Manipulate MCMC Samples.

mcmcr

mcmcr is an R package to manipulate Monte Carlo Markov Chain (MCMC) samples (Brooks et al. 2011).

Installation

To install the latest release from CRAN

install.packages("mcmcr")

To install the developmental version from GitHub

# install.packages("remotes")
remotes::install_github("poissonconsulting/mcmcr")

Introduction

For the purposes of this discussion, an MCMC sample represents the value of a term from a single iteration of a single chain. While a simple parameter such as an intercept corresponds to a single term, more complex parameters such as an interaction between two factors consists of multiple terms with their own inherent dimensionality - in this case a matrix. A set of MCMC samples can be stored in different ways.

Existing Classes

The three most common S3 classes store MCMC samples as follows:

• coda::mcmc stores the MCMC samples from a single chain as a matrix where each each row represents an iteration and each column represents a variable
• coda::mcmc.list stores multiple mcmc objects (with identical dimensions) as a list where each object represents a parallel chain
• rjags::mcarray stores the samples from a single parameter where the initial dimensions are the parameter dimensions, the second to last dimension is iterations and the last dimension is chains.

In the first two cases the terms/parameters are represented by a single dimension which means that the dimensionality inherent in the parameters is stored in the labelling of the variables, ie, "bIntercept", "bInteraction[1,2]", "bInteraction[2,1]", .... The structure of the mcmc and mcmc.list objects emphasizes the time-series nature of MCMC samples and is optimized for thining. In contrast mcarray objects preserve the dimensionality of the parameters.

New Classes

The mcmcr package defines three related S3 classes which also preserve the dimensionality of the parameters:

• mcmcr::mcmcarray is very similar to rjags::mcarray except that the first dimension is the chains, the second dimension is iterations and the subsequent dimensions represent the dimensionality of the parameter (it is called mcmcarray to emphasize that the MCMC dimensions ie the chains and iterations come first);
• mcmcr::mcmcr stores multiple uniquely named mcmcarray objects with the same number of chains and iterations.
• mcmcr::mcmcrs stores multiple mcmcr objects with the same parameters, chains and iterations.

All five classes (mcmc, mcmc.list, mcarray, mcmcarray, mcmcr and mcmcrs) are collectively referred to as MCMC objects.

Why mcmcr?

mcmcarray objects were developed to facilitate manipulation of the MCMC samples. mcmcr objects were developed to allow a set of dimensionality preserving parameters from a single analysis to be manipulated as a whole. mcmcrs objects were developed to allow the results of multiple analyses using the same model to be manipulated together.

The mcmcr package (together with the term and nlist packages) introduces a variety of (often) generic functions to manipulate and query mcmcarray, mcmcr and mcmcrs objects (and term and nlist and nlists objects).

In particular it provides functions to

• coerce from and to mcarray, mcmc and mcmc.list objects;
• extract an objects coef table (as a tibble);
• query an object’s nchains, niters, term::npars, term::nterms, nlist::nsims and nlist::nsams as well as it’s parameter dimensions (term::pdims) and term indices (term::tindex);
• subset objects by chains, iterations and/or parameters;
• bind_xx a pair of objects by their xx_chains, xx_iterations, xx_parameters or (parameter) xx_dimensions;
• combine the samples of two (or more) MCMC objects using combine_samples (or combine_samples_n) or combine the samples of a single MCMC object by reducing its dimensions using combine_dimensions;
• collapse_chains or split_chains an object’s chains;
• mcmc_map over an objects values;
• transpose an objects parameter dimensions using mcmc_aperm;
• assess if an object has converged using rhat and esr (effectively sampling rate);
• and of course thin, rhat, ess (effective sample size), print, plot etc said objects.

The code is opinionated which has the advantage of providing a small set of stream-lined functions. For example the only ‘convergence’ metric is the uncorrected, untransformed, univariate split R-hat (potential scale reduction factor). If you can convince me that additional features are important I will add them or accept a pull request (see below). Alternatively you might want to use the mcmcr package to manipulate your samples before coercing them to an mcmc.list to take advantage of all the summary functions in packages such as coda.

Demonstration

library(mcmcr)

mcmcr_example
#> $alpha
#> [1] 3.718025 4.718025
#> 
#> nchains:  2 
#> niters:  400 
#> 
#> $beta
#>           [,1]     [,2]
#> [1,] 0.9716535 1.971654
#> [2,] 1.9716535 2.971654
#> 
#> nchains:  2 
#> niters:  400 
#> 
#> $sigma
#> [1] 0.7911975
#> 
#> nchains:  2 
#> niters:  400

coef(mcmcr_example, simplify = TRUE)
#>        term  estimate     lower    upper   svalue
#> 1  alpha[1] 3.7180250 2.2120540 5.232403 9.645658
#> 2  alpha[2] 4.7180250 3.2120540 6.232403 9.645658
#> 3 beta[1,1] 0.9716535 0.2514796 1.713996 5.397731
#> 4 beta[2,1] 1.9716535 1.2514796 2.713996 7.323730
#> 5 beta[1,2] 1.9716535 1.2514796 2.713996 7.323730
#> 6 beta[2,2] 2.9716535 2.2514796 3.713996 9.645658
#> 7     sigma 0.7911975 0.4249618 2.559520 9.645658
rhat(mcmcr_example, by = "term")
#> $alpha
#> [1] 2.002 2.002
#> 
#> $beta
#>       [,1]  [,2]
#> [1,] 1.147 1.147
#> [2,] 1.147 1.147
#> 
#> $sigma
#> [1] 1
plot(mcmcr_example[["alpha"]])

Inspiration

coda and rjags

Contribution

Please report any issues.

Pull requests are always welcome.

Code of Conduct

Please note that the mcmcr project is released with a Contributor Code of Conduct. By contributing to this project, you agree to abide by its terms.

References

Brooks, S., Gelman, A., Jones, G.L., and Meng, X.-L. (Editors). 2011. Handbook for Markov Chain Monte Carlo. Taylor & Francis, Boca Raton. ISBN: 978-1-4200-7941-8.