In Example 6.13 (Hepatitis A) estimate a latent category Markov chain model with \(m=4\) states, and identify the time points with highest probabilities of shifts into the highest incidence state.

Data from Example 6.13

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Consider weekly counts y, (2001 through to 2004, with T = 209 observations) of Hepati- tis A incidence in Germany from the SurvStat@RKI database (see Figure 6.8). The goal is to identify major shifts (especially epidemic onsets) as against stable occurrence levels. A modified version of the survival-birth process described in section 6.6.2 is applied. Thus y = x + Zr, with x~Po(v), log(v) = Po + B cos(2t/52) + 2sin(2t/52) + u, u ~ N(0, 1/) ~ Ztly-1 Po(y-1)