12.1 Overview

In this chapter, we will be working up to simple univariate state-space JAGS models. We will write each of the models with the same univariate state-space form.

\[\begin{equation} \begin{gathered} x_t = b x_{t-1} + u + w_t, \, w_t \sim N(0,q)\\ y_t = x_t + a + v_t, \, v_t \sim \,\text{N}(0, r) \end{gathered} \tag{12.1} \end{equation}\]

We will be fitting linear regressions with this form, and this will mean the JAGS code is more verbose than necessary, but the goal is to build up to our univariate state-space code by building off simpler models.