StatisticalRethinking

This package will contain Julia versions of selected code snippets contained in the R package "rethinking" associated with the book Statistical Rethinking by Richard McElreath.

In the book and associated R package rethinking, statistical models are defined as illustrated below:

m4.3 <- map(
    alist(
        height ~ dnorm( mu , sigma ) ,
        mu <- a + b*weight ,
        a ~ dnorm( 156 , 100 ) ,
        b ~ dnorm( 0 , 10 ) ,
        sigma ~ dunif( 0 , 50 )
    ) ,
    data=d2
)

The author states: "If that (the statistical model) doesn't make much sense, good. ... you're holding the right textbook, since this book teaches you how to read and write these mathematical descriptions" (page 77).

This package is intended to allow experimenting with this learning process using 3 available mcmc options in Julia.

Layout of the package

Instead of having all snippets in a single file, the snippets are organized by chapter and grouped in clips by related snippets. E.g. chapter 0 of the R package has snippets 0.1 to 0.5. Those have been combined into 2 clips:

1. clip_01_03.jl - contains snippets 0.1 through 0.3
2. clip_04_05.jl - contains snippets 0.4 and 0.5.

These 2 files are in chapters/00. These files are later on processed by Literate.jl to create 2 derived versions, e.g. from clip_01_03.jl in chapters/00:

1. clip_01_03.md - included in the documentation
2. clip_01_03.ipynb - stored in the notebooks directory for use in Jupyter

Occasionally a clip will contain just a single snippet and will be referred to as 03/clip_02.jl.

Clips with names such as 02/clip_08t.jl, clip_08s.jl and clip_08m.jl contain mcmc implementations using Turing.jl, CmdStan.jl and Mamba.jl respectively. Examples have been added to chapter 2.

From chapter 8 onwards, the Turing versions of the mcmc models are available as e.g. chapters/08/m8.1t.jl. Equivalent CmdStan versions and, in a few cases Mamba models, are provided as well.

Almost identical clips are named e.g. 04/clip_07.0s.jl and 04/clip_07.1s.jl. In that specific example just the priors differ.

Acknowledgements

Richard Torkar has taken the lead in developing the Turing versions of the models in chapter 8.

The TuringLang team and #turing contributors on Slack have been extremely helpful!

The mcmc components are based on:

1. TuringLang
2. StanJulia
3. Mamba

At least 2 other mcmc options are available for mcmc in Julia:

1. DynamicHMC
2. Klara

Time constraints prevents inclusion of those right now, although e.g. the example chapters/04/clip_38.1m.jl almost begs for a clip_38d.jl. For now the linear regression example in DynamicHMCExamples is a good starting point.

As a final note, the Mamba examples should really use @everywhere using Mamba in stead of using Mamba. This was done to get around a limitation in Literate.jl to test the notebooks when running in distributed mode.

maximum_a_posteriori

maximum_a_posteriori(model, lower_bound, upper_bound)

* `model::Turing model`
* `lower_bound::Float64`

* `result`                       : Maximum_a_posterior vector