[Apologies for lack of URLs, I’m a new user so limited to only 2. I can provide more in a follow up as requested]
I’m writing to inquire about the current state of Julia with respect to the Laplace approximation for mixed effects statistical models. I was recently turned on to Julia from a nice talk by Sam (which is posted on discourse but not linked here). I think the biggest hurdle for recruiting new users to Julia in our field (quantitative ecology/fisheries science) is that it needs to provide similar or improved functionality over the software package Template Model Builder. This has been discussed briefly on forums here before (see especially this discussion).
From a user perspective the beauty of TMB is you simply write your objective function in a simple C++ template. TMB then does the Laplace approximation to integrate out arbitrary subsets of parameters (typically random effects), declared in R after compilation, while automatically detecting and using sparsity for calculations (unlike INLA where sparsity must be known a priori). See the adcomp github repo tutorial for a flavor of the syntax and user experience.
Per the previously linked thread, it’s been used widely in glmmTMB. But more importantly, TMB scales incredibly well to diverse mixed models beyond regressions, and has led to recent a surge in methods in ecology and related fields (e.g., spatial factor analysis, state-space population dynamics, life history theory, and especially spatio-temporal models). TMB is great, but there would be an undeniable elegance to doing the whole statistical analysis in a single programming language. I haven’t used Julia but am certainly intrigued and I think that if Julia had similar functionality it would make an attractive alternative for cutting edge statistical model development. Not to mention it would be good to have an alternative to TMB just for benchmarking, checking, and testing.
It was clear in 2019 that “…many of the pieces are in place…” What is the current status of this kind of functionality in Julia now? In particular, what are the existing capabilities for (higher-order) AD, Hessian sparsity detection, Laplace approximation, sparse Cholesky decomposition? How active is development on these features, and how much work would it take to implement TMB’s functionality in Julia?
Thanks in advance!