A comparison of Rejection Sampling and Metropolis - Hastingsalgorithm
نویسنده
چکیده
When doing stochastic modeling one often face the problem of sampling from a posterior pdf on the form const l p where the normalizing constant is unknown The corresponding likelihood function l tends to be complicated and computational expensive while the prior p tends to be simpler This work origin from stochastic reservoir charac terization and history matching where calculation of the likelihood function requires a uid ow simulation which may take hours or even days on a fast computer The prior may also have a complicated form but a sample from the prior is usually relatively fast obtained Analytical forms for the posterior are usually available only in simple cases The Metropolis Hastings algorithm is widely used to sample posterior pdfs where the normalizing constant is unknown It is a class of Markov chain Monte Carlo algorithm de ned by Hastings The Metropolis Hastings algorithm is iterative and hence time consuming and it is di cult to diagnose convergence Moreover the realizations from the Markov chain are usually highly dependent The Rejection Sampling algorithm could also be used see Ripley This algorithm gives independent samples from but requires the normalizing constant or an upper bound for it to be known which may be impossible in practice Independent samples could however be convenient when estimating various quantities from the same sample from the posterior pdf
منابع مشابه
Markov Chain Monte Carlo methods: Implementation and comparison
The paper and presentation will focus on MCMC methods, implemented together in MC2Pack, an ox package which allows you to run a range of sampling algorithm (MH, Gibbs, Griddy Gibbs, Adaptive Polar Importance Sampling, Adaptive Polar Sampling, and Adaptive Rejection Metropolis Sampling) on a given posterior. Computation of the marginal likelihood for the model is also done automatically, allowin...
متن کاملMonte Carlo Integration With Acceptance-Rejection
This article considers Monte Carlo integration under rejection sampling or Metropolis-Hastings sampling. Each algorithm involves accepting or rejecting observations from proposal distributions other than a target distribution. While taking a likelihood approach, we basically treat the sampling scheme as a random design, and define a stratified estimator of the baseline measure. We establish tha...
متن کاملScaling analysis of delayed rejection MCMC methods
In this paper, we study the asymptotic efficiency of the delayed rejection strategy. In particular, the efficiency of the delayed rejection Metropolis-Hastings algorithm is compared to that of the regular Metropolis algorithm. To allow for a fair comparison, the study is carried under optimal mixing conditions for each of these algorithms. After introducing optimal scaling results for the delay...
متن کاملExploring an Adaptive Metropolis Algorithm
While adaptive methods for MCMC are under active development, their utility has been under-recognized. We briefly review some theoretical results relevant to adaptive MCMC. We then suggest a very simple and effective algorithm to adapt proposal densities for random walk Metropolis and Metropolis adjusted Langevin algorithms. The benefits of this algorithm are immediate, and we demonstrate its p...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1997