MCMC implementation for Bayesian hidden semi-Markov models with illustrative applications

Copyright © Springer 2013. The final publication is available at Springer via http://dx.doi.org/10.1007/s11222-013-9399-zHidden Markov models (HMMs) are flexible, well established models useful in a diverse range of applications. However, one potential limitation of such models lies in their inability to explicitly structure the holding times of each hidden state. Hidden semi-Markov models (HSMMs) are more useful in the latter respect as they incorporate additional temporal structure by explicit modelling of the holding times. However, HSMMs have generally received less attention in the literature, mainly due to their intensive computational requirements. Here a Bayesian implementation of HSMMs is presented. Recursive algorithms are proposed in conjunction with Metropolis-Hastings in such a way as to avoid sampling from the distribution of the hidden state sequence in the MCMC sampler. This provides a computationally tractable estimation framework for HSMMs avoiding the limitations associated with the conventional EM algorithm regarding model flexibility. Performance of the proposed implementation is demonstrated through simulation experiments as well as an illustrative application relating to recurrent failures in a network of underground water pipes where random effects are also included into the HSMM to allow for pipe heterogeneity

Two-dimensional simulation of a pulsed-power electronegative discharge

A two-dimensional self-consistent fluid model was developed to study the spatio-temporal dynamics of a pulsed power (square-wave modulated) inductively coupled electronegative (chlorine) discharge. The coupled equations for plasma power deposition, electron temperature, and charged and neutral species densities were solved simultaneously to capture the spatio-temporal evolution of the discharge. Simulation results showed separation of the plasma into an electronegative core and an electropositive edge during the active glow (power on) fraction of the cycle, and the formation of a positive ion/negative ion (ion-ion) plasma in the afterglow (power off) fraction of the cycle. During the early active glow, the negative ion flux is convection dominated near the quartz window under the planar coil of the ICP reactor. This is due to the emergence of relatively large electrostatic fields, leading to a self-sharpening negative ion front propagating into the plasma