Contents
Is MCMC Bayesian?
MCMC methods are generally used on Bayesian models which have subtle differences to more standard models. As most statistical courses are still taught using classical or frequentist methods we need to describe the differences before going on to consider MCMC methods.
What does intractable mean in statistics?
Intractable Problem: a problem that cannot be solved by a polynomial-time algorithm. If a distribution is in a closed-form expression, the probability of this distribution can definitely be calculated in polynomial-time, which, in the world of academia, means the distribution is tractable.
What are the recent advances in Bayesian inference?
Bayesian inference has experienced a boost in recent years due to important advances in computational statistics. This book will focus on the integrated nested Laplace approximation (INLA, Havard Rue, Martino, and Chopin 2009) for approximate Bayesian inference.
What is the purpose of INLA in Bayesian inference?
INLA is one of several recent computational breakthroughs in Bayesian statistics that allows fast and accurate model fitting. The aim of this introduction is not to provide a thorough introduction to Bayesian inference but to introduce some notation and context for the other chapters of the book.
Which is the nested Laplace approximation for Bayesian inference?
This book will focus on the integrated nested Laplace approximation (INLA, Havard Rue, Martino, and Chopin 2009) for approximate Bayesian inference. INLA is one of several recent computational breakthroughs in Bayesian statistics that allows fast and accurate model fitting.
How are MCMC methods used in Bayesian inference?
Markov chain Monte Carlo (MCMC) methods (Gilks et al. 1996; Brooks et al. 2011) are a class of computational methods to draw samples from the joint posterior distribution. These methods are based on constructing a Markov Chain with stationary distribution the posterior distribution.