In this paper, we study a special case of the Metropolis algorithm, the Independence Metropolis Sampler (IMS), in the finite state space case. The IMS is often used in designing components of more complex Markov Chain Monte Carlo algorithms. We present new results related to the first hitting time of individual states for the IMS. These results are expressed mostly in terms of the eigenvalues o...

This study compared several parameter estimation methods for multi-unidimensional graded response models using their corresponding statistical software programs and packages. Specifically, we compared two marginal maximum likelihood (MML) approaches (Bock-Aitkin expectation-maximum algorithm, adaptive quadrature approach), four fully Bayesian algorithms (Gibbs sampling, Metropolis-Hastings, Has...

We propose a new Metropolis-Hastings algorithm for sampling from smooth, unimodal distributions; a restriction to the method is that the target be optimizable. The method can be viewed as a mixture of two types of MCMC algorithm; specifically, we seek to combine the versatility of the random walk Metropolis and the efficiency of the independence sampler as found with various types of target dis...

We present a generalisation of the standard well known and widely used Metropolis-Hastings algorithm which, unlike the Metropolis-Hastings sampler, can mix well over a target distribution which has separated and possibly narrow modes. The idea arose via a consideration of a space augmented slice sampler where the uniform space required to be sampled for the slice sampler, say I , is augmented w...

The Monte Carlo procedure of MetropOliS et al. 1,2 is widely used to determine the equilibrium structural and ther:modynamic properties of gases, liquids, solids, and mesophases. In a previous paper we introduced a modification of the usual Metropolis procedure that gives more rapid convergence and thereby much more efficient Monte Carlo runs. In this new procedure each particle move is chosen ...

The Metropolis algorithm is simulated annealing with a fixed temperature. Surprisingly enough, many problems cannot be solved more efficiently by simulated annealing than by the Metropolis algorithm with the best temperature. The problem of finding a natural example (artificial examples are known) where simulated annealing outperforms the Metropolis algorithm for all temperatures has been discu...

Recently developed adaptive Markov chain Monte Carlo (MCMC) methods have been applied successfully to many problems in Bayesian statistics. Grapham is a new open source implementation covering several such methods, with emphasis on graphical models for directed acyclic graphs. The implemented algorithms include the seminal Adaptive Metropolis algorithm adjusting the proposal covariance accordin...

Metropolis–Hastings algorithms are used to simulate Markov chains with limiting distribution equal to a specified target distribution. The current paper studies target densities on R. In directional Metropolis–Hastings algorithms each iteration consists of three steps i) generate a line by sampling an auxiliary variable, ii) propose a new state along the line, and iii) accept/reject according t...