About Me Blog
A tutorial on tidy cross-validation with R Analyzing NetHack data, part 1: What kills the players Analyzing NetHack data, part 2: What players kill the most Building a shiny app to explore historical newspapers: a step-by-step guide Classification of historical newspapers content: a tutorial combining R, bash and Vowpal Wabbit, part 1 Classification of historical newspapers content: a tutorial combining R, bash and Vowpal Wabbit, part 2 Dealing with heteroskedasticity; regression with robust standard errors using R Easy time-series prediction with R: a tutorial with air traffic data from Lux Airport Exporting editable plots from R to Powerpoint: making ggplot2 purrr with officer Forecasting my weight with R From webscraping data to releasing it as an R package to share with the world: a full tutorial with data from NetHack Getting data from pdfs using the pdftools package Getting the data from the Luxembourguish elections out of Excel Going from a human readable Excel file to a machine-readable csv with {tidyxl} How Luxembourguish residents spend their time: a small {flexdashboard} demo using the Time use survey data Imputing missing values in parallel using {furrr} Looking into 19th century ads from a Luxembourguish newspaper with R Making sense of the METS and ALTO XML standards Manipulate dates easily with {lubridate} Manipulating strings with the {stringr} package Maps with pie charts on top of each administrative division: an example with Luxembourg's elections data Missing data imputation and instrumental variables regression: the tidy approach Objects types and some useful R functions for beginners Pivoting data frames just got easier thanks to `pivot_wide()` and `pivot_long()` R or Python? Why not both? Using Anaconda Python within R with {reticulate} Searching for the optimal hyper-parameters of an ARIMA model in parallel: the tidy gridsearch approach Some fun with {gganimate} The best way to visit Luxembourguish castles is doing data science + combinatorial optimization The year of the GNU+Linux desktop is upon us: using user ratings of Steam Play compatibility to play around with regex and the tidyverse Using Data Science to read 10 years of Luxembourguish newspapers from the 19th century Using a genetic algorithm for the hyperparameter optimization of a SARIMA model Using the tidyverse for more than data manipulation: estimating pi with Monte Carlo methods What hyper-parameters are, and what to do with them; an illustration with ridge regression {pmice}, an experimental package for missing data imputation in parallel using {mice} and {furrr} Building formulae Functional peace of mind Get basic summary statistics for all the variables in a data frame Getting {sparklyr}, {h2o}, {rsparkling} to work together and some fun with bash Importing 30GB of data into R with sparklyr Introducing brotools It's lists all the way down It's lists all the way down, part 2: We need to go deeper Keep trying that api call with purrr::possibly() Lesser known dplyr 0.7* tricks Lesser known dplyr tricks Lesser known purrr tricks Make ggplot2 purrr Mapping a list of functions to a list of datasets with a list of columns as arguments Predicting job search by training a random forest on an unbalanced dataset Teaching the tidyverse to beginners Why I find tidyeval useful tidyr::spread() and dplyr::rename_at() in action Easy peasy STATA-like marginal effects with R Functional programming and unit testing for data munging with R available on Leanpub How to use jailbreakr My free book has a cover! Work on lists of datasets instead of individual datasets by using functional programming Method of Simulated Moments with R New website! Nonlinear Gmm with R - Example with a logistic regression Simulated Maximum Likelihood with R Bootstrapping standard errors for difference-in-differences estimation with R Careful with tryCatch Data frame columns as arguments to dplyr functions Export R output to a file I've started writing a 'book': Functional programming and unit testing for data munging with R Introduction to programming econometrics with R Merge a list of datasets together Object Oriented Programming with R: An example with a Cournot duopoly R, R with Atlas, R with OpenBLAS and Revolution R Open: which is fastest? Read a lot of datasets at once with R Unit testing with R Update to Introduction to programming econometrics with R Using R as a Computer Algebra System with Ryacas

Using the tidyverse for more than data manipulation: estimating pi with Monte Carlo methods

This blog post is an excerpt of my ebook Modern R with the tidyverse that you can read for free here. This is taken from Chapter 5, which presents the {tidyverse} packages and how to use them to compute descriptive statistics and manipulate data. In the text below, I show how you can use the {tidyverse} functions and principles for the estimation of \(\pi\) using Monte Carlo simulation.

Going beyond descriptive statistics and data manipulation

The {tidyverse} collection of packages can do much more than simply data manipulation and descriptive statisics. You can use the principles we have covered and the functions you now know to do much more. For instance, you can use a few {tidyverse} functions to do Monte Carlo simulations, for example to estimate \(\pi\).

Draw the unit circle inside the unit square, the ratio of the area of the circle to the area of the square will be \(\pi/4\). Then shot K arrows at the square; roughly \(K*\pi/4\) should have fallen inside the circle. So if now you shoot N arrows at the square, and M fall inside the circle, you have the following relationship \(M = N*\pi/4\). You can thus compute \(\pi\) like so: \(\pi = 4*M/N\).

The more arrows N you throw at the square, the better approximation of \(\pi\) you’ll have. Let’s try to do this with a tidy Monte Carlo simulation. First, let’s randomly pick some points inside the unit square:

n <- 5000

points <- tibble("x" = runif(n), "y" = runif(n))

Now, to know if a point is inside the unit circle, we need to check wether \(x^2 + y^2 < 1\). Let’s add a new column to the points tibble, called inside equal to 1 if the point is inside the unit circle and 0 if not:

points <- points %>% 
    mutate(inside = map2_dbl(.x = x, .y = y, ~ifelse(.x**2 + .y**2 < 1, 1, 0))) %>% 

Let’s take a look at points:

## # A tibble: 5,000 x 4
##        N       x      y inside
##    <int>   <dbl>  <dbl>  <dbl>
##  1     1 0.770   0.984       0
##  2     2 0.713   0.0107      1
##  3     3 0.303   0.133       1
##  4     4 0.618   0.0378      1
##  5     5 0.0505  0.677       1
##  6     6 0.0432  0.0846      1
##  7     7 0.820   0.727       0
##  8     8 0.00961 0.0758      1
##  9     9 0.102   0.373       1
## 10    10 0.609   0.676       1
## # … with 4,990 more rows

The rowid_to_column() function, from the {tibble} package, adds a new column to the data frame with an id, going from 1 to the number of rows in the data frame. Now, I can compute the estimation of \(\pi\) at each row, by computing the cumulative sum of the 1’s in the inside column and dividing that by the current value of N column:

points <- points %>% 
    mutate(estimate = 4*cumsum(inside)/N)

cumsum(inside) is the M from the formula. Now, we can finish by plotting the result:

ggplot(points) + 
    geom_line(aes(y = estimate, x = N), colour = "#82518c") + 
    geom_hline(yintercept = pi) +

In Chapter 6, we are going to learn all about {ggplot2}.

As the number of tries grows, the estimation of \(\pi\) gets better.

Using a data frame as a structure to hold our simulated points and the results makes it very easy to avoid loops, and thus write code that is more concise and easier to follow. If you studied a quantitative field in u8niversity, you might have done a similar exercise at the time, very likely by defining a matrix to hold your points, and an empty vector to hold whether a particular point was inside the unit circle. Then you wrote a loop to compute whether a point was inside the unit circle, save this result in the before-defined empty vector and then compute the estimation of \(\pi\). Again, I take this opportunity here to stress that there is nothing wrong with this approach per se, but R, with the {tidyverse} is better suited for a workflow where lists or data frames are the central objects and where the analyst operates over them with functional programming techniques.

Hope you enjoyed! If you found this blog post useful, you might want to follow me on twitter for blog post updates and buy me an espresso or paypal.me.

Buy me an EspressoBuy me an Espresso