Fitting Ornstein-Uhlenbeck-type Student's t-processes in Stan

Modeling
1

I want to apply @aaronjg’s wonderful StanCon 2018 work to model stochastic volatility.

I have some questions, thanks in advance for your help !

Parameterization

I can try both centered and non-centered with my data, but I’m confused about the findings.

In the talk:

Centered … are much slower than the non-centered…

But in the notebook p.6-7:

switch to using the centered… This model runs in roughly 1/10th the time

As for conditional vs multivariate parameterizations, in the notebook p.7:

We can use the multivariate expression of the stochastic process… This offers further speed up over the conditional probability formulation.

Replicates

The examples in the notebook have replicates = 1 but the Stan code allows for replicates > 1. What are replicates ?

2

Hi Shira,

It’s been a while since I looked at that code. It is entirely possible that I mispoke in my talk, or there is a typo in the notebook.

However, which is best between centered vs. non-centered will depend on the specifics of your model, so it’s hard to give guidance as to which one is generally better.

The replicates parameter is if you have data from multiple replicates with the same OU parameters. So if you were doing a population dynamic study on a lab grown ecosystem, and you had multiple biological replicates of the system that you wanted to model.

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