Generalized Convergence Diagnostics for Difficult MCMC Algorithms.

genMCMCDiag

Determining the convergence of Markov Chain Monte Carlo (MCMC) algorithms run on highly-dimensional or un-ordered spaces is an active area of research. This package implements several distance based algorithms for the creation of diagnostics in these situations. A forthcoming paper describes the methodology used in detail.

Installation

#Install from CRAN
install.packages('genMCMCDiag')

#Install from gitHub
# install.packages("devtools")
devtools::install_github("LukeDuttweiler/genMCMCDiag")

A Simple Example

Consider the results of a multi-chain MCMC algorithm over a univariate space. The genMCMCDiag package provides a simple interface to retrieve traceplots, the effective sample size (ESS), and the Gelman-Rubin (GR) diagnostic.

We demonstrate the usage of genMCMCDiag in this simple scenario, using the included simulated MCMC results uniMCMCResults. The output of genDiagnostic is a traceplot and tables containing the ESS and GR results. The method is set to ‘standard’ here as we don’t want to transform the data prior to running the diagnostics, as it is already univariate.

#Load package
library(genMCMCDiag)

#View structure of uniMCMCResults
str(uniMCMCResults)
#> List of 7
#>  $ : num [1:2000] 5.72 5.72 5.72 -5.67 -5.67 ...
#>  $ : num [1:2000] -3.98 -3.98 -3.98 3.81 3.61 ...
#>  $ : num [1:2000] 2.17 2.34 -2.35 -2.35 -2.42 ...
#>  $ : num [1:2000] 0.1266 0.058 0.0436 0.0103 0.0194 ...
#>  $ : num [1:2000] 2 2 2 2 2 ...
#>  $ : num [1:2000] 3.86 -3.74 3.75 3.75 3.75 ...
#>  $ : num [1:2000] 5.87 -5.83 5.81 5.81 5.81 ...

#View Diagnostics
genDiagnostic(uniMCMCResults, method = 'standard')

#> ----------------------------------------------------
#> Generalized MCMC Diagnostics using standard Method 
#> ----------------------------------------------------
#> 
#> |Effective Sample Size: 
#> |---------------------------
#> | Chain 1| Chain 2| Chain 3| Chain 4| Chain 5|  Chain 6|  Chain 7|      Sum|
#> |-------:|-------:|-------:|-------:|-------:|--------:|--------:|--------:|
#> | 847.966| 908.501| 885.617|  828.86|  694.21| 1052.483| 1019.646| 6237.283|
#> 
#> |Gelman-Rubin Diagnostic: 
#> |---------------------------
#> | Point est.| Upper C.I.|
#> |----------:|----------:|
#> |      1.014|      1.015|

A More Complex Example

Consider the results of a more complex multi-chain MCMC algorithm run on the space of Bayesian network (BN) partitions. The space of BN partitions does not have a natural distance based order (unlike the real-line used in the previous example), and so standard traceplots and MCMC diagnostics cannot be used.

genMCMCDiag includes transformation methods to help deal with this issue, based on a user-supplied (or built in) distance function. In this instance we will use the built-in partitionDistance and the ts transformation method (details to be published in a forthcoming paper), to view a diagnostic traceplot and transformed calculations of the ESS and GR diagnostics.

#View Diagnostics from ts method
genDiagnostic(bnMCMCResults, method = 'ts', distance = partitionDist)

#> ----------------------------------------------------
#> Generalized MCMC Diagnostics using ts Method 
#> ----------------------------------------------------
#> 
#> |Effective Sample Size: 
#> |---------------------------
#> | Chain 1| Chain 2| Chain 3| Chain 4| Chain 5|    Sum|
#> |-------:|-------:|-------:|-------:|-------:|------:|
#> |  30.553|  25.257|  18.956|  74.901|  32.204| 181.87|
#> 
#> |Gelman-Rubin Diagnostic: 
#> |---------------------------
#> | Point est.| Upper C.I.|
#> |----------:|----------:|
#> |      2.921|      5.161|

The diagnostic results clearly reveal a complete lack of mixing!