Chains not Mixing in State Space Models/ Factor Analysis

Modeling
1

Hi all,

I am fitting a State Space Model with two latent states to a data set of 6 observations and around 700 time points. The model works with simulated data.

Some preliminary analyses showed that only observations 1,3,5 are influenced by the second latent state. Hence, there are six parameters tau_obs1[1],…,tau_obs1[6] describing the “loadings” between the six observations and the first latent state and three parameters tau_obs2[1],…,tau_obs2[3] for the “loadings” between the observations 1,3,5 and the second state.

Unfortunately, the chains do not mix well for the parameter tau_obs2[3] and I don’t see why. For now, I am using uniform priors on the parameters (which are in (0,1)) but also a Beta(10,1.5) prior on tau_obs2[3] doesn’t solve this. Increasing adapt_delta doesn’t help either.

Is there anything I am missing here? Can you think of something else I could try to solve this problem?

Thanks!

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2

But not with real data? If not that may indicate it’s not well specified. You can try to figure out where it’s failing to capture aspects of real data using posterior predictive checks.

Usually you see this kind of pattern when there’s strong dependencies of the parameter with other parameters. Without seeing your model specification, it’s hard to say more.

I’m also not sure what this means. How can there only be 6 observations if there are 700 time points? I’d expect at least 700 observations.