Fast MCMC sampling for Markov jump processes and continuous time Bayesian networks
نویسندگان
چکیده
Markov jump processes and continuous time Bayesian networks are important classes of continuous time dynamical systems. In this paper, we tackle the problem of inferring unobserved paths in these models by introducing a fast auxiliary variable Gibbs sampler. Our approach is based on the idea of uniformization, and sets up a Markov chain over paths by sampling a finite set of virtual jump times and then running a standard hidden Markov model forward filteringbackward sampling algorithm over states at the set of extant and virtual jump times. We demonstrate significant computational benefits over a state-of-the-art Gibbs sampler on a number of continuous time Bayesian networks.
منابع مشابه
Fast MCMC sampling for Markov jump processes and extensions
Markov jump processes (or continuous-time Markov chains) are a simple and important class of continuous-time dynamical systems. In this paper, we tackle the problem of simulating from the posterior distribution over paths in these models, given partial and noisy observations. Our approach is an auxiliary variable Gibbs sampler, and is based on the idea of uniformization. This sets up a Markov c...
متن کاملMarkov chain Monte Carlo for continuous-time discrete-state systems
A variety of phenomena are best described using dynamical models which operate on a discrete state space and in continuous time. Examples include Markov (and semiMarkov) jump processes, continuous-time Bayesian networks, renewal processes and other point processes. These continuous-time, discrete-state models are ideal building blocks for Bayesian models in fields such as systems biology, genet...
متن کاملSequential Mcmc for Bayesian Model Selection
In this paper, we address the problem of sequential Bayesian model selection. This problem does not usually admit any closed-form analytical solution. We propose here an original sequential simulation-based method to solve the associated Bayesian computational problems. This method combines sequential importance sampling, a resampling procedure and reversible jump MCMC moves. We describe a gene...
متن کاملReasoning with Uncertainties Over Existence Of Objects
In this paper we consider planning problems in relational Markov processes where objects may “appear” or “disappear”, perhaps depending on previous actions or properties of other objects. For instance, problems which require to explicitly generate or discover objects fall into this category. In our formulation this requires to explicitly represent the uncertainty over the number of objects (dim...
متن کاملUnbiased Bayesian inference for population Markov jump processes via random truncations
We consider continuous time Markovian processes where populations of individual agents interact stochastically according to kinetic rules. Despite the increasing prominence of such models in fields ranging from biology to smart cities, Bayesian inference for such systems remains challenging, as these are continuous time, discrete state systems with potentially infinite state-space. Here we prop...
متن کامل