The Metropolis-Hastings algorithm has been important in the recent development of Bayes methods. This algorithm generates random draws from a target distribution utilizing a sampling (or proposal) distribution. This article compares the properties of three sampling distributions—the independence chain, the random walk chain, and the Taylored chain suggested by Geweke and Tanizaki (Geweke, J., T...

Importance sampling and Metropolis-Hastings sampling (of which Gibbs sampling is a special case) are two methods commonly used to sample multi-variate probability distributions (that is, Bayesian networks). Heretofore, the sampling of Bayesian networks has been done on a conventional “classical computer”. In this paper, we propose methods for doing importance sampling and Metropolis-Hastings sa...

Presented here are the results of a Metropolis–Hastings Markov chain Monte Carlo routine applied to the problem of determining parameters for coalescing binary systems observed with laser interferometric detectors. The Metropolis– Hastings routine is described in detail, and examples show that signals may be detected and analysed from within noisy data. Using the Bayesian framework of statistic...

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...

2. The Metropolis-Hastings Algorithm. Metropolis’ idea is to start with a Markov chain Xn on the state space X with a fairly arbitrary Markov transition density q(x, y)dy and then modify it to define a Markov chain X∗ n that has π(x) as a stationary measure. By definition, q(x, y) is a Markov transition density if q(x, y) ≥ 0 and ∫ y∈X q(x, y)dy = 1. If the transformed random walk X ∗ n is irre...

We consider the previously unsolved problem of sampling cycle-free paths according to a given distribution from a general network. The problem is difficult because of the combinatorial number of alternatives, which prohibits a complete enumeration of all paths and hence also forbids to compute the normalizing constant of the sampling distribution. The problem is important because the ability to...

Particle Metropolis-Hastings enables Bayesian parameter inference in general nonlinear state space models (SSMs). However, in many implementations a random walk proposal is used and this can result in poor mixing if not tuned correctly using tedious pilot runs. Therefore, we consider a new proposal inspired by quasi-Newton algorithms that may achieve better mixing with less tuning. An advantage...

1 Basic Concepts 2 1.1 Terminology and Definitions . . . . . . . . . . . . . . . . . . . . . 2 1.2 Hardy-Weinberg Equilibrium . . . . . . . . . . . . . . . . . . . . 2 1.3 Gametic Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.4 Crossingover and Recombination . . . . . . . . . . . . . . . . . . 3 1.5 Interference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1...