Consider again the AR(1) model with mixture observational errors de scribed in Example 4.10. Modify the MCMC algorithm in order to per form posterior inference when t has the following Markovian structure:

Pr( t = 2 t 1= 2)=Pr( t=1 t 1=1)=p and Pr( t = 2 t 1=1)=Pr( t=1 t 1= 2)=(1 p)

where p is known. For suggestions see, for instance, Carter and Kohn

(1994).