ABSTRACT
State-space models clearly have a Bayesian connection since one can view x(t), t = 0, . . . , n, as parameters whose prior distributions are determined from the state equation (1.20). When the u(·) and x(0) vectors are specified to be normal, as is often the case in Bayesian settings, the responses are also normal provided that the e(·) are normally distributed. In any case, whether one views state-space models from a Bayesian or frequentist perspective, there will be a closed form expression for the sample likelihood when both the x(·) and e(·) processes are normal. The KF Algorithm 4.3 has some additional utility for
normal state-space models. In that instance it can be used to efficiently evaluate the likelihood function which, in turn, can be employed for estimation of any unknown parameters. In this chapter we explore how the KF can be used for this purpose.
