Gaussian Process & Stochastic Differential Equations

I was looking at the example of a GP in BDA3, and immediately thought that the data could’ve been modeled with a non autonomous SDE with colored noise, but there’s no mention of SDEs in the section (why would there be I guess?).

I’m curious if some problems which are formulated as SDEs might be translated to GPs and more easily solved. What in particular peaked my interest was that the BDA3 examples decompose a time series linearly into model components, which would seem much more difficult to do with an SDE.

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Markovian GPs can be (usually) written as the solutions to SDEs driven by white
(or markovian) noise. This can lead to a useful representation that can be exploited in Stan by ways of a Kalman filter (or a forward-backward algorithm).

There are several GP examples in BDA3, but if you mean the birthday example, then for SDE version see Explicit Link Between Periodic Covariance Functions and State Space Models by Solin and Särkkä.


Thanks for the comment and the reference; I’m starting to see how I could use either in some of my models, but in the Stan reference I only see zero mean functions… does that mean it’s standard to transform data by the mean first? I’ll take a closer look at the examples.

You can use non-zero mean function. See, for example, my traffic deaths in Finland demo with code in github.

You can always add a non-zero mean to a zero mean process.

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