Bayesian on Batı Şengül
http://www.batisengul.co.uk/tags/bayesian/
Recent content in Bayesian on Batı ŞengülHugo -- gohugo.iobatisengul@gmail.combatisengul@gmail.comFri, 02 Jul 2021 00:00:00 +0000Introduction To Hamiltonian Monte Carlo
http://www.batisengul.co.uk/post/2021-07-02-intro-to-hmc/
Fri, 02 Jul 2021 00:00:00 +0000batisengul@gmail.comhttp://www.batisengul.co.uk/post/2021-07-02-intro-to-hmc/Introduction to Hamiltonian Monte Carlo One thing that has been occupying my head in the past couple of weeks has been HMC and how it can be used in large data/large model context. HMC stands for Hamiltonian Monte Carlo and it’s the de facto Bayesian method for sampling due to it’s speed. Before getting into big datasets and big models, let me motivate this problem a little bit.
If you are new to Bayesian modelling, I have a little primer on the topic so I will assume for the most part you are familiar with basic Bayesianism.Variational inference, the art of approximate sampling
http://www.batisengul.co.uk/post/variational-inference-the-art-of-approximate-sampling/
Sat, 21 Jul 2018 00:00:00 +0000batisengul@gmail.comhttp://www.batisengul.co.uk/post/variational-inference-the-art-of-approximate-sampling/In the spirit of looking at fancy word topics, this post is about variational inference. Suppose you granted me one super power and I chose the ability to sample from any distribution in a fast and accurate way. Now, you might think that’s a crappy super-power, but that basically enables me to fit any model I want and provide uncertainty estimates.
To make the problem concrete, lets suppose you are trying to sample from a distribution \(p(x)\).Spike and slab: Bayesian linear regression with variable selection
http://www.batisengul.co.uk/post/spike-and-slab-bayesian-linear-regression-with-variable-selection/
Wed, 20 Jun 2018 00:00:00 +0000batisengul@gmail.comhttp://www.batisengul.co.uk/post/spike-and-slab-bayesian-linear-regression-with-variable-selection/Spike and slab is a Bayesian model for simultaneously picking features and doing linear regression. Spike and slab is a shrinkage method, much like ridge and lasso regression, in the sense that it shrinks the “weak” beta values from the regression towards zero. Don’t worry if you have never heard of any of those terms, we will explore all of these using Stan. If you don’t know anything about Bayesian statistics, you can read my introductory post before reading this one.Bayesian analysis of Premier League football
http://www.batisengul.co.uk/post/bayesian-analysis-of-premier-league-football/
Mon, 02 Apr 2018 00:00:00 +0000batisengul@gmail.comhttp://www.batisengul.co.uk/post/bayesian-analysis-of-premier-league-football/In this post we are going to look at some football statistics. In particular, we will examine English football, the Premier League, using Bayesian statistics with Stan. If you have no idea what Bayesian statistics is, you can read my introductory post on it. Otherwise this post shouldn’t be a difficult read.
All right, let’s get to it. First, we need some data. I will use all the matches from the Premier League seasons 16/17 and 17/18 (which is still ongoing at the time of the writing).Causal impact and Bayesian structural time series
http://www.batisengul.co.uk/post/causal-impact-and-bayesian-structural-time-series/
Sat, 03 Feb 2018 00:00:00 +0000batisengul@gmail.comhttp://www.batisengul.co.uk/post/causal-impact-and-bayesian-structural-time-series/Causal impact is a tool for estimating the impact of a one time action. As an example (which we will actually look at the data) consider the BP oil spill in 2010. Let’s say you want to evaluate the impact that this had on BP stocks. Typically with questions like this, we would like to be able to collect multiple samples from a control group and a test group. As this is not possible we would have to try something else.Bayes of our lives: a gentle introduction to Bayesian statistics
http://www.batisengul.co.uk/post/bayes-of-our-lives-a-gentle-introduction-to-bayesian-statistics/
Tue, 07 Nov 2017 00:00:00 +0000batisengul@gmail.comhttp://www.batisengul.co.uk/post/bayes-of-our-lives-a-gentle-introduction-to-bayesian-statistics/Bayesian statistics is an interpretation of statistics. It is used to help explain the frequentist methods and can give much more information. Even if you have never really learnt about Bayesian statistics, I guarantee you have encountered it in some way.
Bayes, it’s everywhere
In this post, we will only consider a linear model: \(y = \beta x + \epsilon\) where \(\epsilon\) is a standard normal. Suppose we have gathered some data \((Y=\{y_i\}_{i=1}^n, X=\{\{x_{k,i}\}_{k=1}^p\}_{i=1}^n)\), which consist of \(p\) predictors and \(n\) observations, and we wish to fit a linear model.