Method: A verbal autopsy questionnaire was used to interview close relatives of women within the reproductive age group who had died of pregnancy-related complications in the Sokoto metropolis during the preceding two years. A multistage sampling method using simple random sampling at each step was used to select areas of study within the Sokoto metropolis. Data analysis was carried out using a...

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...

The velocity of multimodal information shared on web has increased significantly. Many reranking approaches try to improve the performance of multimodal retrieval, however not in the direction of true relevancy of a multimodal object. Metropolis-Hastings (MH) is a method based on Monte Carlo Markov Chain (MCMC) for sampling from a distribution when traditional sampling methods such as transform...

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...

The Metropolis-Hastings algorithm is a method of constructing a reversible Markov transition kernel with a speci ed invariant distribution. This note describes necessary and su cient conditions on the candidate generation kernel and the acceptance probability function for the resulting transition kernel and invariant distribution to satisfy the detailed balance conditions. A simple general form...

We construct a rejection-free Monte Carlo algorithm for a system with continuous degrees of freedom. We illustrate the algorithm by applying it to the classical three-dimensional Heisenberg model with canonical Metropolis dynamics. We obtain the lifetime of the metastable state following a reversal of the external magnetic field. Our rejection-free algorithm obtains results in agreement with a ...

The Markov processes deened by random and loop-based schemes for single spin ip attempts in Monte Carlo simulations of the 2D Ising model are investigated, by explicitly constructing their transition matrices. Their analysis reveals that loops over all lattice sites using a Metropolis-type single spin ip probability often do not deene ergodic Markov chains, and have distorted dynamical properti...

We connect known results about diffusion limits of Markov chain Monte Carlo (MCMC) algorithms to the computer science notion of algorithm complexity. Ourmain result states that any weak limit of a Markov process implies a corresponding complexity bound (in an appropriate metric). We then combine this result with previously-known MCMC diffusion limit results to prove that under appropriate assum...

We consider the optimal scaling problem for proposal distributions in Hastings-Metropolis algorithms derived from Langevin diffusions. We prove an asymptotic diffusion limit theorem and show that the relative efficiency of the algorithm can be characterised by its overall acceptance rate, independently of the target distribution. The asymptotically optimal acceptance rate is 0.574. We show that...

We propose an adaptive independent Metropolis–Hastings algorithm with the ability to learn from all previous proposals in the chain except the current location. It is an extension of the independent Metropolis–Hastings algorithm. Convergence is proved provided a strong Doeblin condition is satisfied, which essentially requires that all the proposal functions have uniformly heavier tails than th...