brms VS ParBayesianOptimization

[2] https://paul-buerkner.github.io/brms/

Maybe something like the Logistic Normal ? (e.g. see this issue from brms). If that fits what you are looking for, you can use brms to generate the Stan code for you (brms::make_stan_code()) and work from that.

Okay so first off, I recommend that you read [this](https://link.springer.com/article/10.3758/s13423-016-1221-4) article about "The Bayesian New Statistics", which highlights estimation rather than hypothesis testing from a Bayesian perspective (see Fig. 1, second row, second column). Instead of a t-test, then, we can *estimate the difference* between two groups/variables. If you want to go deeper than JASP etc, I recommend that you use [brms](https://paul-buerkner.github.io/brms/), or, if you want to go even deeper, [Stan](https://mc-stan.org/) (brms is a front-end to Stan).

I think the brms package (https://github.com/paul-buerkner/brms) or the blavaan package (http://ecmerkle.github.io/blavaan/) have support for SEM. I've never done it myself, so I unfortunately can't give you any direction for that in particular. However, I have used stan in multi-level meta-analysis regression (combining multiple CRISPRa experiments to find determinants of CRISPRa activity, see https://github.com/timydaley/CRISPRa-sgRNA-determinants/blob/master/metaAnalysis/NeuronAndSelfRenewalMetaMixtureRegression.Rmd) and had some success.

brms baby

Could also be done using brms and the gr term. See this for the motivation behind this syntax.

Anyway, I found I can include weights into the brm function by using gr(RE, by = var) to deal with the heterogeneous variance and it should automatically assume that each observation within a group is correlated according to the brms reference manual.

This is what actually should work- I must be declaring my variables incorrectly. The issue I'm having is that what you refer to as lin , I tried calling a few things, from b to LinPred (which worked in the link here: brms issue 47). When I've tried doing this, I receive errors that say "The following variables are missing from the dataset....[insert variable used to symbolize linear part of the model)". But I believe you're code is on the right path for what needs to be done- I'll try altering my syntax to be sure it resembles yours let you know if it works.

Disclaimer: I am the maintainer of ParBayesianOptimization. That readme has a pretty good walkthrough of how Bayesian optimization works.