A Geometric Interpretation of the Metropolis–Hastings Algorithm

نویسنده

  • Louis J. Billera
چکیده

The Metropolis-Hastings algorithm transforms a given stochastic matrix into a reversible stochastic matrix with a prescribed stationary distribution. We show that this transformation gives the minimum distance solution in an L1 metric.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Approximating Bayes Estimates by Means of the Tierney Kadane, Importance Sampling and Metropolis-Hastings within Gibbs Methods in the Poisson-Exponential Distribution: A Comparative Study

Here, we work on the problem of point estimation of the parameters of the Poisson-exponential distribution through the Bayesian and maximum likelihood methods based on complete samples. The point Bayes estimates under the symmetric squared error loss (SEL) function are approximated using three methods, namely the Tierney Kadane approximation method, the importance sampling method and the Metrop...

متن کامل

Geometric Convergence of the Metropolis Hastings Simulation Algorithm Lars Holden Norwegian Computing Center and University of Oslo

Necessary and su cient conditions for geometric con vergence in the relative supremum norm of the Metropolis Hastings simulation algorithm with a general generating function are estab lished An explicit expression for the convergence rate is given Introduction This paper discusses the convergence rate for the Metropolis Hastings simulation algorithm proposed in Hastings The Metropolis Hastings ...

متن کامل

On the Geometric Ergodicity of Metropolis-Hastings Algorithms

Abstract Under a compactness assumption, we show that a φ-irreducible and aperiodic MetropolisHastings chain is geometrically ergodic if and only if its rejection probability is bounded away from unity. In the particular case of the Independence Metropolis-Hastings algorithm, we obtain that the whole spectrum of the induced operator is contained in (and in many cases equal to) the essential ran...

متن کامل

Variance Bounding Markov Chains by Gareth

We introduce a new property of Markov chains, called variance bounding. We prove that, for reversible chains at least, variance bounding is weaker than, but closely related to, geometric ergodicity. Furthermore, variance bounding is equivalent to the existence of usual central limit theorems for all L functionals. Also, variance bounding (unlike geometric ergodicity) is preserved under the Pesk...

متن کامل

Geometric analysis for the metropolis algorithm on Lipschitz domains

This paper gives geometric tools: comparison, Nash and Sobolev inequalities for pieces of the relevent Markov operators, that give useful bounds on rates of convergence for the Metropolis algorithm. As an example, we treat the random placement of N hard discs in the unit square, the original application of the Metropolis algorithm.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2002