Bayesian Statistics and Functional Programming – Bayesian Inference and Functional Programming

Model Comparison with Hierarchical Models

R

Bayesian

Machine Learning

Comparing the performance of multiple machine learning models using Bayesian Hierarchical models.

Uncertainty in Neural Networks

Python

Deep Learning

Bayesian

Using MC Dropout to get probability intervals for neural network predictions.

Entity Embeddings

Python

Deep Learning

Creating entity embeddings for categorical predictors using Python.

Neural Networks in R

R

Deep Learning

This post explores how to create a simple neural network to learn a linear function and a non-linear function using both standard R and the Torch library for R.

Functional Programming and Hidden Markov Models

Bayesian

R

The hidden Markov model is a state-space model with a discrete latent state,

x_{1 : T}

and noisy observations

y_{1 : T}

. The model can be described mathematically as

Multi State Models

R

Bayesian

Multi-state models are used to model disease progression. The model is a continuous time Markov process. The states and time of transitions are fully observed. There are…

Tidy Tuesday: Tour de France

R

The Tour de France is the biggest annual sporting event in the world featuring 21 days of bicycle racing and two rest days around France (sometimes starting other countries…

Bayesian Inference for an SIR Model

R

Bayesian

Johns Hopkins University have put together a repository containing confirmed cases of COVID19, deaths and recovered patients. Below we plot the confirmed cases, confirmed…

Tidy Tuesday: The Office

tidy-tuesday

R

Bayesian

First we download the ratings for each office episode using the tidytuesdayR package.

Tidy Tuesday: US Tuition Data

tidy-tuesday

R

This weeks data consists of tuition costs, salary potential and diversity information of US colleges. This includes 2 year colleges which offer associate degrees…

Releasing Harrier League Data

R

The North East Harrier League is a series of cross country running races in the North East of England taking place over the winter from September to March. Results are…

Tidy Tuesday: NHL Goalscorers

R

tidy-tuesday

First install the Tidy Tuesday R package.

Analysing .fit files in R

R

Garmin running watches output a file type called .fit, the developer SDK can be downloaded from the ANT website. There is also Python library named fitparse which has been…

Bayesian Survival Analysis: Exponential Model

R

Bayesian

Consider an arbitrary interval where the expected number of events in the interval is denoted as

λ

. The number of events in this interval is Poisson distributed…

Forward Mode AD in R

R

Automatic differentiation can be used to calculate the exact derivative of a function at a point using applications of the chain rule. Dual numbers provide a straightforward…

Hamiltonian Monte Carlo in R

R

Bayesian

Determining the posterior distribution for the parameters of a real-world Bayesian model inevitably requires calculating high-dimensional integrals. Often these are tedious…

Bayesian Linear Regression with Gibbs Sampling in R

R

Bayesian

Linear regression models are commonly used to explain relationships between predictor variables and outcome variables. The data consists of pairs of independent observations …

Multi-armed Bandits in Scala

Scala

This post uses Almond in order to run Scala code in a Jupyter notebook. See my previous post to learn how to setup Jupyter, Ammonite and Almond. That post examined using the…

Scala and Jupyter Notebook with Almond

Scala

Typically, when programming with Scala I use a combination of ensime in emacs, sbt and the Scala repl. However, sometimes when working on a new project which requires a lot…

Sampling from a distribution with a known CDF

R

A distribution with an inverse cumulative distribution function (CDF) can be sampled from using just samples from

U [0, 1]

. The inverse CDF (sometimes called the quantile…

Bayesian Inference using rejection sampling

R

Bayesian

As an example, consider a (possibly biased) coin flip experiment. The parameter of interest is the probability of heads

p_{h}

. A Beta distribution is chosen for the prior…

A Statistical Model for Finishing Positions at the National Cross Country

R

Download the results from Power of ten for northern, midlands, southern and national.

Efficient Markov chain Monte Carlo in R with Rcpp

R

Bayesian

This post considers how to implement a simple Metropolis scheme to determine the parameter posterior distribution of a bivariate Normal distribution. The implementation is…

Harrier League Cross Country

R

The Harrier League is a cross country running league with seven fixtures across the North East of England in the 2017/18 season across the winter months from September ’17…

MCMC with Scala Breeze

Scala

Bayesian

Scala Breeze is a numerical computing library, which also provides facilities for statistical computing. For instance, implementations of distributions and Markov chain…