Metropolis-Hastings Monte-Carlo method

In 1998. Andrec and Prestegard- measured the coupling constants in antiphase patterns. They introduced a variant using a Metropolis-Hasting Monte Carlo method. Application to the measurement of coupling constants smaller than linewidth is shown to be applicable to simulations and experimental data stemming from INADEQUATE experiments. 

The most commonly used Monte Carlo method with Markov Chain algorithms are the Metropolis-Hastings, here employed, and the Gibbs sampler [28, 29]. 

One approach to providing ergodicity to deterministic systems is to introduce random fluctuations via a Monte-Carlo technique [268]. Several Monte-Carlo methods are described in Appendix C. Randomized steps are taken and then an accept-reject mechanism is introduced in order to ensure that the steps are consistent with the canonical distribution. It is possible to combine the Metropolis-Hastings concept with timestepping procedures in a variety of ways, which are often subsumed under the title Monte-Carlo Markov Chain methods , these include... 

The variational quantum Monte Carlo method (VMC) is both simpler and more efficient than the DMC method, but also usually less accurate. In this method the Rayleigh-Ritz quotient for a trial function 0 is evaluated with Monte Carlo integration. The Metropolis-Hastings algorithm " is used to sample the distribution... 

Thus, we take advantage of the accuracy, robustness and efficiency of the direct problem solution, to tackle the associated inverse heat transfer problem analysis [26, 27] towards the simultaneous estimation of momentum and thermal accommodation coefficients in micro-channel flows with velocity slip and temperature jump. A Bayesian inference approach is adopted in the solution of the identification problem, based on the Monte Carlo Markov Chain method (MCMC) and the Metropolis-Hastings algorithm [28-30]. Only simulated temperature measurements at the external faces of the channel walls, obtained for instance via infrared thermography [30], are used in the inverse analysis in order to demonstrate the capabilities of the proposed approach. A sensitivity analysis allows for the inspection of the identification problem behavior when the external wall Biot number is also included among the parameters to be estimated. 

Bayesian statistical theory had been published, imtil 80 in twenty century Bayesian statistical theory has been in theory research phase, integral calculation is a big barrier in his development and application. However, Markov Chain Monte Carlo (MCMC) has been used to Bayesian statistical inference in recently, a main characteristic of this method is Metropolis-Hastings updating and Gibbs sampling, it can solve well the problem of numerical integration and sampling in multi dimensional distribution, which is convenient for posterior inference of parameters and accelerate the application of Bayesian theory. 

Another simulation approach often used that does not offer a simple deterministic time evolution of the system is the Metropolis Monte Carlo [MMC] method. Based on the Metropolis-Hasting algorithm [3, 4], MMC methods are weighted sampling techniques in which particles are randomly moved about to obtain a statistical ensemble of atoms with a particular probability distribution for some quantity. This is usually the energy but can also be other quantities such as experimental inputs that can be quickly calculated from an atomic... 

This review article is divided into two major sections, the first of which details the theoretical basis of RQMC (Sect. 18.2). Initially we describe quantum Monte Carlo sampling from the pure distribution and mixed distribution F, showing that the RQMC approach to sample from the pure distribution rests on Metropolis-Hastings (MH [25,26]) sampling, as does the variational path integral (VPI [27]) method. As already mentioned, RQMC proposes reptafion-type moves while... 

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