Publications by kjytay
Estimating pi using the method of moments
Happy Pi Day! I don’t encounter very much in my area of statistics, so this post might seem a little forced… In this post, I’m going to show one way to estimate . The starting point is the integral identity There are two ways to see why this identity is true. The first is that the integral is simply computing the area of a quarter-circle ...
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Is the EPL getting more unequal?
I recently heard that Manchester City were so far ahead in the English Premier League (EPL) that the race for first was basically over, even though they were still about 6-7 more games to go (out of a total of 38 games). At the other end of the table, I heard that Sheffield United were so far behind that they are all but certain to be relegated. ...
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What is the Tukey loss function?
The Tukey loss function The Tukey loss function, also known as Tukey’s biweight function, is a loss function that is used in robust statistics. Tukey’s loss is similar to Huber loss in that it demonstrates quadratic behavior near the origin. However, it is even more insensitive to outliers because the loss incurred by large residuals is const...
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Introducing cvwrapr for your cross-validation needs
TLDR: I’ve written an R package, cvwrapr, that helps users to cross-validate hyperparameters. The code base is largely extracted from the glmnet package. The R package is available for download from Github, and contains two vignettes which demonstrate how to use it. Comments, feedback and bug reports welcome! Imagine yourself in the following s...
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Small gotcha when using negative indexing
Negative indexing is a commonly used method in R to drop elements from a vector or rows/columns from a matrix that the user does not want. For example, the code below drops the third column from the matrix M: M <- matrix(1:9, nrow = 3) M # [,1] [,2] [,3] # [1,] 1 4 7 # [2,] 2 5 8 # [3,] 3 6 9 M[, -3] # ...
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NBA playoffs: Visualizing win percentage by seeding
Background With the NBA playoffs going on, I’ve been thinking about the following question: A and B are about to play a game. We know that among all players, A has rank/seed and B has rank/seed . (A higher ranking/seeding corresponds to a smaller value of , with being the best. Players with higher rank/seed are better players.) Knowing only t...
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Estimating win probability from best-of-7 series is not straightforward
(Note: The code in this post is available here as a single R script.) Let’s say A and B play 7 games and A wins 4 of them. What would be a reasonable estimate for A’s win probability (over B)? A natural estimate would be 4/7. More generally, if A wins games, then the estimator is an unbiased estimator of the true win probability . This is n...
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Documentation for internal functions
tl;dr: To avoid triple quotes and R CMD CHECK --as-cran errors due to documentation examples for internal functions, enclose the example code in \dontrun{}. I recently encountered an issue when submitting an R package to CRAN that I couldn’t find a clean answer for. One of the comments from the manual check was the following: Using foo:::f inst...
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Using different fonts with ggplot2
I was recently asked to convert all the fonts in my ggplot2-generated figures for a paper to Times New Roman. It turns out that this is easy, but it brought up a whole host of questions that I don’t have the full answer to. If you want to go all out with using custom fonts, I suggest looking into the extrafont and showtext packages. This post w...
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Getting predictions from an isotonic regression model
TLDR: Pass the output of the isoreg function to as.stepfun to make an isotonic regression model into a black box object that takes in uncalibrated predictions and outputs calibrated ones. Isotonic regression is a method for obtaining a monotonic fit for 1-dimensional data. Let’s say we have data such that . (We assume no ties among the ‘s fo...
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