Bayesian fundamentals

Introduction

The GAUSS platform is a natural environment for conducting Bayesian computation. GAUSS's optimizing compiler, efficient internal code, and easy to use threading capabilities allow it to effortlessly tackle the heavy lifting that Bayesian techniques can require. In addition, the GAUSS matrix language makes transforming textbook ideas and techniques straight forward.

In this series of tutorials, we will examine some of the most important methods of Bayesian simulation -- Monte Carlo integration, importance sampling, Gibbs sampling, and the Metropolis-Hastings algorithm. These tutorials are meant to provide background into conducting Bayesian computations in GAUSS. As such, we will attempt to demonstrate a number of features and tools in GAUSS. At times the tutorials may sacrifice computation efficiency in order to demonstrate GAUSS tools. These are not meant to teach Bayesian computation, they assume that users are familiar with Bayesian theory and technique. In addition, these tutorials assume a basic knowledge of GAUSS.

Throughout these tutorials, we will consistently use the general notation that $p(\theta^{(r)}|y)$ is the posterior distribution of the parameters of a model $\theta$.

Bayesian fundamentals

  1. Monte Carlo integration
  2. Importance sampling
  3. Gibbs sampling from a bivariate normal distribution
  4. Metropolis-Hastings sampler

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