I am trying to understand the structure and, in particular, normality properties of the predictive distribution of a Bayesian structural time-series model. My reasoning is as follows.

The posterior distribution of model parameters (such as various standard deviations) is non-Gaussian in general. The inference via MCMC yields posterior draws from this distribution, and variational inference yields posterior draws from a surrogate, which is a collection of independent Gaussians. For each draw, regardless of the inference method used, the Kalman filter gives a multivariate Gaussian. The final posterior is a mixture of the multivariate Gaussians corresponding to the posterior draws of the model parameters. This implies that the predictive posterior is non-Gaussian; it is a mixture of Gaussians.

Does the above hold? If not, what is the correct explanation?

For some context, I am studying tfp.sts.forecast in TensorFlow Probability:



1 Answer 1


The question has been answered on GitHub by the author of that forecast as follows:

What you've said sounds correct to me. The predictive distribution over multiple timesteps is created explicitly in the code as a mixture of LinearGaussianStateSpaceModel distributions (each of which is multivariate Gaussian). … [S]o the marginal distribution at any given step is a mixture of Gaussians.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.