5 research outputs found
Markov chain Monte Carlo methods for state-space models with point process observations
This letter considers how a number of modern Markov chain Monte Carlo (MCMC) methods can be applied for parameter estimation and inference in state-space models with point process observations. We quantified the efficiencies of these MCMC methods on synthetic data, and our results suggest that the Reimannian manifold Hamiltonian Monte Carlo method offers the best performance. We further compared such a method with a previously tested variational Bayes method on two experimental data sets. Results indicate similar performance on the large data sets and superior performance on small ones. The work offers an extensive suite of MCMC algorithms evaluated on an important class of models for physiological signal analysis
Markov chain monte carlo methods for state-space models with point process observations
This letter considershow a number of modernMarkov chain MonteCarlo (MCMC) methods can be applied for parameter estimation and inference in state-space models with point process observations.We quantified the efficiencies of these MCMC methods on synthetic data, and our results suggest that the Reimannian manifold Hamiltonian Monte Carlo method offers the best performance. We further compared such a method with a previously tested variational Bayes method on two experimental data sets. Results indicate similar performance on the large data sets and superior performance on small ones. The work offers an extensive suite of MCMC algorithms evaluated on an important class of models for physiological signal analysis. © 2012 Massachusetts Institute of Technology
Sparse Approximate Inference for Spatio-Temporal Point Process Models
Spatio-temporal point process models play a central role in the analysis of
spatially distributed systems in several disciplines. Yet, scalable inference
remains computa- tionally challenging both due to the high resolution modelling
generally required and the analytically intractable likelihood function. Here,
we exploit the sparsity structure typical of (spatially) discretised
log-Gaussian Cox process models by using approximate message-passing
algorithms. The proposed algorithms scale well with the state dimension and the
length of the temporal horizon with moderate loss in distributional accuracy.
They hence provide a flexible and faster alternative to both non-linear
filtering-smoothing type algorithms and to approaches that implement the
Laplace method or expectation propagation on (block) sparse latent Gaussian
models. We infer the parameters of the latent Gaussian model using a structured
variational Bayes approach. We demonstrate the proposed framework on simulation
studies with both Gaussian and point-process observations and use it to
reconstruct the conflict intensity and dynamics in Afghanistan from the
WikiLeaks Afghan War Diary