There is much interest in the Hierarchical Dirichlet Process Hidden Markov Model (HDP-HMM) as a natural Bayesian nonparametric extension of the traditional HMM. However, in many settings the HDP-HMM’s strict Markovian constraints are undesirable, particularly if we wish to learn or encode non-geometric state durations. We can extend the HDP-HMM to capture such structure by drawing upon explicit...

The ability of the servers to deliver services to the clients according to pre-defined agreements is becoming an important requirement. These pre-defined agreements are sometimes referred to as service level agreements (SLA). In most practical cases, these agreements are based on the response times observed by the customer. This service level ‘agreeability’ is not captured in the definitions of...

We explore the rating system used by credit agencies with a focus on problems that justify the use of fuzzy set theory. We prove that a fuzzy market is viable if and only if an equivalent martingale measure exists, from which we construct the forward probability measure and under which the discounted price of a default-free bond is a martingale. We model the evolution of credit migration of a d...

The correlation between events is ubiquitous and important for temporal events modelling. In many cases, the correlation exists between not only events’ emitted observations, but also their arrival times. State space models (e.g., hidden Markov model) and stochastic interaction point process models (e.g., Hawkes process) have been studied extensively yet separately for the two types of correlat...

There is much interest in the Hierarchical Dirichlet Process Hidden Markov Model (HDP-HMM) as a natural Bayesian nonparametric extension of the traditional HMM. However, in many settings the HDP-HMM’s strict Markovian constraints are undesirable, particularly if we wish to learn or encode non-geometric state durations. We can extend the HDP-HMM to capture such structure by drawing upon explicit...

In this paper, a novel monitoring method for the repetitive batch operation with two-dimensional dynamic behavior is proposed. It combines dynamic multiway principal component analysis (DMPCA) and hidden segmental semi-Markov models (HSMM) to resolve the problem caused by the two-dimensional behavior of batch processes. DMPCA utilizes the batch-to-batch dynamic characteristics and eliminates th...

The semi-Markov decision model is a powerful tool in analyzing sequential decision processes with random decision epochs. In this paper, we have built the semi-Markov decision process (SMDP) for the maintenance policy optimization of condition-based preventive maintenance problems, and have presented the approach for joint optimization of inspection rate and maintenance policy. Through numerica...

We consider a semi-Markov additive process A(·), i.e., a Markov additive process for which the sojourn times in the various states have general (rather than exponential) distributions. Letting the Lévy processesXi(·), which describe the evolution ofA(·) while the background process is in state i, be increasing, it is shown how double transforms of the type ∫∞ 0 e −qt E[e−αA(t)]dt can be compute...

Continuous-time state transition models may end up having large unwieldy structures when trying to represent all relevant stages of clinical disease processes by means of a standard Markov model. In such situations, a more parsimonious, and therefore easier-to-grasp, model of a patient's disease progression can often be obtained by assuming that the future state transitions do not depend only o...