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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Combinations and permutations in R

Time to get another concept under my belt, combinations and permutations. While I’m at it, I will examine combinations and permutations in R. As you may recall from school, a combination does not take into account the order, whereas a permutation does. Using the example from my favourite website as of late, mathsisfun.com: A fruit…

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Calculus

Calculus in Latin means pebble or small stone, such that we are working with small pieces. There are two main ideas in calculus, the first being differentiation or finding a derivative (finding a slope, which would equal the rate) and the second being integration, which is the joining (or integration) of the small pieces together…

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Distance Matrix Computation

Here I demonstrate the distance matrix computations using the R function dist(). Firstly let’s prepare a small dataset to work with: How does this dataset look in 3 dimensional space? We can see that points 4 and 6 are quite far away from each other.

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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, $$\Omega$$ (upper case omega), is the collection of possible outcomes of an experiment, such as a die roll: $$!\Omega = \{1, 2, 3, 4, 5, 6\}$$…

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Using LaTeX with WordPress

Updated 2017 November 17th WordPress now supports LaTeX. To display LaTeX, just surround the code with “$latex” and “$”, without the quotations. In this post, I show some formulae from this tutorial on SVD. I’ve shown the code for each formula; you can also mouseover the formula to see the code.

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