MCMC Algorithms for Posteriors on Matrix Spaces

MCMC algorithms for Subset Simulation

Subset Simulation is an adaptive simulation method that efficiently solves structural reliability problems with many random variables. The method requires sampling from conditional distributions, which is achieved through Markov Chain Monte Carlo (MCMC) algorithms. This paper discusses different MCMC algorithms proposed for Subset Simulation and introduces a novel approach for MCMC sampling in ...

MCMC With Disconnected State Spaces

Bayes Nets simplify probabilistic models, making it easy to work with these models. Unfortunately, sometimes people devise models that are too complicated to allow calculation of exact probabilities, so they instead use approximate inference, such as Markov Chain Monte Carlo (MCMC). However, MCMC can fail if the Bayes Net has zero-probability states that “disconnect” the state space. In this pa...

Nonasymptotic bounds on the estimation error for regenerative MCMC algorithms∗

MCMC methods are used in Bayesian statistics not only to sample from posterior distributions but also to estimate expectations. Underlying functions are most often defined on a continuous state space and can be unbounded. We consider a regenerative setting and Monte Carlo estimators based on i.i.d. blocks of a Markov chain trajectory. The main result is an inequality for the mean square error. ...

MCMC algorithms for constrained variance matrices

In this paper we consider the problem of nding a generic algorithm for applying Markov chain Monte Carlo MCMC estimation procedures to statistical models that include variance matrices with additional parameter constraints We consider separately the case of additional constraints across variance matrices and review existing work on the case of additional parameter constraints within a variance ...

MCMC algorithms for fitting Bayesian models