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Bayesian Generalized Linear models using `@formula` syntax.

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Hi This issue is based on extensive discussion that took place here: [Turing Samples Slowly #1851](https://github.com/TuringLang/Turing.jl/issues/1851). One of the key observations was that: 1. Turing based Bayesian models can be...

bug

![image](https://user-images.githubusercontent.com/5306213/173663801-65b6c1c7-96eb-48fe-a6e1-d4f55a873611.png)

With large datasets, MCMC can get very slow. Luckily, approximations based on numerical integration usually get better as the sample size increases, and can work in some situations where MCMC...

Multivariate GLMs are very common in econometrics and also very useful in general. I think this is low-hanging fruit in terms of relative effort vs payoff: Multivariate GLMs should be...

- [ ] Group-level effects (Hierarchical Models): - [x] Varying-Slope: `(x_1 | group)` - [ ] Varying-Intercept-Slope: `(1 + x_1 | group)` - [ ] Correlated Group-level effects: - [...

enhancement

We should have a tutorial on comparing the ESS sampler against HMC samplers. HMC is very popular, but partially due to availability in Stan. In many interesting cases with Gaussian...

tutorials

``` For likelihoods, TuringGLM.jl supports: Gaussian() (the default if not specified): linear regression Student(): robust linear regression **Logistic(): logistic regression** Pois(): Poisson count data regression NegBin(): negative binomial robust count...

There are some excellent packages for estimating Bayesian evidence for Turing models. It would allow us to perform model comparisons for various priors and model choices. We should consider supporting...

tutorials

`SimpleVarInfo` in `DynamicPPL` provides significant speedup over the current implementation. We should consider switching to use it once https://github.com/TuringLang/DynamicPPL.jl/pull/360 is merged.

StatsModels provides the notion of "intercept traits" https://github.com/JuliaStats/StatsModels.jl/blob/master/src/traits.jl to control the behavior of the automatic intercept adding that normally happens in GLMs. This package is a great example of a...