Rand Index versus the Adjusted Rand Index

I wrote about the Rand Index (RI) and the Adjusted Rand Index (ARI) in the last two posts but how do we interpret the indices and how are they different? The RI is: where and are the number of times a pair of items was clustered concordantly in two different sets. I wrote some code...

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The Rand index

I've been looking for ways to compare clustering results and through my searching I came across something called the Rand index. In this short post, I explain how this index is calculated.

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Quantile normalisation in R

Updated 2015 January 14th to include a slide from Rafael. From Wikipedia: In statistics, quantile normalization is a technique for making two distributions identical in statistical properties. To quantile normalize two or more distributions to each other, without a reference distribution, sort as before, then set to the average (usually, arithmetical mean) of the distributions....

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Markov chain

A Markov chain is a mathematical system that undergoes transitions from one state to another on a state space in a stochastic (random) manner. Examples of Markov chains include the board game snakes and ladders, where each state represents the position of a player on the board and a player moves between states (different positions...

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Probability

The fundamental idea of inferential statistics is determining the probability of obtaining the observed data when we assume the null hypothesis is true. For example, if we roll a die 10 times and got 10 sixes, what is the probability of observing this result if we assume the null hypothesis that the die was fair?...

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Set notation

I've just started the Mathematical Biostatistics Boot Camp 1 and to help me remember the set notations introduced in the first lecture, I'll include them here: The sample space, (upper case omega), is the collection of possible outcomes of an experiment, such as a die roll: An event, say E, is a subset of ,...

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