Can Jags be used to fit classical inference state space models? Can Jags be used to fit classical inference state space models (that is without using a Bayesian approach by specifying a prior)?
To be fully clear: can I estimate a state space model such as the following:
$y_t = \mu_t + \epsilon_t$
$\mu_{t+1} = \mu_t + \eta_t$
in Jags using classical inference?
I thought of using Jags as it has many options that other state space packages do not have (I am already familiar with those, so I am not looking for answers that suggest those).
 A: The answer is no. JAGS is not designed for such models. However Stan provides such possibility.

Stan provides optimization algorithms which find modes of the density
  specified by a Stan program. Such modes may be used as parameter
  estimates or as the basis of approximations to a Bayesian posterior;
  see Chapter 52 for background on point estimation. Stan provides three
  different optimizers, a Newton optimizer, and two related quasi-Newton
  algorithms, BFGS and L-BFGS (...)

Notice that if uninformative prior is used then 

the posterior mode corresponds to the maximum likelihood estimate
  (MLE) of the parameters. If the prior is not uniform, the posterior
  mode is sometimes called the maximum a posterior (MAP) estimate. If
  parameters (typically hierarchical) have been marginalized out, it’s
  sometimes called a maximum marginal likelihood (MML) estimate.

So with Stan you can use optimization algorithm rather then MCMC sampling and with using flat prior the results obtained are congruent with MLE estimates (see also this).
Source: Stan Development Team (2015). Stan Modeling Language User’s Guide and Reference Manual. Stan Version 2.6.2. pp. 22, 23, 458.
