Cartography in Haskell
Introduction This blog started off life as a blog post on how I use nix but somehow transformed itself into a “how I do data visualisation” blog post. The nix is still here though quietly doing its work in the background. Suppose you want to analyze your local election results and visualize them using a choropleth but you’d like to use Haskell. You could try using the shapefile package but you wil
Haskell for Numerics?
Introduction Summary Back in January, a colleague pointed out to me that GHC did not produce very efficient code for performing floating point abs. I have yet to produce a write-up of my notes about hacking on GHC: in summary it wasn’t as difficult as I had feared and the #ghc folks were extremely helpful. But maybe getting GHC to produce high performance numerical code is “swimming uphill”. Below
Mercator: A Connection with Torsion
Introduction In most presentations of Riemannian geometry, e.g. O’Neill (1983) and Wikipedia, the fundamental theorem of Riemannian geometry (“the miracle of Riemannian geometry”) is given: that for any semi-Riemannian manifold there is a unique torsion-free metric connection. I assume partly because of this and partly because the major application of Riemannian geometry is General Relativity, con
Ecology, Dynamical Systems and Inference via PMMH
Introduction In the 1920s, Lotka (1909) and Volterra (1926) developed a model of a very simple predator-prey ecosystem. Although simple, it turns out that the Canadian lynx and showshoe hare are well represented by such a model. Furthermore, the Hudson Bay Company kept records of how many pelts of each species were trapped for almost a century, giving a good proxy of the population of each species
Every Manifold is Paracompact
Introduction In their paper Betancourt et al. (2014), the authors give a corollary which starts with the phrase “Because the manifold is paracompact”. It wasn’t immediately clear why the manifold was paracompact or indeed what paracompactness meant although it was clearly something like compactness which means that every cover has a finite sub-cover. It turns out that every manifold is paracompact
Naive Particle Smoothing is Degenerate
We wish to determine the position and velocity of the car given noisy observations of the position. In general we need the distribution of the hidden path given the observable path. We use the notation to mean the path of starting a and finishing at . Haskell Preamble > {-# OPTIONS_GHC -Wall #-} > {-# OPTIONS_GHC -fno-warn-name-shadowing #-} > {-# OPTIONS_GHC -fno-warn-type-defaults #-} > {-# OPTI
Girsanov’s Theorem
Introduction We previously used importance sampling in the case where we did not have a sampler available for the distribution from which we wished to sample. There is an even more compelling case for using importance sampling. Suppose we wish to estimate the probability of a rare event. For example, suppose we wish to estimate where . In this case, we can look up the answer . But suppose we could
Population Growth Estimation via Markov Chain Monte Carlo
Introduction Let us see if we can estimate the parameter for population growth using MCMC in the example in which we used Kalman filtering. We recall the model. Preamble > {-# OPTIONS_GHC -Wall #-} > {-# OPTIONS_GHC -fno-warn-name-shadowing #-} > {-# OPTIONS_GHC -fno-warn-type-defaults #-} > {-# OPTIONS_GHC -fno-warn-unused-do-bind #-} > {-# OPTIONS_GHC -fno-warn-missing-methods #-} > {-# OPTIONS_
Fun with (Extended Kalman) Filters
Summary An extended Kalman filter in Haskell using type level literals and automatic differentiation to provide some guarantees of correctness. Population Growth Suppose we wish to model population growth of bees via the logistic equation We assume the growth rate is unknown and drawn from a normal distribution but the carrying capacity is known and we wish to estimate the growth rate by observing
Gibbs Sampling in Haskell
This is really intended as a draft chapter for our book. Given the diverse natures of the intended intended audiences, it is probably a bit light on explanation of the Haskell (use of monad transformers) for those with a background in numerical methods. It is hoped that the explanation of the mathematics is adequate for those with a background in Haskell but not necessarily in numerical methods. A
Laplace’s Equation in Haskell: Using a DSL for Stencils
Introduction Suppose we have a square thin plate of metal and we hold each of edges at a temperature which may vary along the edge but is fixed for all time. After some period depending on the conductivity of the metal, the temperature at every point on the plate will have stabilised. What is the temperature at any point? We can calculate this using by solving Laplace’s equation in 2 dimensions. A
Haskell, Ising, Markov & Metropolis
Introduction About a year ago there was a reddit post on the Ising Model in Haskell. The discussion seems to have fizzled out but Ising models looked like a perfect fit for Haskell using repa. In the end it turns out that they are not a good fit for repa, at least not using the original formulation. It may turn out that we can do better with Swendson-Yang or Wolff. But that belongs to another blog
Parking in Westminster: An Analysis in Haskell
I had a fun weekend analysing car parking data in Westminster at the Future Cities Hackathon along with Amit Nandi Bart Baddeley Jackie Steinitz Ian Ozsvald Mateusz Łapsa-Malawski Apparently in the world of car parking where Westminster leads the rest of UK follows. For example Westminster is rolling out individual parking bay monitors. Our analysis gained an honourable mention. Ian has produced a
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Modelling an Ecosystem via Hamiltonian Monte Carlo
A Type Safe Reverse or Some Hasochism
Fun with (Kalman) Filters Part II
Fun with (Kalman) Filters Part I
Gibbs Sampling in R, Haskell, Jags and Stan
Student’s T and Space Leaks
Bayesian Analysis: A Conjugate Prior and Markov Chain Monte Carlo