I’ve been looking at some of the examples in the manual and on the forums for time-series models and was wondering what the preferred way to parameterize these models is.

It seems that in some cases people use:

`f ~ MultiNormal(0, K(x|alpha,rho))`

and others use:

```
f[1] ~ normal(0,alpha^2)
for(i in 2:length(f))
f[i] ~ normal(f[i-1], c(x[i]-x[i-1],alpha,rho))
```

It seems that these would work out to be the same, but I was wondering if there is a difference in computational effeciency in STAN? Also for some covariance kernels, eg Matern 1/2, there are sparse representations for the precision matrix and could use MultiNormPrecision.

Additionally, using the non-centered parameterization you could rewrite the second using f’ such that f~N(0,1). This seems very similar (equivalent?) to using the Cholesky decomposition of the covariance matrix.

I don’t have a good intuition on what would be best in terms of keeping parameters on unit scales, vectorization, and depth of the autodiff graph. I was going to start exploring these options for a model I am working on but wanted to ask here first if people have experience or reccomendations between:

Multinormal vs. Conditional Specification

and

Centered vs. Non-Centered Parameterization