A vanilla Rao–Blackwellisation of Metropolis-Hastings algorithms

Directional Metropolis–Hastings algorithms on hyperplanes

In this paper we define and study new directional Metropolis–Hastings algorithms that propose states in hyperplanes. Each iteration in directional Metropolis–Hastings algorithms consist of three steps. First a direction is sampled by an auxiliary variable. Then a potential new state is proposed in the subspace defined by this direction and the current state. Lastly, the potential new state is a...

On directional Metropolis-Hastings algorithms

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...

On Metropolis-Hastings algorithms with delayed rejection

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...

Convergence of Conditional Metropolis-Hastings Samplers, with an Application to Inference for Discretely-Observed Diffusions

We consider Markov chain Monte Carlo algorithms which combine Gibbs updates with Metropolis-Hastings updates, resulting in a conditional Metropolis-Hastings sampler. We develop conditions under which this sampler will be geometrically or uniformly ergodic. We apply our results to an algorithm for drawing Bayesian inferences about the entire sample path of a diffusion process, based only upon di...