Markov Chain Monte Carlo Used in Parameter Inference of Magnetic Resonance Spectra

Markov Chain Monte Carlo Used in Parameter Inference of Magnetic Resonance Spectra

In this paper, we use Boltzmann statistics and the maximum likelihood distribution derived from Bayes’ Theorem to infer parameter values for a Pake Doublet Spectrum, a lineshape of historical significance and contemporary relevance for determining distances between interacting magnetic dipoles. A Metropolis Hastings Markov Chain Monte Carlo algorithm is implemented and designed to find the opti...

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.