Online hidden Markov model parameter estimation and minimax robust quickest change detection in uncertain stochastic processes

Stochastic (or random) processes are inherent to numerous fields of human endeavour including engineering, science, and business and finance. This thesis presents multiple novel methods for quickly detecting and estimating uncertainties in several important classes of stochastic processes. The significance of these novel methods is demonstrated by employing them to detect aircraft manoeuvres in video signals in the important application of autonomous mid-air collision avoidance.

A hidden Markov model approach for determining vessel activity from vessel monitoring system data.

Many fisheries worldwide have adopted vessel monitoring systems (VMS) for compliance purposes. An added benefit of these systems is that they collect a large amount of data on vessel locations at very fine spatial and temporal scales. This data can provide a wealth of information for stock assessment, research, and management. However, since most VMS implementations record vessel location at set time intervals with no regard to vessel activity, some methodology is required to determine which data records correspond to fishing activity. This paper describes a probabilistic approach, based on hidden Markov models (HMMs), to determine vessel activity. A HMM provides a natural framework for the problem and, by definition, models the intrinsic temporal correlation of the data. The paper describes the general approach that was developed and presents an example of this approach applied to the Queensland trawl fishery off the coast of eastern Australia. Finally, a simulation experiment is presented that compares the misallocation rates of the HMM approach with other approaches.

Using the hidden Markov model to capture quality of care in Lombardy geriatric wards

Quality of care is an important aspect of healthcare monitoring, which is used to ensure that the healthcare system is delivering care of the highest standard. With populations growing older there is an increased urgency in making sure that the healthcare delivered is of the highest standard. Healthcare providers are under increased pressure to ensure that this is the case with public and government demand expecting a healthcare system of the highest quality. Modelling quality of care is difficult to measure due to the many ways of defining it. This paper introduces a potential model which could be used to take quality of care into account when modelling length of stay. The Coxian phase-type distribution is used to model length of stay and the associated quality of care incorporated into the Coxian using a Hidden Markov model. Covariates are also introduced to determine their impact on the hidden level to find out what potentially can affect quality of care. This model is applied to geriatic patient data from the Lombardy region of Italy. The results obtained highlighted that bed numbers and the type of hospital (public or private) can have an effect on the quality of care delivered.