Predictive Inference Based on Markov Chain Monte Carlo Output

Markov Chain Monte Carlo for Statistical Inference

Markov chain Monte Carlo for Bayesian inference

The chord length transform (CLT) is a useful tool to analyze fibre structures. Assuming e.g. arandom process of straight fibres then a realization of such a process can be observed in a binaryimage. The CLT maps to each point in the foreground of a binary image and to each direction thelength of the related chord, where the chord is the connecting part of a line in the direction...

Markov Chain Monte Carlo

Markov chain Monte Carlo is an umbrella term for algorithms that use Markov chains to sample from a given probability distribution. This paper is a brief examination of Markov chain Monte Carlo and its usage. We begin by discussing Markov chains and the ergodicity, convergence, and reversibility thereof before proceeding to a short overview of Markov chain Monte Carlo and the use of mixing time...

Markov Chain Monte Carlo

This paper gives a brief introduction to Markov Chain Monte Carlo methods, which offer a general framework for calculating difficult integrals. We start with the basic theory of Markov chains and build up to a theorem that characterizes convergent chains. We then discuss the MetropolisHastings algorithm.

Markov chain Monte Carlo

One of the simplest and most powerful practical uses of the ergodic theory of Markov chains is in Markov chain Monte Carlo (MCMC). Suppose we wish to simulate from a probability density π (which will be called the target density) but that direct simulation is either impossible or practically infeasible (possibly due to the high dimensionality of π). This generic problem occurs in diverse scient...