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Monte Carlo (MC) sampling methods are widely applied in Bayesian inference, system simulation and optimization problems. The Markov Chain Monte Carlo (MCMC) algorithms are a well-known class of MC methods which generate a Markov chain with…
Markov chain Monte Carlo (MCMC) is widely used for Bayesian inference in models of complex systems. Performance, however, is often unsatisfactory in models with many latent variables due to so-called poor mixing, necessitating development…
Many problems of practical interest rely on Continuous-time Markov chains~(CTMCs) defined over combinatorial state spaces, rendering the computation of transition probabilities, and hence probabilistic inference, difficult or impossible…
Due to the escalating growth of big data sets in recent years, new Bayesian Markov chain Monte Carlo (MCMC) parallel computing methods have been developed. These methods partition large data sets by observations into subsets. However, for…
The Markov chain Monte Carlo method (MCMC), especially the Metropolis-Hastings (MH) algorithm, is a widely used technique for sampling from a target probability distribution $P$ on a state space $\Omega$ and applied to various problems such…
Sequential Monte Carlo squared (SMC$^2$; Chopin et al., 2012) methods can be used to sample from the exact posterior distribution of intractable likelihood state space models. These methods are the SMC analogue to particle Markov chain…
Markov chain Monte Carlo (MCMC) provides a feasible method for inferring Hidden Markov models, however, it is often computationally prohibitive, especially constrained by the curse of dimensionality, as the Monte Carlo sampler traverses…
Particle MCMC is a class of algorithms that can be used to analyse state-space models. They use MCMC moves to update the parameters of the models, and particle filters to propose values for the path of the state-space model. Currently the…
Particle MCMC involves using a particle filter within an MCMC algorithm. For inference of a model which involves an unobserved stochastic process, the standard implementation uses the particle filter to propose new values for the stochastic…
Markov chain Monte Carlo (MCMC) is a powerful methodology for the approximation of posterior distributions. However, the iterative nature of MCMC does not naturally facilitate its use with modern highly parallel computation on HPC and cloud…
Probabilistic modeling provides the capability to represent and manipulate uncertainty in data, models, predictions and decisions. We are concerned with the problem of learning probabilistic models of dynamical systems from measured data.…
As it has become common to use many computer cores in routine applications, finding good ways to parallelize popular algorithms has become increasingly important. In this paper, we present a parallelization scheme for Markov chain Monte…
Monte Carlo methods, such as Markov chain Monte Carlo (MCMC), remain the most regularly-used approach for implementing Bayesian inference. However, the computational cost of these approaches usually scales worse than linearly with the…
Monte Carlo (MC) methods are widely used for Bayesian inference and optimization in statistics, signal processing and machine learning. A well-known class of MC methods are Markov Chain Monte Carlo (MCMC) algorithms. In order to foster…
High-dimensional state trajectories of state-space models pose challenges for Bayesian inference. Particle Gibbs (PG) methods have been widely used to sample from the posterior of a state space model. Basically, particle Gibbs is a Particle…
We elaborate the idea behind Markov chain Monte Carlo (MCMC) methods in a mathematically coherent, yet simple and understandable way. To this end, we proof a pivotal convergence theorem for finite Markov chains and a minimal version of the…
Variable selection is a key issue when analyzing high-dimensional data. The explosion of data with large sample sizes and dimensionality brings new challenges to this problem in both inference accuracy and computational complexity. To…
Nonlinear non-Gaussian state-space models are ubiquitous in statistics, econometrics, information engineering and signal processing. Particle methods, also known as Sequential Monte Carlo (SMC) methods, provide reliable numerical…
We develop a novel advanced Particle Markov chain Monte Carlo algorithm that is capable of sampling from the posterior distribution of non-linear state space models for both the unobserved latent states and the unknown model parameters. We…
We propose sequential Monte Carlo (SMC) methods for sampling the posterior distribution of state-space models under highly informative observation regimes, a situation in which standard SMC methods can perform poorly. A special case is…