Store information about which sampling method or algorithm was used

[topipa]

This was briefly discussed in #130 , but I am making it a separate issue so that the discussion does not get lost. I will copy what was discussed there:

It would be convenient to store information about which algorithm the elpd values come from. Since moment matching and refitting operate on individual observations, the information should be stored separately for each observation. For example, by default this value could be the same as is_method for all observations, but moment matching or refitting could change it from, say, psis to refit or psis-mm for some observations.

Details to discuss that come to my head at this moment

• Where to store it? pointwise is currently a matrix, could we make it a data frame to include a column with text? It could also be an element in diagnostics?
• What kind of information to include and how to name the different options (is method/moment matching/refit)? It seems that even is_method is currently not stored anywhere. Probably subsampling would be indicated here as well?

[topipa]

@MansMeg commented:

So without looking in the actual code, I thought is_method` was stored for every observation?

The subsampling loo is a little different since it can essentially use any is algorithm, either as a surrogate or for the subsampled observation. I would for example like to use moment_match_loo on the subsampled observations, but maybe just the training error or TIS for the surrogates?