Solutions-to-Problems-in-Bayesian-Statistics

This repository contains my solutions to the assignments in the book: "A Student’s Guide to Bayesian Statistics" by Ben Lambert. I will update the repository with my solutions continuously.

Content

An introduction to Bayesian inference

Chapter 2 - The subjective worlds of Frequentist and Bayesian statistics

The code for this section can be found: HERE The report can be found: HERE

Chapter 3 - Probability - the nuts and bolts of Bayesian inference

The code for this section can be found: HERE The report can be found: HERE

Understanding the Bayesian formula

Chapter 4 - Likelihoods

The report can be found: HERE

Excerpt of some results

Chapter 5 - Priors

The report can be found: HERE

Chapter 6 - The devil is in the denominator

The report can be found: HERE

Excerpt of some results

Chapter 7 - The posterior - The goal of Bayesian inference

Analytic Bayesian methods

Chapter 8 - Distributions

Excerpt of some results

Chapter 9 - Conjugate priors

Excerpt of some results

Chapter 10 - Evaluation of model fit and hypothesis testing

Chapter 11 - Making Bayesian analysis objective?

Computational Bayes

Chapter 12 - Leaving conjugates behind: Markov chain Monte Carlo

Chapter 13 - Metropolis Hastings

The report can be found: HERE

Modeling presence of Borrelia amongst Ticks

Symmetric Kernel - Random Walk Metropolis

Using a Binomial likelihood, a Beta prior and an symmetric Normal jumping kernel.

Assymmetric Kernel - Metropolis Hastings

Using a Beta-Binomial likelihood, a Gamma prior and an assymmetric log-Normal jumping kernel.

Modeling Mosquito Death Rate

Using a Poisson Likelihood, a Gamma prior, a Beta Prior, a log-Normal jumping kernel and a beta jumping kernel.

Chapter 14 - Gibbs Sampling

The report can be found: HERE

The sensitivity and specificity of a test for a disease - Gibbs Sampling

Coal mining disasters in the UK - Gibbs Sampling

Using Gibbs sampling to estimate the point in time when legislative and societal changes caused a reduction in coal mining disasters in the UK. The number of disasters per year pre and post legislations were modeled using Poisson Likelihoods: Possion(lambda_1), Possion(lambda_2) with Gamma priors. The point in time when the new legislations were enacted is called n.

Chapter 15 - Hamiltonian Monte Carlo

Chapter 16 - Stan

Hierarchical models and regression

Chapter 17 - Hierarchical models

Chapter 18 - Linear regression models

Chapter 19 - Generalized linear models and other animals