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Introduction

This file is meant to present the function runMCMC_btadjust() in the runMCMCbtadjust package. The main aim of this function is to run a Markov Chain Monte Carlo (MCMC) for a specified Bayesian model while adapting automatically the burn-in and thinning parameters to meet pre-specified targets in terms of MCMC convergence and number of effective values of MCMC outputs - where the term “number of effective values” for the MCMC outputs refers to sample size adjusted for autocorrelation. This is done in only one call to the function that repeatedly calls the MCMC until criteria for convergence and number of effective values are met. This allows to obtain a MCMC output that is out of the transient phase of the MCMC (convergence) and that contains a pre-specified number of nearly independent draws from the posterior distribution (number of effective values).

This function has four main advantages:

(i) it saves the analyst's programming time since he/she does not have to repeatedly diagnose and re-run MCMCs until desired levels of convergence and number of effective values are reached;

(ii) it allows a minimal, normalized quality control of MCMC outputs by allowing to meet pre-specified levels in terms of convergence and number of quasi-independent values;

(iii) it may save computer’s time when compared to cases where we have to restart the MCMC from the beginning if it has not converged or reached the specified number of effective values (as e.g. with `runMCMC` function in `NIMBLE`);

and (iv) it can be applied with different MCMC R languages. Indeed, `runMCMC_btadjust()` uses other Bayesian packages to fit the MCMC. At present, only `JAGS`, `NIMBLE` and `greta` can be used as these are the main Bayesian fitting tools in R known by the package author and that permit to continue an already fitted MCMC - which is required for numerical efficiency. We will here show how to fit and compare a very simple model under these three languages, using the possibilities allowed by `runMCMC_btadjust()`.

runMCMC_btadjust() has a stronger integration with NIMBLE, for which it has the additional advantage of somewhat easying MCMC sampler control and extra calculations, i.e. calculations on the fitted model, after the end of the MCMC (see the separate two vignettes on these two topics).

We will here show how to fit and compare a very simple model under these three languages, using the possibilities allowed by runMCMC_btadjust().

Our model is one of the simplest statistical model we could think of: inspired from @Kery_2010, we model data of weights of 1,000 Pilgrim falcons (Falco peregrinus) simulated from a Gaussian distribution with mean 600 grams and standard error 30 grams:


set.seed(1)
y1000<-rnorm(n=1000,mean=600,sd=30)

NIMBLE

We start with fitting the example with NIMBLE (cf. https://r-nimble.org/).


library(runMCMCbtadjust)
library(nimble)

As NIMBLE distinguishes data that have random distributions from other data, we specify two distinct lists to contain these:


ModelData <-list(mass = y1000)
ModelConsts <- list(nobs = length(y1000))

We then write our Bayesian code within R with the nimbleCode function in the nimble package:

 ModelCode<-nimbleCode(
  {
    # Priors
    population.mean ~ dunif(0,5000)
    population.sd ~ dunif(0,100)
    
    # Normal distribution parameterized by precision = 1/variance in Nimble
    population.variance <- population.sd * population.sd
    precision <- 1 / population.variance
  
    # Likelihood
    for(i in 1:nobs){
      mass[i] ~ dnorm(population.mean, precision)
    }
  })

The model is a simple linear - and Gaussian - model with only an intercept -, actually the same model - for the likelihood section - as the probabilistic model used to generate the data.

Our - optional - next step is to specify starting values for model’s parameters. This is done by first writing a function that is repetitively called for each chain. We - also optionally - indicate the names of parameters to be saved and diagnosed in a vector called params:

ModelInits <- function()
{list (population.mean = rnorm(1,600,90), population.sd = runif(1, 1, 30))}
  
Nchains <- 3

set.seed(1)
Inits<-lapply(1:Nchains,function(x){ModelInits()})

#specifying the names of parameters to analyse and save:
params <- c("population.mean", "population.sd") 

#devising the maximum level allowed for the Geweke diagnostic of convergence (cf. following)
npars<-length(params)
Gew.Max<-as.double(format(quantile(sapply(1:100000,function(x,N){max(abs(rnorm(N)))},npars),0.95),digits=3,scientific=FALSE))

We are now ready to launch runMCMC_btadjust(): since we use NIMBLE, we must specify arguments code, data, constants (see below), which are specific to NIMBLE, as well as MCMC_language="Nimble". The next arguments of runMCMC_btadjust() that we will here work with are for most of them shared among MCMC_languages. We first do it on one chain (argument Nchains=1) using in the control list argument neff.method="Coda" to use the Coda method to calculate the number of effective parameters and convtype="Geweke" to use the Geweke method to diagnose convergence, with the pre-specified maximum - over analyzed parameters - convergence of 2.24 (conv.max=2.24) - coming from simulated 95% quantiles from standard gaussian distributions that Geweke diagnostics should theoretically follow - and the minimum - over analyzed parameters - number of effective values of 1,000 (neff.min=1000). Other arguments that are the same for all MCMC languages include params (parameter names to diagnose and save), inits (initial values - which are here provided through the list of values Inits[1] but could also have been specified through a function giving such a result - such as here ModInits), niter.min (minimum number of iterations), niter.max (maximum number of iterations), nburnin.min, nburnin.max thin.min, thin.max (minimum and maximum number of iterations for respectively the burn-in and thinning parameters):

out.mcmc.Coda.Geweke<-runMCMC_btadjust(code=ModelCode, constants = ModelConsts, data = ModelData, MCMC_language="Nimble",
    Nchains=1, params=params, inits=Inits[1],
    niter.min=1000, niter.max=300000,
    nburnin.min=100, nburnin.max=200000, 
    thin.min=1, thin.max=1000,
    conv.max=Gew.Max, neff.min=1000,
    control=list(neff.method="Coda", convtype="Geweke"))
#> [1] "control$seed is NULL. Replaced by 1"
#> ===== Monitors =====
#> thin = 1: population.mean, population.sd
#> ===== Samplers =====
#> RW sampler (2)
#>   - population.mean
#>   - population.sd
#> [1] "###################################################################################"
#> |-------------|-------------|-------------|-------------|
#> |-------------------------------------------------------|
#> [1] "###################################################################################"
#> |-------------|-------------|-------------|-------------|
#> |-------------------------------------------------------|
#> [1] "Raw multiplier of thin:  4.761"
#> [1] "###################################################################################"
#> [1] "Testing multiplier of thin:  5 :"
#> [1] "Retained multiplier of thin:  5 :"
#> [1] "###################################################################################"
#> [1] "Case of niter update: Convergence and trying to reach end of MCMC at the end of next cycle"
#> [1] "###################################################################################"
#> [1] "###################################################################################"
#> |-------------|-------------|-------------|-------------|
#> |-------------------------------------------------------|
#> [1] "###################################################################################"
#> [1] "Main MCMC sampling finished."
#> [1] "###################################################################################"
#> [1] "Final max raw multiplier of thin:  1.25"
#> [1] "###################################################################################"
#> [1] "Retained final multiplier of thin:  1"
#> [1] "###################################################################################"
#> [1] "###################################################################################"
#> [1] "MCMC has reached the required level of convergence."
#> [1] "###################################################################################"
#> [1] "MCMC has reached the required level of effective values."
#> [1] "###################################################################################"

The above information printed during running runMCMC_btadjust() is somewhat elusive. It is possible to get more information printed with components identifier.to.print, print.diagnostics, print.thinmult and innerprint of the argument control of runMCMC_btadjust() or the component showCompilerOutput of control.MCMC - this last one being active only with MCMC_language=="Nimble". See the help file of runMCMC_btadjust() for more information. By default, only print.thinmult is TRUE and therefore activated. We hereafter just show the activation of the print.diagnostics component to show the reader that it can produce useful information to better realize what is being done in terms of control of convergence and number of effective values.

out.mcmc.Coda.Geweke.with.print.diagnostics<-runMCMC_btadjust(code=ModelCode, constants = ModelConsts, data = ModelData, MCMC_language="Nimble",
    Nchains=1, params=params, inits=Inits[1],
    niter.min=1000, niter.max=300000,
    nburnin.min=100, nburnin.max=200000, 
    thin.min=1, thin.max=1000,
    conv.max=Gew.Max, neff.min=1000,
    control=list(neff.method="Coda", convtype="Geweke",print.diagnostics=TRUE))
#> [1] "control$seed is NULL. Replaced by 1"
#> ===== Monitors =====
#> thin = 1: population.mean, population.sd
#> ===== Samplers =====
#> RW sampler (2)
#>   - population.mean
#>   - population.sd
#> [1] "###################################################################################"
#> |-------------|-------------|-------------|-------------|
#> |-------------------------------------------------------|
#> [1] "###################################################################################"
#> [1] "Current state of diagnostics:"
#>                 Nchains thin niter.tot Nvalues nu.burn
#> MCMC parameters       1    1      1000     900     101
#> [1] "###################################################################################"
#>          max median  mean      name_max prop_ab_p975 prop_ab_p995 prop_ab_p9995
#> Geweke 1.523  1.057 1.057 population.sd            0            0             0
#> [1] "###################################################################################"
#>                      min  median    mean      name_min prop_bel_1000 prop_bel_5000 prop_bel_10000
#> Neff             140.649 146.973 146.973 population.sd             1             1              1
#> [1] "###################################################################################"
#> [1] "###################################################################################"
#> |-------------|-------------|-------------|-------------|
#> |-------------------------------------------------------|
#> [1] "###################################################################################"
#> [1] "Current state of diagnostics:"
#>                 Nchains thin niter.tot Nvalues nu.burn
#> MCMC parameters       1    1      2000    1900     101
#> [1] "###################################################################################"
#>          max median  mean        name_max prop_ab_p975 prop_ab_p995 prop_ab_p9995
#> Geweke 1.165  1.008 1.008 population.mean            0            0             0
#> [1] "###################################################################################"
#>                      min  median    mean        name_min prop_bel_1000 prop_bel_5000 prop_bel_10000
#> Neff             399.096 404.953 404.953 population.mean             1             1              1
#> [1] "###################################################################################"
#> [1] "Raw multiplier of thin:  4.761"
#> [1] "###################################################################################"
#> [1] "Testing multiplier of thin:  5 :"
#> [1] "###################################################################################"
#> [1] "Current state of diagnostics:"
#>                 Nchains thin niter.tot Nvalues nu.burn
#> MCMC parameters       1    5      2000     380     101
#> [1] "###################################################################################"
#>        max median  mean      name_max prop_ab_p975 prop_ab_p995 prop_ab_p9995
#> Geweke 1.7  1.636 1.636 population.sd            0            0             0
#> [1] "###################################################################################"
#>                      min  median    mean        name_min prop_bel_1000 prop_bel_5000 prop_bel_10000
#> Neff             291.839 299.673 299.673 population.mean             1             1              1
#> [1] "###################################################################################"
#> [1] "Retained multiplier of thin:  5 :"
#> [1] "###################################################################################"
#> [1] "Case of niter update: Convergence and trying to reach end of MCMC at the end of next cycle"
#> [1] "###################################################################################"
#> [1] "###################################################################################"
#> |-------------|-------------|-------------|-------------|
#> |-------------------------------------------------------|
#> [1] "###################################################################################"
#> [1] "Current state of diagnostics:"
#>                 Nchains thin niter.tot Nvalues nu.burn
#> MCMC parameters       1    5      6545    1289     104
#> [1] "###################################################################################"
#>          max median  mean      name_max prop_ab_p975 prop_ab_p995 prop_ab_p9995
#> Geweke 1.506  0.776 0.776 population.sd            0            0             0
#> [1] "###################################################################################"
#>                       min   median     mean      name_min prop_bel_1000 prop_bel_5000 prop_bel_10000
#> Neff             1031.204 1050.428 1050.428 population.sd             0             1              1
#> [1] "###################################################################################"
#> [1] "###################################################################################"
#> [1] "Main MCMC sampling finished."
#> [1] "###################################################################################"
#> [1] "###################################################################################"
#> [1] "Current state of diagnostics:"
#>                 Nchains thin niter.tot Nvalues nu.burn
#> MCMC parameters       1    5      6545    1289     104
#> [1] "###################################################################################"
#>          max median  mean      name_max prop_ab_p975 prop_ab_p995 prop_ab_p9995
#> Geweke 1.506  0.776 0.776 population.sd            0            0             0
#> [1] "###################################################################################"
#>                       min   median     mean      name_min prop_bel_1000 prop_bel_5000 prop_bel_10000
#> Neff             1031.204 1050.428 1050.428 population.sd             0             1              1
#> [1] "###################################################################################"
#> [1] "Final max raw multiplier of thin:  1.25"
#> [1] "###################################################################################"
#> [1] "Retained final multiplier of thin:  1"
#> [1] "###################################################################################"
#> [1] "###################################################################################"
#> [1] "Current state of diagnostics:"
#>                 Nchains thin niter.tot Nvalues nu.burn
#> MCMC parameters       1    5      6545    1289     104
#> [1] "###################################################################################"
#>          max median  mean      name_max prop_ab_p975 prop_ab_p995 prop_ab_p9995
#> Geweke 1.506  0.776 0.776 population.sd            0            0             0
#> [1] "###################################################################################"
#>                       min   median     mean      name_min prop_bel_1000 prop_bel_5000 prop_bel_10000
#> Neff             1031.204 1050.428 1050.428 population.sd             0             1              1
#> [1] "###################################################################################"
#> [1] "###################################################################################"
#> [1] "MCMC has reached the required level of convergence."
#> [1] "###################################################################################"
#> [1] "MCMC has reached the required level of effective values."
#> [1] "###################################################################################"

We advise the reader to use the print.diagnostics functionality but do not in the following to keep the length of the document to a minimum.

Before turning to other model fits, let us depict the nature of the result of runMCMC_btadjust() function. The length of the output 1 is always equal to the number of Markov Chains - argument Nchains. Its class is mcmc.list - a type of object classical for MCMC outputs and defined in the coda package. Each component of this list contains the successive retained values for each saved parameter as well as attributes that give information on the MCMC they come from - see the beginning of the first component below:


length(out.mcmc.Coda.Geweke)
#> [1] 1

class(out.mcmc.Coda.Geweke)
#> [1] "mcmc.list"

head(out.mcmc.Coda.Geweke[[1]])
#> Markov Chain Monte Carlo (MCMC) output:
#> Start = 104 
#> End = 134 
#> Thinning interval = 5 
#>      population.mean population.sd
#> [1,]        603.7687      28.83656
#> [2,]        601.8702      29.74222
#> [3,]        600.8838      28.94277
#> [4,]        601.8738      29.73782
#> [5,]        600.8760      29.16368
#> [6,]        600.4063      29.67855
#> [7,]        601.3168      29.41725

The output - i.e. the whole list - however has extra information in its attributes: indeed, attributes has 5 components, whose name are: call.params, final.params, final.diags, sessionInfo, class: in addition to containing the class of the object - here “mcmc.list” -, these attributes include information on the R session in which the function was executed - component sessionInfo -, the final diagnostics of the model - component final.diags -, the arguments used in the call of the runMCMC_btadjust() function - component call.params - and finally the final “parameters” of the function - component final.params. In case MCMC_language is not “Greta”, the call.params component contains either the entire data and /or the constants or a summary of these (to keep the output to a controlled object size) - this choice is controlled by the component save.data of parameter control. The component final.params has a series of heterogeneous parameters including whether the model has converged, has reached its targets in terms of numbers of effective values…, as well as information in terms of duration of the different sections of the analysis - which we will use in the sequence of this document. See the help file for more information as well as the below printing. The final.diags component contains the information on the convergence and number of effective values of the parameters. Finally, the sessionInfo component has many interesting info relative to the context in which the function runMCMC_btadjust() was executed (including platform, version of R, versions of packages…).


names(attributes(out.mcmc.Coda.Geweke))
#> [1] "call.params"  "final.params" "final.diags"  "sessionInfo"  "class"

names(attributes(out.mcmc.Coda.Geweke)$package.versions)
#> NULL

attributes(out.mcmc.Coda.Geweke)$final.params
#> $converged
#> [1] TRUE
#> 
#> $neffs.reached
#> [1] TRUE
#> 
#> $final.Nchains
#> [1] 1
#> 
#> $removed.chains
#> integer(0)
#> 
#> $burnin
#> [1] 104
#> 
#> $thin
#> [1] 5
#> 
#> $niter.tot
#> [1] 6545
#> 
#> $Nvalues
#>                     
#> MCMC parameters 1289
#> 
#> $neff.min
#>                          
#> Neff             1031.204
#> 
#> $neff.median
#>                          
#> Neff             1050.428
#> 
#> $WAIC
#> NULL
#> 
#> $extraResults
#> NULL
#> 
#> $Temps
#> $Temps$chain1
#> NULL
#> 
#> 
#> $duration
#> Time difference of 67.50935 secs
#> 
#> $duration.MCMC.preparation
#> Time difference of 27.49336 secs
#> 
#> $duration.MCMC.transient
#> Time difference of 0.01715085 secs
#> 
#> $duration.MCMC.asymptotic
#> Time difference of 1.062198 secs
#> 
#> $duration.MCMC.after
#> Time difference of 6.985664e-05 secs
#> 
#> $duration.btadjust
#> Time difference of 38.93657 secs
#> 
#> $CPUduration
#> [1] 5.64
#> 
#> $CPUduration.MCMC.preparation
#> [1] 4.2
#> 
#> $CPUduration.MCMC.transient
#> [1] 0.01652559
#> 
#> $CPUduration.MCMC.asymptotic
#> [1] 1.023474
#> 
#> $CPUduration.MCMC.after
#> [1] 0
#> 
#> $CPUduration.btadjust
#> [1] 0.4
#> 
#> $childCPUduration
#> [1] NA
#> 
#> $childCPUduration.MCMC.preparation
#> [1] NA
#> 
#> $childCPUduration.MCMC.transient
#> [1] NA
#> 
#> $childCPUduration.MCMC.asymptotic
#> [1] NA
#> 
#> $childCPUduration.MCMC.after
#> [1] NA
#> 
#> $childCPUduration.btadjust
#> [1] NA
#> 
#> $time_end
#> [1] "2024-08-09 09:18:52 CEST"

attributes(out.mcmc.Coda.Geweke)$final.diags
#> $params
#>                 Nchains thin niter.tot Nvalues nu.burn
#> MCMC parameters       1    5      6545    1289     104
#> 
#> $conv_synth
#>          max median  mean      name_max prop_ab_p975 prop_ab_p995 prop_ab_p9995
#> Geweke 1.506  0.776 0.776 population.sd            0            0             0
#> 
#> $neff_synth
#>                       min   median     mean      name_min prop_bel_1000 prop_bel_5000 prop_bel_10000
#> Neff             1031.204 1050.428 1050.428 population.sd             0             1              1
#> 
#> $conv
#> population.mean   population.sd 
#>      0.04481887      1.50621756 
#> 
#> $neff
#> population.mean   population.sd 
#>        1069.652        1031.204

attributes(out.mcmc.Coda.Geweke)$sessionInfo
#> R version 4.4.0 (2024-04-24 ucrt)
#> Platform: x86_64-w64-mingw32/x64
#> Running under: Windows 10 x64 (build 19045)
#> 
#> Matrix products: default
#> 
#> 
#> Random number generation:
#>  RNG:     L'Ecuyer-CMRG 
#>  Normal:  Inversion 
#>  Sample:  Rejection 
#>  
#> locale:
#> [1] LC_COLLATE=French_France.utf8  LC_CTYPE=French_France.utf8    LC_MONETARY=French_France.utf8
#> [4] LC_NUMERIC=C                   LC_TIME=French_France.utf8    
#> 
#> time zone: Europe/Paris
#> tzcode source: internal
#> 
#> attached base packages:
#> [1] parallel  stats     graphics  grDevices utils     datasets  methods   base     
#> 
#> other attached packages:
#> [1] runMCMCbtadjust_1.1.2 coda_0.19-4.1         tensorflow_2.16.0     R6_2.5.1              greta_0.4.5          
#> [6] nimble_1.2.1         
#> 
#> loaded via a namespace (and not attached):
#>   [1] RColorBrewer_1.1-3  rstudioapi_0.16.0   jsonlite_1.8.8      magrittr_2.0.3      rmarkdown_2.27     
#>   [6] fs_1.6.4            vctrs_0.6.5         memoise_2.0.1       base64enc_0.1-3     htmltools_0.5.8.1  
#>  [11] usethis_2.2.3       progress_1.2.3      curl_5.2.1          rjags_4-15          runjags_2.2.2-4    
#>  [16] Formula_1.2-5       parallelly_1.37.1   StanHeaders_2.32.9  pracma_2.4.4        htmlwidgets_1.6.4  
#>  [21] desc_1.4.3          plyr_1.8.9          testthat_3.2.1.1    cachem_1.1.0        whisker_0.4.1      
#>  [26] igraph_2.0.3        mime_0.12           lifecycle_1.0.4     pkgconfig_2.0.3     Matrix_1.7-0       
#>  [31] fastmap_1.2.0       rcmdcheck_1.4.0     future_1.33.2       shiny_1.8.1.1       digest_0.6.35      
#>  [36] numDeriv_2016.8-1.1 colorspace_2.1-0    GGally_2.2.1        ps_1.7.7            rprojroot_2.0.4    
#>  [41] pkgload_1.3.4       Hmisc_5.1-3         fansi_1.0.6         tfruns_1.5.3        httr_1.4.7         
#>  [46] abind_1.4-5         compiler_4.4.0      remotes_2.5.0       withr_3.0.1         htmlTable_2.4.2    
#>  [51] backports_1.5.0     inline_0.3.19       ggstats_0.6.0       QuickJSR_1.2.0      pkgbuild_1.4.4     
#>  [56] highr_0.11          ggmcmc_1.5.1.1      rappdirs_0.3.3      sessioninfo_1.2.2   loo_2.7.0          
#>  [61] tools_4.4.0         foreign_0.8-86      httpuv_1.6.15       nnet_7.3-19         glue_1.7.0         
#>  [66] callr_3.7.6         promises_1.3.0      grid_4.4.0          checkmate_2.3.1     cluster_2.1.6      
#>  [71] nimbleAPT_1.0.6     generics_0.1.3      gtable_0.3.5        tidyr_1.3.1         data.table_1.15.4  
#>  [76] hms_1.1.3           xml2_1.3.6          utf8_1.2.4          pillar_1.9.0        stringr_1.5.1      
#>  [81] later_1.3.2         dplyr_1.1.4         moments_0.14.1      lattice_0.22-6      tidyselect_1.2.1   
#>  [86] miniUI_0.1.1.1      knitr_1.48          gridExtra_2.3       V8_4.4.2            stats4_4.4.0       
#>  [91] xfun_0.44           devtools_2.4.5      brio_1.1.5          matrixStats_1.3.0   rstan_2.32.6       
#>  [96] stringi_1.8.4       xopen_1.0.1         yaml_2.3.8          evaluate_0.24.0     codetools_0.2-20   
#> [101] tibble_3.2.1        cli_3.6.2           RcppParallel_5.1.7  rpart_4.1.23        xtable_1.8-4       
#> [106] reticulate_1.37.0   munsell_0.5.1       processx_3.8.4      roxygen2_7.3.1      Rcpp_1.0.13        
#> [111] globals_0.16.3      png_0.1-8           ellipsis_0.3.2      ggplot2_3.5.1       prettyunits_1.2.0  
#> [116] profvis_0.3.8       urlchecker_1.0.1    listenv_0.9.1       scales_1.3.0        purrr_1.0.2        
#> [121] crayon_1.5.3        rlang_1.1.4

We then run the MCMC with r NchainsMCMC chains, the - default - Gelman-Rubin diagnostic of convergence and the -default-rstan` method for calculating the number of effective values:

out.mcmc<-runMCMC_btadjust(code=ModelCode, constants = ModelConsts, data = ModelData, MCMC_language="Nimble",
    Nchains=Nchains, params=params, inits=Inits,
    niter.min=1000, niter.max=300000,
    nburnin.min=100, nburnin.max=200000, 
    thin.min=1, thin.max=1000,
    conv.max=1.05, neff.min=1000)
#> [1] "control$seed is NULL. Replaced by 1"
#> ===== Monitors =====
#> thin = 1: population.mean, population.sd
#> ===== Samplers =====
#> RW sampler (2)
#>   - population.mean
#>   - population.sd
#> ===== Monitors =====
#> thin = 1: population.mean, population.sd
#> ===== Samplers =====
#> RW sampler (2)
#>   - population.mean
#>   - population.sd
#> ===== Monitors =====
#> thin = 1: population.mean, population.sd
#> ===== Samplers =====
#> RW sampler (2)
#>   - population.mean
#>   - population.sd
#> [1] "###################################################################################"
#> |-------------|-------------|-------------|-------------|
#> |-------------------------------------------------------|
#> |-------------|-------------|-------------|-------------|
#> |-------------------------------------------------------|
#> |-------------|-------------|-------------|-------------|
#> |-------------------------------------------------------|
#> [1] "###################################################################################"
#> |-------------|-------------|-------------|-------------|
#> |-------------------------------------------------------|
#> |-------------|-------------|-------------|-------------|
#> |-------------------------------------------------------|
#> |-------------|-------------|-------------|-------------|
#> |-------------------------------------------------------|
#> [1] "Raw multiplier of thin:  4.415"
#> [1] "###################################################################################"
#> [1] "Testing multiplier of thin:  4 :"
#> [1] "Retained multiplier of thin:  4 :"
#> [1] "###################################################################################"
#> [1] "Case of niter update: Convergence and trying to reach end of MCMC at the end of next cycle"
#> [1] "###################################################################################"
#> [1] "###################################################################################"
#> |-------------|-------------|-------------|-------------|
#> |-------------------------------------------------------|
#> |-------------|-------------|-------------|-------------|
#> |-------------------------------------------------------|
#> |-------------|-------------|-------------|-------------|
#> |-------------------------------------------------------|
#> [1] "###################################################################################"
#> [1] "Main MCMC sampling finished."
#> [1] "###################################################################################"
#> [1] "Final max raw multiplier of thin:  1.265"
#> [1] "###################################################################################"
#> [1] "Retained final multiplier of thin:  1"
#> [1] "###################################################################################"
#> [1] "###################################################################################"
#> [1] "MCMC has reached the required level of convergence."
#> [1] "###################################################################################"
#> [1] "MCMC has reached the required level of effective values."
#> [1] "###################################################################################"

We compare the characteristics of the two MCMCs, both in terms of burn-in, thinning parameter, number of iterations and in terms of time (both total time and CPU time).

Table: Comparison of the efficiency of first two NIMBLE models:

	Nimble.Coda.Geweke	Nimble.default
converged	1.00000000	1.00000000
neffs.reached	1.00000000	1.00000000
final.Nchains	1.00000000	3.00000000
burnin	104.00000000	575.00000000
thin	5.00000000	4.00000000
niter.tot	6545.00000000	2528.00000000
Nvalues	1289.00000000	1467.00000000
neff.min	1031.20400000	1160.00000000
neff.median	1050.42800000	1163.50000000
duration	67.50935102	99.66728711
duration.MCMC.preparation	27.49336219	58.22134900
duration.MCMC.transient	0.01715085	0.26636985
duration.MCMC.asymptotic	1.06219843	0.90473100
duration.MCMC.after	0.00006986	0.00006914
duration.btadjust	38.93656969	40.27476811
CPUduration	5.64000000	17.08000000
CPUduration.MCMC.preparation	4.20000000	15.20000000
CPUduration.MCMC.transient	0.01652559	0.27294304
CPUduration.MCMC.asymptotic	1.02347441	0.92705696
CPUduration.MCMC.after	0.00000000	0.00000000
CPUduration.btadjust	0.40000000	0.68000000
childCPUduration	NA	NA
childCPUduration.MCMC.preparation	NA	NA
childCPUduration.MCMC.transient	NA	NA
childCPUduration.MCMC.asymptotic	NA	NA
childCPUduration.MCMC.after	NA	NA
childCPUduration.btadjust	NA	NA

We also wished to run a third MCMC on one chain with Geweke diagnostic but the default, rstan method for number of effective values, assumed to be more consertaive - i.e. to estimate lower numbers of effective values.


out.mcmc.Geweke<-runMCMC_btadjust(code=ModelCode, constants = ModelConsts, data = ModelData, MCMC_language="Nimble",
    Nchains=1, params=params, inits=Inits[1],
    niter.min=1000, niter.max=300000,
    nburnin.min=100, nburnin.max=200000, 
    thin.min=1, thin.max=1000,
    conv.max=Gew.Max, neff.min=1000,
    control=list(convtype="Geweke"))
#> [1] "control$seed is NULL. Replaced by 1"
#> ===== Monitors =====
#> thin = 1: population.mean, population.sd
#> ===== Samplers =====
#> RW sampler (2)
#>   - population.mean
#>   - population.sd
#> [1] "###################################################################################"
#> |-------------|-------------|-------------|-------------|
#> |-------------------------------------------------------|
#> [1] "###################################################################################"
#> |-------------|-------------|-------------|-------------|
#> |-------------------------------------------------------|
#> [1] "Raw multiplier of thin:  5.278"
#> [1] "###################################################################################"
#> [1] "Testing multiplier of thin:  5 :"
#> [1] "Retained multiplier of thin:  5 :"
#> [1] "###################################################################################"
#> [1] "Case of niter update: Convergence and trying to reach end of MCMC at the end of next cycle"
#> [1] "###################################################################################"
#> [1] "###################################################################################"
#> |-------------|-------------|-------------|-------------|
#> |-------------------------------------------------------|
#> [1] "###################################################################################"
#> [1] "Main MCMC sampling finished."
#> [1] "###################################################################################"
#> [1] "Final max raw multiplier of thin:  1.23"
#> [1] "###################################################################################"
#> [1] "Retained final multiplier of thin:  1"
#> [1] "###################################################################################"
#> [1] "###################################################################################"
#> [1] "MCMC has reached the required level of convergence."
#> [1] "###################################################################################"
#> [1] "MCMC has reached the required level of effective values."
#> [1] "###################################################################################"

We compare the characteristics of the three NIMBLE MCMCs,

Table: Comparison of the efficiency of the three NIMBLE models:

	Nimble.Coda.Geweke	Nimble.Geweke	Nimble.default
converged	1.00000000	1.00000000	1.00000000
neffs.reached	1.00000000	1.00000000	1.00000000
final.Nchains	1.00000000	1.00000000	3.00000000
burnin	104.00000000	104.00000000	575.00000000
thin	5.00000000	5.00000000	4.00000000
niter.tot	6545.00000000	6575.00000000	2528.00000000
Nvalues	1289.00000000	1295.00000000	1467.00000000
neff.min	1031.20400000	1053.00000000	1160.00000000
neff.median	1050.42800000	1057.00000000	1163.50000000
duration	67.50935102	63.38089490	99.66728711
duration.MCMC.preparation	27.49336219	21.55250192	58.22134900
duration.MCMC.transient	0.01715085	0.01686375	0.26636985
duration.MCMC.asymptotic	1.06219843	1.04928191	0.90473100
duration.MCMC.after	0.00006986	0.00006795	0.00006914
duration.btadjust	38.93656969	40.76217937	40.27476811
CPUduration	5.64000000	6.41000000	17.08000000
CPUduration.MCMC.preparation	4.20000000	5.10000000	15.20000000
CPUduration.MCMC.transient	0.01652559	0.01692471	0.27294304
CPUduration.MCMC.asymptotic	1.02347441	1.05307529	0.92705696
CPUduration.MCMC.after	0.00000000	0.00000000	0.00000000
CPUduration.btadjust	0.40000000	0.24000000	0.68000000
childCPUduration	NA	NA	NA
childCPUduration.MCMC.preparation	NA	NA	NA
childCPUduration.MCMC.transient	NA	NA	NA
childCPUduration.MCMC.asymptotic	NA	NA	NA
childCPUduration.MCMC.after	NA	NA	NA
childCPUduration.btadjust	NA	NA	NA

Results did not completely corroborate our above expectations: the thinning parameter was not increased when changing from Coda.Geweke to Geweke as expected above (row “thin”).

We now turn to the comparison of the statistical parameter outputs. We use two sample Kolmogorov-Smirnov tests to compare each parameter by pairs of MCMC methods:

Table: P-values of paired Kolmogorov-Smirnov tests of output parameters (columns) between the first three NIMBLE models (rows):

	mean	sd
default vs. Geweke	0.4837	0.4528
Coda.Geweke vs. Geweke	1.0000	1.0000
Default vs. Coda.Geweke	0.4946	0.4210

The p-values associated to the KS tests are not very small. This indicates that the MCMC outputs can be considered as being drawn from the same distributions.

These parameters are summarized in the next tables.

Table: Summary of the statistical parameters of the Nimble Coda.Geweke model:

	Mean	SD	Naive SE	Time-series SE
population.mean	600.606	0.949	0.026	0.029
population.sd	29.340	0.667	0.019	0.021

Table: Summary of the statistical parameters of the Nimble Geweke model:

	Mean	SD	Naive SE	Time-series SE
population.mean	600.607	0.949	0.026	0.029
population.sd	29.338	0.666	0.019	0.021

Table: Summary of the statistical parameters of the Nimble default model:

	Mean	SD	Naive SE	Time-series SE
population.mean	600.578	0.914	0.024	0.026
population.sd	29.320	0.644	0.017	0.016

We notice that parameter values are very close, that naive standard errors (SEs) are very close to Time-series SEs - which is linked to the automatic tuning of the thinning parameter which produces output samples which are nearly independent - and that differences between mean estimators are within several units of Time series-SEs - which we interpret is mostly due to the control of convergence.

JAGS

We now turn to analyzing the same data with the same statistical model using JAGS with runMCMC_btadjust(). We rely on the data simulated above. In JAGS, we now put all the data in the same list:

ModelData.Jags <-list(mass = y1000, nobs = length(y1000))

We then propose the use of JAGS with a specification of the model from within R - which we find more convenient. We therefore write the JAGS model within R as a character chain:


modeltotransfer<-"model {

		# Priors
			population.mean ~ dunif(0,5000)
			population.sd ~ dunif(0,100)

			# Normal distribution parameterized by precision = 1/variance in Jags
    	population.variance <- population.sd * population.sd
      precision <- 1 / population.variance

			# Likelihood
			for(i in 1:nobs){
			  mass[i] ~ dnorm(population.mean, precision)
			}
		}"

The other objects useful or required for running runMCMC_btadjust with JAGS are similar to those required with NIMBLE (Inits, Nchains, params) and are not repeated here.

We then launch runMCMC_btadjust() with MCMC_language="Jags", specifying arguments code and data which are required in this case. Note that if we had written the JAGS code in a text file named "ModelJags.txt", we would just have replaced in the command above code=modeltotransfer by code="ModelJags.txt".


set.seed(1)
out.mcmc.Jags<-runMCMC_btadjust(code=modeltotransfer,  data = ModelData.Jags, MCMC_language="Jags", 
    Nchains=Nchains, params=params, inits=Inits,
    niter.min=1000,niter.max=300000,
    nburnin.min=100,nburnin.max=200000,
    thin.min=1,thin.max=1000,
		conv.max=1.05,neff.min=1000)
#> [1] "control$seed is NULL. Replaced by 1"
#> Compiling model graph
#>    Resolving undeclared variables
#>    Allocating nodes
#> Graph information:
#>    Observed stochastic nodes: 1000
#>    Unobserved stochastic nodes: 2
#>    Total graph size: 1009
#> 
#> Initializing model
#> 
#> [1] "###################################################################################"
#> [1] "Main MCMC sampling finished."
#> [1] "###################################################################################"
#> [1] "Final max raw multiplier of thin:  1.473"
#> [1] "###################################################################################"
#> [1] "Retained final multiplier of thin:  1"
#> [1] "###################################################################################"
#> [1] "###################################################################################"
#> [1] "MCMC has reached the required level of convergence."
#> [1] "###################################################################################"
#> [1] "MCMC has reached the required level of effective values."
#> [1] "###################################################################################"

Here is a summary of the parameter estimates:

Table: Summary of the statistical parameters of the Jags model:

	Mean	SD	Naive SE	Time-series SE
population.mean	600.5742	0.9279	0.0123	0.0142
population.sd	29.3443	0.6395	0.0085	0.0103

Results seem in line with those of NIMBLE. We check this using a paired Kolmogorov-Smirnov tests with NIMBLE models:

Table: P-values of paired Kolmogorov-Smirnov tests of output parameters (columns) of the Jags model with the three NIMBLE models (rows):

	mean	sd
Nimble.Geweke vs. Jags	0.8939	0.3086
Nimble.Coda.Geweke vs. Jags	0.9225	0.3562
Nimble.Default vs. Jags	0.6345	0.5148

Our results do confirm that the JAGS result cannot be considered as stemming from a different probability distribution than NIMBLE results.

We finally compare the efficiency of the JAGS and default NIMBLE MCMCs:

Table: Comparison of the efficiency of the default NIMBLE model and the Jags model:

	Nimble.default	Jags
converged	1.00000000	1.00000000
neffs.reached	1.00000000	1.00000000
final.Nchains	3.00000000	3.00000000
burnin	575.00000000	100.00000000
thin	4.00000000	1.00000000
niter.tot	2528.00000000	2000.00000000
Nvalues	1467.00000000	5700.00000000
neff.min	1160.00000000	3870.00000000
neff.median	1163.50000000	3980.50000000
duration	99.66728711	44.15068889
duration.MCMC.preparation	58.22134900	6.74938297
duration.MCMC.transient	0.26636985	0.31298219
duration.MCMC.asymptotic	0.90473100	5.94666160
duration.MCMC.after	0.00006914	0.00006700
duration.btadjust	40.27476811	31.14159513
CPUduration	17.08000000	9.37000000
CPUduration.MCMC.preparation	15.20000000	2.96000000
CPUduration.MCMC.transient	0.27294304	0.30850000
CPUduration.MCMC.asymptotic	0.92705696	5.86150000
CPUduration.MCMC.after	0.00000000	0.00000000
CPUduration.btadjust	0.68000000	0.24000000
childCPUduration	NA	NA
childCPUduration.MCMC.preparation	NA	NA
childCPUduration.MCMC.transient	NA	NA
childCPUduration.MCMC.asymptotic	NA	NA
childCPUduration.MCMC.after	NA	NA
childCPUduration.btadjust	NA	NA

The conclusion is that JAGS is much faster than NIMBLE on this example (row named duration in the previous table), due to much less time devoted to MCMC preparation - as well as to burn-in/thinning adjustment (rows named duration.MCMC.preparation and duration.btadjust in the previous table). Actually there is no adjustment with JAGS (niter.tot is equal to the initial number of iterations). Yet, NIMBLE is quicker regarding MCMC updating by iteration since it took NIMBLE less time than JAGS for the transient phase (respectively less than twice time for the asymptotic phase) although using more than 5.75 (resp. 1.0278947 for the asymptotic phase) times more iterations than JAGS.

At first sight, we would also conclude that MCMC efficiency per effective value is also better with NIMBLE since both languages had the same target for the minimum number of effective value - 1,000 - and the total MCMC time was lower with NIMBLE. Yet, the number of effective values are different:

Table: Comparison of the number of effective values between the default NIMBLE model and the JAGS model:

	Nimble.default	Jags
Min. Number Eff. values	1160.000000	3870.000000
MCMC CPU time per Effective Value	0.001034	0.001594

Indeed, “JAGS” with just the first iterations produced a higher number of effective values - actually bigger than the targeted “neff.min” - than “NIMBLE”. Yet, the MCMC time per effective value remained lower with “NIMBLE” than with “JAGS” with this model (cf. table above).

Greta

We finally run the greta version of our model with runMCMC_btadjust(). greta is rather different from JAGS and NIMBLE in that the model defines objects in R and thus does not require a model code to be passed to runMCMC_btadjust(), nor Data or Constants. The coding with greta is as follows:

#in my setting I need to load not only greta but R6 & tensorflow packages
library(greta)
library (R6)
library(tensorflow)

#first requirement of greta: declaring the data that will be analyzed with the function as_data
Y<-as_data(y1000)

#we then proceed by writing the model directly in R, starting with the priors of the parameters using greta functions for probability distributions - here uniform()
population.mean<-uniform(0,5000)
population.sd<-uniform(0,100)
    
#we then define the distribution of the data - here with the normal distribution - by default parametrized with a standard deviation in greta:
try({distribution(Y)<-normal(population.mean,population.sd) })

#we finally declare the greta model, which will be the object passed to runMCMC_btadjust 
m<-model(population.mean, population.sd)

### we finally have to prepare initial values with a specific greta function - initials:
ModelInits.Greta <- function()
    {initials(population.mean = rnorm(1,600,90), population.sd = runif(1, 1, 30))}

set.seed(1)
  Inits.Greta<-lapply(1:Nchains,function(x){ModelInits.Greta()})

We are now ready to fit the model with runMCMC_btadjust(), specifying MCMC_language="Greta" and giving the argument model instead of code and data:

out.mcmc.greta<-runMCMC_btadjust(model=m, MCMC_language="Greta",
    Nchains=Nchains,params=params,inits=Inits.Greta,
		niter.min=1000,niter.max=300000,
    nburnin.min=100,nburnin.max=200000,
		thin.min=1,thin.max=1000,
		conv.max=1.05, neff.min=1000)
#> [1] "control$seed is NULL. Replaced by 1"
#> [1] "###################################################################################"
#> 
#> [1] "Raw multiplier of thin:  6.237"
#> [1] "###################################################################################"
#> [1] "Testing multiplier of thin:  6 :"
#> [1] "Retained multiplier of thin:  6 :"
#> [1] "###################################################################################"
#> [1] "Case of niter update: Convergence and trying to reach end of MCMC at the end of next cycle"
#> [1] "###################################################################################"
#> [1] "###################################################################################"
#> 
#> [1] "Raw multiplier of thin:  1.377"
#> [1] "###################################################################################"
#> [1] "Retained multiplier of thin:  1 :"
#> [1] "###################################################################################"
#> [1] "Case of niter update: Convergence and trying to reach end of MCMC at the end of next cycle"
#> [1] "###################################################################################"
#> [1] "###################################################################################"
#> 
#> [1] "###################################################################################"
#> [1] "Main MCMC sampling finished."
#> [1] "###################################################################################"
#> [1] "Final max raw multiplier of thin:  1.418"
#> [1] "###################################################################################"
#> [1] "Retained final multiplier of thin:  1"
#> [1] "###################################################################################"
#> [1] "###################################################################################"
#> [1] "MCMC has reached the required level of convergence."
#> [1] "###################################################################################"
#> [1] "MCMC has reached the required level of effective values."
#> [1] "###################################################################################"

Table: Summary of the statistical parameters of the greta model:

	Mean	SD	Naive SE	Time-series SE
population.mean	600.573	0.907	0.023	0.026
population.sd	29.342	0.647	0.016	0.015

We first check that estimations are similar to those with NIMBLE and JAGS with paired Kolmogorov-Smirnov tests:

Table: P-values of paired Kolmogorov-Smirnov tests of output parameters of the greta model with the default NIMBLE model and the JAGS model:

	mean	sd
Nimble vs. greta	0.9249	0.3846
Jags vs. greta	0.9834	0.4925

We then report the efficiency of the MCMCs.

Table: Comparison of the efficiency of the default NIMBLE, the JAGS and the greta models:

	Nimble.default	Jags	Greta
converged	1.00000000	1.00000000	1.00000000
neffs.reached	1.00000000	1.00000000	1.00000000
final.Nchains	3.00000000	3.00000000	3.00000000
burnin	575.00000000	100.00000000	3.00000000
thin	4.00000000	1.00000000	6.00000000
niter.tot	2528.00000000	2000.00000000	3124.00000000
Nvalues	1467.00000000	5700.00000000	1563.00000000
neff.min	1160.00000000	3870.00000000	1102.00000000
neff.median	1163.50000000	3980.50000000	1393.00000000
duration	99.66728711	44.15068889	72.26697588
duration.MCMC.preparation	58.22134900	6.74938297	3.54183006
duration.MCMC.transient	0.26636985	0.31298219	6.86132239
duration.MCMC.asymptotic	0.90473100	5.94666160	21.35013677
duration.MCMC.after	0.00006914	0.00006700	0.00006604
duration.btadjust	40.27476811	31.14159513	40.51362062
CPUduration	17.08000000	9.37000000	108.82000000
CPUduration.MCMC.preparation	15.20000000	2.96000000	0.01000000
CPUduration.MCMC.transient	0.27294304	0.30850000	26.40536130
CPUduration.MCMC.asymptotic	0.92705696	5.86150000	82.16463870
CPUduration.MCMC.after	0.00000000	0.00000000	0.00000000
CPUduration.btadjust	0.68000000	0.24000000	0.24000000
childCPUduration	NA	NA	NA
childCPUduration.MCMC.preparation	NA	NA	NA
childCPUduration.MCMC.transient	NA	NA	NA
childCPUduration.MCMC.asymptotic	NA	NA	NA
childCPUduration.MCMC.after	NA	NA	NA
childCPUduration.btadjust	NA	NA	NA

MCMC time (rows duration.MCMC.transient & duration.MCMC.asymptotic) was far greater with greta than with JAGS and NIMBLE, for a minimum number of effective values with greta of 1102. Total duration is rather close with greta compared with NIMBLE, due to the great time required by NIMBLE for MCMC preparation - while this preparation is done outside runMCMC_btadjust() with greta. Yet, when we compare CPU total durations (CPUduration), greta gets worse than NIMBLE while it was the reverse for total duration (duration), simply because greta parallelized its process and therefore required more CPU time per time unit.

We tried to give a second chance to greta, based on the following post: https://forum.greta-stats.org/t/size-and-number-of-leapfrog-steps-in-hmc/332. The idea was to let greta have more information to adapt its hmc parameters during the warm-up phase by just having more chains to run - hereafter, 15.

Nchains.Greta<-15
ModelInits.Greta <- function()
    {initials(population.mean = rnorm(1,600,90), population.sd = runif(1, 1, 30))}

set.seed(1)
Inits.Greta<-lapply(1:Nchains.Greta,function(x){ModelInits.Greta()})
  
  out.mcmc.greta.morechains<-runMCMC_btadjust(model=m, MCMC_language="Greta",
    Nchains=Nchains.Greta,params=params,inits=Inits.Greta,
		niter.min=1000,niter.max=300000,
    nburnin.min=100,nburnin.max=200000,
		thin.min=1,thin.max=1000,
		conv.max=1.05, neff.min=1000)
#> [1] "control$seed is NULL. Replaced by 1"
#> [1] "###################################################################################"
#> 
#> [1] "###################################################################################"
#> [1] "Main MCMC sampling finished."
#> [1] "###################################################################################"
#> [1] "Final max raw multiplier of thin:  4.916"
#> [1] "###################################################################################"
#> [1] "Testing final multiplier of thin:  5 :"
#> [1] "Retained final multiplier of thin:  5"
#> [1] "###################################################################################"
#> [1] "###################################################################################"
#> [1] "MCMC has reached the required level of convergence."
#> [1] "###################################################################################"
#> [1] "MCMC has reached the required level of effective values."
#> [1] "###################################################################################"

Table: Summary of the statistical parameters of the greta model with 15 chains:

	Mean	SD	Naive SE	Time-series SE
population.mean	600.542	0.920	0.017	0.018
population.sd	29.360	0.664	0.012	0.014

This run was indeed much faster. Parameter estimates were still not significantly different from those with NIMBLE and JAGS based on paired Kolmogorov-Smirnov tests:

Table: P-values of paired Kolmogorov-Smirnov tests of output parameters of the greta model with 15 chains with the default NIMBLE model and the JAGS model:

	mean	sd
Nimble vs. greta.morechains	0.3659	0.2652
Jags vs. greta.morechains	0.2364	0.5704

We now report the efficiency of the MCMCs:

Table: Comparison of the efficiency of the default NIMBLE, the JAGS and the greta.morechains models:

	Nimble.default	Jags	Greta.morechains
converged	1.00000000	1.00000000	1.00000000
neffs.reached	1.00000000	1.00000000	1.00000000
final.Nchains	3.00000000	3.00000000	15.00000000
burnin	575.00000000	100.00000000	0.00000000
thin	4.00000000	1.00000000	5.00000000
niter.tot	2528.00000000	2000.00000000	1000.00000000
Nvalues	1467.00000000	5700.00000000	3000.00000000
neff.min	1160.00000000	3870.00000000	1984.00000000
neff.median	1163.50000000	3980.50000000	2262.50000000
duration	99.66728711	44.15068889	47.76610494
duration.MCMC.preparation	58.22134900	6.74938297	3.47832203
duration.MCMC.transient	0.26636985	0.31298219	11.78189743
duration.MCMC.asymptotic	0.90473100	5.94666160	11.78189743
duration.MCMC.after	0.00006914	0.00006700	0.00006795
duration.btadjust	40.27476811	31.14159513	20.72392011
CPUduration	17.08000000	9.37000000	158.78000000
CPUduration.MCMC.preparation	15.20000000	2.96000000	0.01000000
CPUduration.MCMC.transient	0.27294304	0.30850000	79.12000000
CPUduration.MCMC.asymptotic	0.92705696	5.86150000	79.12000000
CPUduration.MCMC.after	0.00000000	0.00000000	0.00000000
CPUduration.btadjust	0.68000000	0.24000000	0.53000000
childCPUduration	NA	NA	NA
childCPUduration.MCMC.preparation	NA	NA	NA
childCPUduration.MCMC.transient	NA	NA	NA
childCPUduration.MCMC.asymptotic	NA	NA	NA
childCPUduration.MCMC.after	NA	NA	NA
childCPUduration.btadjust	NA	NA	NA

We still observed more CPU duration with greta, although the associated number of effective values for greta was now 1984, which rendered MCMC CPU efficiency with greta closer to NIMBLE.

Parallelization

The function runMCMC_btadjust() now allows automatic parallelization of different Markov chains of the MCMC parts of the algorithm which can be of interest when we have several Markov chains. When the user wishes to use parallelization, the only difference with the preceding calls are the addition of control.MCMC=list(parallelize=TRUE) - or of parallelize=TRUE in control.MCMC if already present. Here are examples below, with 2 chains only (a condition required by CRAN to accept parallelization in vignettes).


library(parallel)

### put here to pass CRAN tests: https://stackoverflow.com/questions/41307178/error-processing-vignette-failed-with-diagnostics-4-simultaneous-processes-spa
options(mc.cores=2)

### adapted the number of chains for the same reason
Nchains.parallel<-2

out.mcmc.Nimble.parallel<-runMCMC_btadjust(code=ModelCode, constants = ModelConsts, data = ModelData, MCMC_language="Nimble",
    Nchains=Nchains.parallel, params=params, inits=Inits[1:Nchains.parallel],
    niter.min=1000, niter.max=300000,
    nburnin.min=100, nburnin.max=200000, 
    thin.min=1, thin.max=1000,
    conv.max=1.05, neff.min=1000,
    control.MCMC=list(parallelize=TRUE))
#> [1] "control$seed is NULL. Replaced by 1"
#> [1] "###################################################################################"
#> [1] "###################################################################################"
#> [1] "Raw multiplier of thin:  6.189"
#> [1] "###################################################################################"
#> [1] "Testing multiplier of thin:  6 :"
#> [1] "Retained multiplier of thin:  6 :"
#> [1] "###################################################################################"
#> [1] "Case of niter update: Convergence and trying to reach end of MCMC at the end of next cycle"
#> [1] "###################################################################################"
#> [1] "###################################################################################"
#> [1] "###################################################################################"
#> [1] "Main MCMC sampling finished."
#> [1] "###################################################################################"
#> [1] "Final max raw multiplier of thin:  1.231"
#> [1] "###################################################################################"
#> [1] "Retained final multiplier of thin:  1"
#> [1] "###################################################################################"
#> [1] "###################################################################################"
#> [1] "MCMC has reached the required level of convergence."
#> [1] "###################################################################################"
#> [1] "MCMC has reached the required level of effective values."
#> [1] "###################################################################################"

out.mcmc.Jags.parallel<-runMCMC_btadjust(code=modeltotransfer,  data = ModelData.Jags, MCMC_language="Jags", 
    Nchains=Nchains.parallel, params=params, inits=Inits[1:Nchains.parallel],
    niter.min=1000,niter.max=300000,
    nburnin.min=100,nburnin.max=200000,
    thin.min=1,thin.max=1000,
		conv.max=1.05,neff.min=1000,
    control.MCMC=list(parallelize=TRUE))
#> [1] "control$seed is NULL. Replaced by 1"
#> [1] "###################################################################################"
#> [1] "###################################################################################"
#> [1] "###################################################################################"
#> [1] "Main MCMC sampling finished."
#> [1] "###################################################################################"
#> [1] "Final max raw multiplier of thin:  1.5"
#> [1] "###################################################################################"
#> [1] "Retained final multiplier of thin:  1"
#> [1] "###################################################################################"
#> [1] "###################################################################################"
#> [1] "MCMC has reached the required level of convergence."
#> [1] "###################################################################################"
#> [1] "MCMC has reached the required level of effective values."
#> [1] "###################################################################################"

Automatic removal of chains

We finally present an attractive feature of runMCMC_btadjust() which is to remove chains whose parameters are all invariable during the firs cycle of the MCMC. This is an issue that can appear for some chains, especially when initial values of parameters are far away from likely values and the MCMC sampler cannot move from the corresponding value. We here illustrate this on a simplified version of the above model in which the standard deviation is given (i.e. is not estimated) - simply because in the case the sampler can move for this parameter. We introduce a low standard deviation value in the normal distribution. Here is the code:


ModelCode<-nimbleCode(
  {
    # Priors
    population.mean ~ dunif(0,5000)
    
    # Likelihood
    for(i in 1:nobs){
      mass[i] ~ dnorm(population.mean, 1)
    }
  })

We then update the initial values, introducing a very unlikely value in the second chain:

Nchains <- 3

ModelInits <- function()
{list (population.mean = rnorm(1,600,2))}
  

set.seed(1)
Inits<-lapply(1:Nchains,function(x){ModelInits()})

Inits[[2]]<-list(population.mean=-600)


#specifying the names of parameters to analyse and save:
params <- c("population.mean")

We then launch runMCMC_btadjust() in this setting:


out.mcmc.pbIV<-runMCMC_btadjust(code=ModelCode, constants = ModelConsts, data = ModelData, MCMC_language="Nimble",
    Nchains=Nchains, params=params, inits=Inits,
    niter.min=1000, niter.max=300000,
    nburnin.min=100, nburnin.max=200000, 
    thin.min=1, thin.max=1000,
    conv.max=1.05, neff.min=1000)
#> [1] "control$seed is NULL. Replaced by 1"
#> ===== Monitors =====
#> thin = 1: population.mean
#> ===== Samplers =====
#> RW sampler (1)
#>   - population.mean
#> ===== Monitors =====
#> thin = 1: population.mean
#> ===== Samplers =====
#> RW sampler (1)
#>   - population.mean
#> ===== Monitors =====
#> thin = 1: population.mean
#> ===== Samplers =====
#> RW sampler (1)
#>   - population.mean
#> [1] "###################################################################################"
#> |-------------|-------------|-------------|-------------|
#> |-------------------------------------------------------|
#> warning: problem initializing stochastic node population.mean: logProb is -Inf.
#> |-------------|-------------|-------------|-------------|
#> |-------------------------------------------------------|
#> |-------------|-------------|-------------|-------------|
#> |-------------------------------------------------------|
#> [1] "###################################################################################"
#> |-------------|-------------|-------------|-------------|
#> |-------------------------------------------------------|
#> |-------------|-------------|-------------|-------------|
#> |-------------------------------------------------------|
#> [1] "Raw multiplier of thin:  4.442"
#> [1] "###################################################################################"
#> [1] "Testing multiplier of thin:  4 :"
#> [1] "Retained multiplier of thin:  4 :"
#> [1] "###################################################################################"
#> [1] "Case of niter update: Convergence and trying to reach end of MCMC at the end of next cycle"
#> [1] "###################################################################################"
#> [1] "###################################################################################"
#> |-------------|-------------|-------------|-------------|
#> |-------------------------------------------------------|
#> |-------------|-------------|-------------|-------------|
#> |-------------------------------------------------------|
#> [1] "Raw multiplier of thin:  1.412"
#> [1] "###################################################################################"
#> [1] "Retained multiplier of thin:  1 :"
#> [1] "###################################################################################"
#> [1] "Case of niter update: Convergence and trying to reach end of MCMC at the end of next cycle"
#> [1] "###################################################################################"
#> [1] "###################################################################################"
#> |-------------|-------------|-------------|-------------|
#> |-------------------------------------------------------|
#> |-------------|-------------|-------------|-------------|
#> |-------------------------------------------------------|
#> [1] "###################################################################################"
#> [1] "Main MCMC sampling finished."
#> [1] "###################################################################################"
#> [1] "Final max raw multiplier of thin:  1.44"
#> [1] "###################################################################################"
#> [1] "Retained final multiplier of thin:  1"
#> [1] "###################################################################################"
#> [1] "###################################################################################"
#> [1] "MCMC has reached the required level of convergence."
#> [1] "###################################################################################"
#> [1] "MCMC has reached the required level of effective values."
#> [1] "###################################################################################"

Despite the very unlikely value for chain 2, the model converges and reached the number of effective values. We also notice in the above that only two chains were updated - chains number 1 and 3. Actually, only two chains are present in the results and the output specifies that chain 2 was removed.

length(out.mcmc.pbIV)
#> [1] 2

attributes(out.mcmc.pbIV)$final.params$final.Nchains
#> [1] 2

attributes(out.mcmc.pbIV)$final.params$removed.chains
#> [1] 2

Note that if the removal of chains makes the number of chains pass from more than 1 to 1, the MCMC is stopped because the convergence diagnostic type and its targets would not adapt to a situation where there is only one chain.


out.mcmc.pbIV.2chains<-runMCMC_btadjust(code=ModelCode, constants = ModelConsts, data = ModelData, MCMC_language="Nimble",
    Nchains=2, params=params, inits=Inits[1:2],
    niter.min=1000, niter.max=300000,
    nburnin.min=100, nburnin.max=200000, 
    thin.min=1, thin.max=1000,
    conv.max=1.05, neff.min=1000)
#> [1] "control$seed is NULL. Replaced by 1"
#> ===== Monitors =====
#> thin = 1: population.mean
#> ===== Samplers =====
#> RW sampler (1)
#>   - population.mean
#> ===== Monitors =====
#> thin = 1: population.mean
#> ===== Samplers =====
#> RW sampler (1)
#>   - population.mean
#> [1] "###################################################################################"
#> |-------------|-------------|-------------|-------------|
#> |-------------------------------------------------------|
#> warning: problem initializing stochastic node population.mean: logProb is -Inf.
#> |-------------|-------------|-------------|-------------|
#> |-------------------------------------------------------|
#> Error in system.time({: Impossible to use the Gelman-Rubin convergence diagnostic with only one MCMC chain (***after update of Nchains***): please change Nchain or control$convtype or update your initial values

Removed chains are removed from the convergence and effective number diagnostics as well as from the outputs of runMCMC_btadjust(). If used with Nimble, it is also removed from the updated chains - thus saving computer resources. Such was not found possible with Jags and Greta. This

Conclusion

We hope we have convinced the R user of Bayesian models that runMCMC_btadjust() can help having a more efficient, quality oriented use of these types of models while saving analyst’s and potentially computer time. Indeed, to recap, the aim of this function is to run a Markov Chain Monte Carlo (MCMC) for a specified Bayesian model while adapting automatically the burn-in and thinning parameters to meet pre-specified targets in terms of MCMC convergence and number of effective values of MCMC outputs. This is done in only one call to the function that repeatedly calls the MCMC until criteria for convergence and number of effective values are met. The function has four main advantages:

(i) it saves the analyst’s programming time since he/she does not have to repeatedly diagnose and re-run MCMCs until desired levels of convergence and number of effective values are reached;

(ii) it allows a minimal, normalized quality control of MCMC outputs by allowing to meet pre-specified levels in terms of convergence and number of quasi-independent values;

(iii) it may save computer’s time when compared to cases where we have to restart the MCMC from the beginning if it has not converged or reached the specified number of effective values;

(iv) it can be applied with different MCMC fitting tools available in R - at present greta, NIMBLE and JAGS. This comes with two positive consequences in practice: first, allowing the user a more rigorous comparison between the three Bayesian fitting languages in terms of comparability of inference and of MCMC efficiency - especially in terms of CPU time per effective value; second, making it easier to develop the same Bayesian model with these different languages, which is to our experience welcome in practical cases, since these different languages have advantages over the other ones that vary from one context to the other.

Acknowledgements

I wished to thank Frédéric Mortier (ANR Gambas project supervisor, project in which the initial versions of the package were developed), Pierre Bouchet, Ugoline Godeau and Marion Gosselin (INRAE, for collaboration on some codes that were preliminary to this package) and NIMBLE and greta users mailing lists.

The initial development of this package (up to version 1.1.1) was performed within the GAMBAS project funded by the French Agence Nationale pour la Recherche (ANR-18-CE02-0025) (cf. https://gambas.cirad.fr/).

References

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
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runMCMCbtadjust Presentation

Frédéric Gosselin

2024-08-09