Category: R

Bryan Shalloway explains how odds and probabilities intertwine:

However human understanding of odds predates our formal understanding of probability. You can find references to odds dating back to Shakespeare:

Knew that we ventured on such dangerous seas
That if we wrought out life ’twas ten to one;
– Shakespeare’s Henry IV, Part II, 1597

Yet, in most common settings, modern society has largely supplanted odds for probabilities. You can imagine if Shakespeare were writing today the line might end “’twas ten out of eleven.”

Read the whole thing.

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Steven Sanderson tests a distribution fit:

There are two main ways to fit a gamma distribution to a dataset in R:

1. Maximum likelihood estimation (MLE): This method estimates the parameters of the gamma distribution that are most likely to have produced the observed data.
2. Method of moments: This method estimates the parameters of the gamma distribution by equating the sample mean and variance to the theoretical mean and variance of the gamma distribution.

Click through to see which technique Steven uses and an example of how it all works.

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Steven Sanderson unleashes the power of the triangle:

The Triangular Distribution is a continuous probability distribution with a triangular shape, hence the name. It is defined by three parameters: min, max, and mode. These parameters determine the range of values the distribution can take and the most likely value within that range. In mathematical terms, the probability density function (PDF) of the Triangular Distribution is given by:

Read on to see the definition, as well as how you can use the four functions around the Triangular Distribution.

By the way, the best-known case of the Triangular Distribution is combining the results of two fair dice, which gives us a peak at the number 7 (1/6 of the time) for a pair of fair, six-sided dice and moving symmetrically down from there, so p(6) = p(8), p(5) = p(9), and so on.

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Steven Sanderson isn’t satisfied with the binomial:

The multinomial distribution is a probability distribution that describes the probability of obtaining a specific number of counts for k different outcomes, when each outcome has a fixed probability of occurring.

In R, we can use the rmultinom() function to simulate random samples from a multinomial distribution, and the dmultinom() function to calculate the probability of a specific outcome.

Click through to see how you can build a multinomial distribution and what the difference is between rmultinom() and dmultinom().

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Steven Sanderson digs into the uniform distribution:

Randomness is an essential part of many statistical and machine learning tasks. In R, there are a number of functions that can be used to generate random numbers, but the runif() function is the most commonly used.

Something mildly embarrassing for me is that it took me a while to figure out why they call the command runif(). That’s because, at first, I didn’t pronounce it r unif but rather run if.

In reality, *unif() means “uniform distribution” and r stands for “random number.” There are several other functions based on the uniform distribution and Steven looks at those as well in this post.

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I decided to test a common narrative:

A common theme among Buffalo Bills fans is the idea that the Bills run too many plays out of shotgun near the opposing team’s goal line, and this is hampering their ability to score points. Instead, these fans argue, they should run from under center, either a direct handoff or a quarterback sneak. If you were to press fans on this, I believe you’d also hear that the Bills are unique, or at least uniquely bad, at running such plays.

I’m going to use the nflfastR package to analyze play-by-play data and see just how well this bit of fan wisdom holds up.

Spoiler alert: it doesn’t.

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Steven Sanderson performs a logistic regression:

Logistic regression is a statistical method used for predicting the probability of a binary outcome. It’s a fundamental tool in machine learning and statistics, often employed in various fields such as healthcare, finance, and marketing. We use logistic regression when we want to understand the relationship between one or more independent variables and a binary outcome, which can be “yes/no,” “1/0,” or any two-class distinction.

Click through to learn how to do this.

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