bayesian
brms
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bayesian  brms  

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bayesian

How do you train a Bayesian model
There's MLMod and Bayesian which are TidyModels wrappers for stan_glm and brms (brms is my go to) but I haven't seen anything that indicates how to tune them.
brms

Bayesian Structural Equation Modeling using blavaan
[2] https://paulbuerkner.github.io/brms/

Stepbystep example of Bayesian ttest?
Okay so first off, I recommend that you read [this](https://link.springer.com/article/10.3758/s1342301612214) 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 ttest, 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://paulbuerkner.github.io/brms/), or, if you want to go even deeper, [Stan](https://mcstan.org/) (brms is a frontend to Stan).

[R] Are there methods for ridge and lasso regression that allow the introduction of weights to give more importance to some observations?
I think the brms package (https://github.com/paulbuerkner/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 multilevel metaanalysis regression (combining multiple CRISPRa experiments to find determinants of CRISPRa activity, see https://github.com/timydaley/CRISPRasgRNAdeterminants/blob/master/metaAnalysis/NeuronAndSelfRenewalMetaMixtureRegression.Rmd) and had some success.

I have a small sample size time series with potentially lagged predictor values which are also time series. What could be potential methods to analyse these data?
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.

Brms: adding on a nonlinear component to working MLM model
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.
Unfortunately, I can't just tag it onto to the working linear piece because brms doesn't allow for more than 2 level factor covariates in NL formulas. After much googling, I was able to find these brms github posts: 46 47 where they discuss how a NL component can be added. I've tried the syntax used, but it's still throwing errors. Here is one syntax I tried, going off of the information on those two links (where b1=lambda, b2= kappa)
What are some alternatives?
rstan  RStan, the R interface to Stan
stan  Stan development repository. The master branch contains the current release. The develop branch contains the latest stable development. See the Developer Process Wiki for details.
tinytex  A lightweight, crossplatform, portable, and easytomaintain LaTeX distribution based on TeX Live
stat_rethinking_2020  Statistical Rethinking Course Winter 2020/2021
rBAPS  R implementation of the BAPS software for Bayesian Analysis of Population Structure
testsaslinear  Common statistical tests are linear models (or: how to teach stats)
CRISPRasgRNAdeterminants
bambi  BAyesian ModelBuilding Interface (Bambi) in Python.
multilevelmod  Parsnip wrappers for mixedlevel and hierarchical models