I’ve recently gotten interested in scenarios like this too.

@sakrejda what would one use as the intial values? Medians from the previous posterior? Also, is there any opportunity at any stage of sampling where we can gain more info about the best mass matrix?

I’m specifically thinking of the following scenario:

- Adapt using data x, yielding mass matrix M_x
- using M_x, sample using data x, obtaining posterior samples S_x
- observe new data y, concatenate with x to yield data xy
- using M_x and initial values informed by S_{x}, sample using data xy, yielding samples S_{xy}
- observe new data z, concatenate with xy to yield data xyz
- using M_x and initial values informed by S_{xy}, sample using data xyz, yielding samples S_{xyz}

etc…

So with the above, after the initial adaptation, the same mass matrix is used for all future sampling. I’m wondering, however, if there is any opportunity for updating whereby, for example, there’s information in S_{xy} that can be used to derive a new mass matrix M_{xy} to be used in step 6 instead of M_x. Or if there isn’t the proper info in S_{xy} to update the mass matrix, might the required info be anywhere in the latent dynamics observed during sampling?