INLA extensions for the distant future

Confirm-Solutions / confirmasaurus

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INLA extensions for the distant future #40

Open tbenthompson opened 2 years ago

tbenthompson commented 2 years ago

Things that I'd like to record as potentially useful thoughts or links but that aren't currently tasks that we should actually work on.

This could also be a source of good student or intern projects since they're exciting, self-contained and could be useful.

tbenthompson commented 2 years ago

This vignette explains how R-INLA computes multi-dimensional marginals. It also discusses the skew-normal correction for multivariate normal problems as developed in their 2015 paper. https://inla.r-inla-download.org/r-inla.org/doc/vignettes/jmarginal.pdf

tbenthompson commented 2 years ago

The basic improved skew-normal approximation is great, but there are a few dimensions in which it might be improvable:

using the extended skew-normal approximation. See the 2014 Azzalini and Capitanio book. (Ben has a PDF)
using more derivatives: are there recursive formulas for derivatives for the skew-normal? for the Binomial likelihood or other particular outcome types (survival)?

tbenthompson commented 2 years ago

Numerical differentiation could have some advantages in some circumstances:

might be faster if the JAX gradients/hessians are expensive.
might save JIT compilation time.
might allow using a wider range of models, including ones not implemented via JAX since all that is needed is a log joint density function.

tbenthompson commented 2 years ago

Raw CUDA Berry INLA implementation I really really don't think we should do this for all our fast code since it's going to be a lot of extra work, but I think doing it once will give us a sense of what is achievable and provide a useful reference point for what is achievable. If it's 10x faster or 10x slower than the current JAX implementation, that is good information to keep in mind.