For my latest blog posts see below. If you wish to look for a post on a specific topic please use the search or tags features of the site.
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Posts
In this blog post we turn our attention away from sampling from generic distributions to the problem of Monte-Carlo integration. Building up from a simple estimator we look at various variance reduction methods and approximations.
Jun 1, 2020
In this blog post we extend the copula ideas from the previous blog post to look at the vine copula. Another flexible method for efficiently sampling from multi-variate distributions.
May 25, 2020
In this blog post we continue to look at Monte Carlo methods and how they can be used. We move from sampling from univariate distributions to multi-variate distributions.
May 18, 2020
In this blog post we will begin to look at Monte Carlo methods and how they can be used. These form the backbone of (essentially) all statistical computer modelling.
May 11, 2020
In this blog post we will look at entropy in 3 classical settings: Thermodynamics, Information Theory and Statistics. We will show that while under certain conditions they have the same functional form this is not true in general. Moreover we will look at how we can define entropy in relation to complex systems.
May 4, 2020
In this blog post we will look at Percolation. Starting with some motivating examples we will solve the percolation problem on both a 1d and infinite dimensional lattice. We will use percolation to help understand how power-law behaviour arises from criticality near phase transitions.
Apr 28, 2020
In this blog post we will look at cellular automata and iterative computation. We shall look at how simple deterministic rules can lead to surprising results. We will start by studying 1d cellular automata before moving on to 2d. We will then look at some example models: Conway's game of life, the termite-woodchip model and the Schelling segregation model.
Apr 21, 2020
In this blog post we will look at the grand-daddy of stochastic simulation methods: the Gillespie Algorithm (otherwise known as the stochastic simulation algorith SSA). If you have ever done any form of stochastic simulation you will owe a great deal of gratitude to the Gillespie algorithm which likely inspired the techniques you used.
Apr 14, 2020
In this blog post we will look at an agent based model of flocking. We will see how complex behaviour can emerge from relatively simple rules. We will let predators loose within the flock to see how the flock can respond.
Apr 7, 2020
In this blog post we will take another look at spin-glasses, in particular we look at some of the areas where spin-glass conecepts have been used. In particular we will look at applications and extensions to our existing methods.
Mar 31, 2020
In this blog post we will introduce ways of simulating the Ising models introduced in the previous post. We start by looking at a fairly basic MCMC implementation. From this we will introduce a computational technique that has implications way beyond spin glasses. We will end with a more modern higher performance approach to simulating the Ising model.
Mar 24, 2020
In this blog post we will introduce another model of spin glasses: the Ising model. We relax some of the simplifications of previous models to create something that more accurately captures the structure of real spin-glasses. We will look at this model mathematically to gain insight into its properties.
Mar 17, 2020
Following on from the previous blog post introducing spin-glass models we now look at an example model from Sherrington-Kirkpatrick dating back to 1975. We outline some mathematical tools for analysing the model use Python to simulate and explore its behaviour.
Mar 10, 2020
In this blog post I will provide a quick overview of spin glass models. These models can be mathematically very dense, in this blog post I just aim to give a flavour - in future posts I will come back and look at the models in more detail. Fortunately there tends to be a simple visual representation which we can use to gain an insight. (Note: I look at spin glasses mostly through a mathematical lense, some of the physics interpretations may be a bit ropey.)
Mar 3, 2020
This is just a quick fun blog post about a model for standing ovations as proposed by Scott Page and John Miller - it provides a great introduction to agent based modelling for those unfamiliar.
Feb 25, 2020
