Monte Carlo Simulations Made Easy and Tidy.

tidyMC

Monte Carlo Simulations aim to study the properties of statistical inference techniques. At its core, a Monte Carlo Simulation works through the application of the techniques to repeatedly drawn samples from a pre-specified data generating process. The tidyMC package aims to cover and simplify the whole workflow of running a Monte Carlo simulation in either an academic or professional setting. Thus, tidyMC aims to provide functions for the following tasks:

• Running a Monte Carlo Simulation for a user defined function over a parameter grid using future_mc()
• Summarizing the results by (optionally) user defined summary functions using summary.mc()
• Creating plots of the Monte Carlo Simulation results, which can be modified by the user using plot.mc() and plot.summary.mc()
• Creating a LaTeX table summarizing the results of the Monte Carlo Simulation using tidy_mc_latex()

Installing tidyMC

Until now, the tidyMC package is not on CRAN, thus you need to download the development version from GitHub as follows:

# install.packages("devtools")
devtools::install_github("stefanlinner/tidyMC", build_vignettes = TRUE)

Afterwards you can load the package:

library(tidyMC)

Example

library(magrittr)
library(ggplot2)
library(kableExtra)

This is a basic example which shows you how to solve a common problem. For a more elaborate example please see the vignette:

browseVignettes(package = "tidyMC")
#> starte den http Server für die Hilfe fertig

Run your first Monte Carlo Simulation using your own parameter grid:

test_func <- function(param = 0.1, n = 100, x1 = 1, x2 = 2){
  
  data <- rnorm(n, mean = param) + x1 + x2
  stat <- mean(data)
  stat_2 <- var(data)
  
  if (x2 == 5){
    stop("x2 can't be 5!")
  }
  
  return(list(mean = stat, var = stat_2))
}

param_list <- list(param = seq(from = 0, to = 1, by = 0.5),
                   x1 = 1:2)

set.seed(101)

test_mc <- future_mc(
  fun = test_func,
  repetitions = 1000,
  param_list = param_list,
  n = 10,
  x2 = 2, 
  check = TRUE
)
#> Running single test-iteration for each parameter combination...
#> 
#>  Test-run successfull: No errors occurred!
#> Running whole simulation: Overall 6 parameter combinations are simulated ...
#> 
#>  Simulation was successfull!
#>  Running time: 00:00:05.836134

test_mc
#> Monte Carlo simulation results for the specified function: 
#>  
#>  function (param = 0.1, n = 100, x1 = 1, x2 = 2) 
#> {
#>     data <- rnorm(n, mean = param) + x1 + x2
#>     stat <- mean(data)
#>     stat_2 <- var(data)
#>     if (x2 == 5) {
#>         stop("x2 can't be 5!")
#>     }
#>     return(list(mean = stat, var = stat_2))
#> } 
#>  
#>  The following 6 parameter combinations: 
#> # A tibble: 6 × 2
#>   param    x1
#>   <dbl> <int>
#> 1   0       1
#> 2   0.5     1
#> 3   1       1
#> 4   0       2
#> 5   0.5     2
#> 6   1       2
#> are each simulated 1000 times. 
#>  
#>  The Running time was: 00:00:05.836134 
#>  
#>  Parallel: TRUE 
#>  
#>  The following parallelisation plan was used: 
#> $strategy
#> multisession:
#> - args: function (..., workers = availableCores(), lazy = FALSE, rscript_libs = .libPaths(), envir = parent.frame())
#> - tweaked: FALSE
#> - call: NULL
#> 
#> 
#>  Seed: TRUE

Summarize your results:

sum_res <- summary(test_mc)
sum_res
#> Results for the output mean: 
#>    param=0, x1=1: 3.015575 
#>    param=0, x1=2: 4.003162 
#>    param=0.5, x1=1: 3.49393 
#>    param=0.5, x1=2: 4.480855 
#>    param=1, x1=1: 3.985815 
#>    param=1, x1=2: 4.994084 
#>  
#>  
#> Results for the output var: 
#>    param=0, x1=1: 0.9968712 
#>    param=0, x1=2: 1.026523 
#>    param=0.5, x1=1: 0.9933278 
#>    param=0.5, x1=2: 0.9997529 
#>    param=1, x1=1: 0.9979682 
#>    param=1, x1=2: 1.005633 
#>  
#> 

Plot your results / summarized results:

returned_plot1 <- plot(test_mc, plot = FALSE)

returned_plot1$mean +
 ggplot2::theme_minimal() +
 ggplot2::geom_vline(xintercept = 3)

returned_plot2 <- plot(test_mc, which_setup = test_mc$nice_names[1:2], plot = FALSE)
returned_plot2$mean

returned_plot3 <- plot(test_mc, join = test_mc$nice_names[1:2], plot = FALSE)
returned_plot3$mean

returned_plot1 <- plot(summary(test_mc), plot = FALSE)

returned_plot1$mean +
  ggplot2::theme_minimal()

returned_plot2 <- plot(summary(test_mc), which_setup = test_mc$nice_names[1:2], plot = FALSE)
 returned_plot2$mean

returned_plot3 <- plot(summary(test_mc), join = test_mc$nice_names[1:2], plot = FALSE)
returned_plot3$mean

Show your results in a LaTeX table:

tidy_mc_latex(summary(test_mc)) %>% 
  print()
#> \begin{table}
#> 
#> \caption{\label{tab:unnamed-chunk-9}Monte Carlo simulations results}
#> \centering
#> \begin{tabular}[t]{cccc}
#> \toprule
#> param & x1 & mean & var\\
#> \midrule
#> 0.0 & 1 & 3.016 & 0.997\\
#> 0.0 & 2 & 4.003 & 1.027\\
#> 0.5 & 1 & 3.494 & 0.993\\
#> 0.5 & 2 & 4.481 & 1.000\\
#> 1.0 & 1 & 3.986 & 0.998\\
#> \addlinespace
#> 1.0 & 2 & 4.994 & 1.006\\
#> \bottomrule
#> \multicolumn{4}{l}{\textsuperscript{} Total repetitions = 1000,}\\
#> \multicolumn{4}{l}{total parameter combinations}\\
#> \multicolumn{4}{l}{= 6}\\
#> \end{tabular}
#> \end{table}

tidy_mc_latex(
    summary(test_mc),
    repetitions_set = c(10,1000),
    which_out = "mean",
    kable_options = list(caption = "Mean MCS results")
) %>% 
  print()
#> \begin{table}
#> 
#> \caption{\label{tab:unnamed-chunk-9}Mean MCS results}
#> \centering
#> \begin{tabular}[t]{ccc}
#> \toprule
#> param & x1 & mean\\
#> \midrule
#> \addlinespace[0.3em]
#> \multicolumn{3}{l}{\textbf{N = 10}}\\
#> \hspace{1em}0.0 & 1 & 3.193\\
#> \hspace{1em}0.0 & 2 & 3.810\\
#> \hspace{1em}0.5 & 1 & 3.434\\
#> \hspace{1em}0.5 & 2 & 4.550\\
#> \hspace{1em}1.0 & 1 & 4.156\\
#> \hspace{1em}1.0 & 2 & 5.030\\
#> \addlinespace[0.3em]
#> \multicolumn{3}{l}{\textbf{N = 1000}}\\
#> \hspace{1em}0.0 & 1 & 3.016\\
#> \hspace{1em}0.0 & 2 & 4.003\\
#> \hspace{1em}0.5 & 1 & 3.494\\
#> \hspace{1em}0.5 & 2 & 4.481\\
#> \hspace{1em}1.0 & 1 & 3.986\\
#> \hspace{1em}1.0 & 2 & 4.994\\
#> \bottomrule
#> \multicolumn{3}{l}{\textsuperscript{} Total repetitions =}\\
#> \multicolumn{3}{l}{1000, total}\\
#> \multicolumn{3}{l}{parameter}\\
#> \multicolumn{3}{l}{combinations = 6}\\
#> \end{tabular}
#> \end{table}