StatisticalRethinking using Turing and Pluto notebooks
Author StatisticalRethinkingJulia
38 Stars
Updated Last
1 Year Ago
Started In
August 2020

Purpose of StatisticalRethinkingTuring.jl

As stated many times by the author in his online lectures, StatisticalRethinking is a hands-on course. This project is intended to assist with the hands-on aspect of learning the key ideas in StatisticalRethinking.

StatisticalRethinkingTuring is a Julia project that uses Pluto notebooks for this purpose. Each notebook demonstrates Julia versions of code snippets and mcmc models contained in the R package "rethinking" associated with the book Statistical Rethinking by Richard McElreath.

This Julia project uses Turing as the underlying mcmc implementation. A companion project ( StatisticalRethinkingStan.jl ) uses Stan.


To (locally) reproduce and use this project, do the following:

  1. Download this project from Github and move to the downloaded directory, e.g.:
$ git clone
$ cd StatisticalRethinkingTuring.jl
$ julia

and in the Julia REPL:

julia> ]                                        # Actvate Pkg mode
(@v1.5) pkg> activate .                         # Activate pkg in .
(StatisticalRethinkingTuring) pkg> instantiate  # Install in pkg environment
(StatisticalRethinkingTuring) pkg> <delete>     # Exit package mode

If above procedure fails, if present, try to delete the Manifest.toml file and repeat above steps. As mentioned above, these steps are only needed the first time.

The next step assumes your Julia setup includes Pkg, DrWatson, Pluto and PlutoUI.

  1. Start a Pluto notebook server.
$ julia

julia> using Pluto
  1. A Pluto page should open in a browser.

Select a notebook in the open a file entry box, e.g. type ./ and step to ./notebooks/00/clip-00-01-03t.jl. All notebooks will activate the project StatisticalRethinkingTuring.


Note: StatisticalRethinkingTuring requires StatisticalRethinking.jl v 3.0.0.

StatisticalRethinkingTuring.jl is a DrWatson project, with some added/re-purposed subdirectories:

  1. models, which contains a subset of the Turing language models,
  2. notebooks, used to store the Pluto notebooks,
  3. scripts, Julia scrips generated from the notebooks.

The data directory, in DrWatson accessible through datadir(), can be used for locally generated data, exercises, etc. All "rethinking" data files are stored and maintained in StatisticalRethinking.jl and can be accessed via sr_datadir(...).

The scripts in the scripts subdirectory are directly generated from the notebooks and thus adhere to Pluto's programming restrictions.

This leads to a typical set of opening lines in each notebook:

using Pkg, DrWatson

# Note: Below sequence is important. First activate the project
# followed by `using` or `import` statements. Pretty much all
# scripts use StatisticalRethinking. If mcmc sampling is
# needed, it must be loaded before StatisticalRethinking:

@quickactivate "StatisticalRethinkingTuring"
using Turing
using StatisticalRethinking

# To access e.g. the Howell1.csv data file:
df ="Howell1.csv"), DataFrame)
df = df[df.age .>= 18, :]

Naming conventions

All R snippets (fragments) have been organized in clips. Each clip is a notebook.

Clips are named as clip-cc-fs-ls[s|t|d].jl where

  • cc : Chapter number
  • fs : First snippet in clip
  • ls : Last snippet in cli
  • [s|sl|t|d|m] : Mcmc flavor used (s : Stan, t : Turing)

Note: d is reserved for a combination Soss/DynamicHMC, sl is reserved for Stan models using the logpdf formulation and m is reserved for Mamba.

The notebooks containing the clips are stored by chapter. In addition to clips, in the early notebook chapters (0-3) it is also shown how to create some of the figures in the book, e.g. Fig2.5t.jl in notebooks/chapter/02.

Special introductory notebooks have been included in notebooks/intros, e.g. in subdirectries intro-R-users, intro-pluto and intro-turing. They are intended to illustrate ways of using Julia and Pluto and of basic patterns to work with Turing models.

Additional introductory notebooks showing Julia and statistics ( based on the Statistics with Julia book ) can be found in StatisticsWithJuliaPlutoNotebooks.

One goal for the changes in StatisticalRethinking v3 was to make it easier to compare and mix and match results from different mcmc implementations. Hence consistent naming of models and results is important. The models and the results of simulations are stored as follows:


  1. ppl5_1 : DynamicPPL language program (function)

  2. m5_1t : The Turing model based on m5_1 with data (Turing.Model)

  3. q5_1t : The Turing quap model (NamedTuple)

  4. chns5_1t : MCMCChains object (4000 samples collected from 4 chains)

  5. part5_1t : Turing samples (Particle notations)

  6. quap5_1t : Turing quap() samples (NamedTuple in Particle notation)

  7. prior5_1t_df : Prior samples (DataFrame)

  8. post5_1t_df : Posterior Turing samples (DataFrame)

  9. quap5_1t_df : Posterior quap() approximation (DataFrame)

  10. pred5_1t_df : Posterior predictions (DataFrame)

As before, the t at the end of the model number indicates Turing.

All models in the models subdirectory return 0 and 1.



StatisticalRethinkingTuring.jl is compatible with the 2nd edition of the book.

StructuralCausalModels.jl is included as en experimental dependency in the StatisticalRethinking.jl v3 package.

Any feedback is appreciated. Please open an issue.


Of course, without the excellent textbook by Richard McElreath, this package would not have been possible. The author has also been supportive of this work and gave permission to use the datasets.

This repository and format is derived from work by Karajan, previous versions of StatisticalRethinking.jl and many other contributors.


Version 1.0.0 (in preparation, expected late Nov 2020)

  1. Initial version