter learning assuming independent Gaussian priors on and and an inverse-gamma prior on w