Suppose i have a simple linear regression like this:
y_t \sim{\mathcal{N}}(x_t\beta, \sigma_y)
\beta \sim{\mathcal{N}}(0,5)
\sigma_y \sim{\mathcal{C}^+}(0,1)
For some reason we assume that y_t is assumed to also follow the random walk as followed:
y_t \sim{\mathcal{N}}(\alpha + y_{t-1}, \sigma_{yy})
every draw of in NUTS algorithm we replace y_t generated from state space model and replace y_t in first equation.
Is it possible to replace y_t in any blocks rather than in generated quantities?