Search Results (6)

The phase-type aging model (PTAM) belongs to a class of Coxian-type Markovian models that can provide a quantitative description of well-known aging characteristics that are part of a genetically determined, progressive, and irreversible process. Due to its unique parameter structure, estimation via the MLE method presents a considerable estimability issue, whereby profile likelihood functions are flat and analytically intractable. In this study, a Markov chain Monte Carlo (MCMC)-based Bayesian methodology is proposed and applied to the PTAM, with a view to improving parameter estimability. The proposed method provides two methodological extensions based on an existing MCMC inference method. First, we propose a two-level MCMC sampling scheme that makes the method applicable to situations where the posterior distributions do not assume simple forms after data augmentation. Secondly, an existing data augmentation technique for Bayesian inference on continuous phase-type distributions is further developed in order to incorporate left-truncated data. While numerical results indicate that the proposed methodology improves parameter estimability via sound prior distributions, this approach may also be utilized as a stand-alone statistical model-fitting technique. Full article

The phase-type aging model (PTAM) is a class of Coxian-type Markovian models that can provide a quantitative description of the effects of various aging characteristics. Owing to the unique structure of the PTAM, parametric inference on the model is affected by a significant estimability issue, its profile likelihood functions being flat. While existing methods for assessing distributional non-estimability require the subjective specification of thresholds, this paper objectively quantifies estimability in the context of general statistical models. More specifically, this is achieved via a carefully designed cumulative distribution function sensitivity measure, under which the threshold is tailored to the empirical cumulative distribution function, thus becoming an experiment-based quantity. The proposed definition, which is validated to be innately sound, is then employed to determine and enhance the estimability of the PTAM. Full article

The problem of hospital patients’ delayed discharge or ‘bed blocking’ has long been a challenge for healthcare managers and policymakers. It negatively affects the hospital performance metrics and has other severe consequences for the healthcare system, such as affecting patients’ health. In our previous work, we proposed the phase-type survival tree (PHTST)-based analysis to cluster patients into clinically meaningful patient groups and an extension of this approach to examine the relationship between the length of stay in hospitals and the destination on discharge. This paper describes how PHTST-based clustering can be used for modelling delayed discharge and its effects in a stroke care unit, especially the extra beds required, additional cost, and bed blocking. The PHTST length of stay distribution of each group of patients (each PHTST node) is modelled separately as a finite state continuous-time Markov chain using Coxian-phase-type distributions. Delayed discharge patients waiting for discharge are modelled as the Markov chain, called the ‘blocking state’ in a special state. We can use the model to recognise the association between demographic factors and discharge delays and their effects and identify groups of patients who require attention to resolve the most common delays and prevent them from happening again. The approach is illustrated using five years of retrospective data of patients admitted to the Belfast City Hospital with a stroke diagnosis. Full article

The model discussed in this paper provides an efficient mechanism for the selection and allocation of available limited spectra for transmission of heterogeneous data in a network. The data packets (customers), belonging to different classes, arrive according to a batch marked the Markovian arrival process (BMMAP). The inventory considered is of multi-type (different types of channels becoming available) and are generated according to a marked Markovian arrival process (MMAP). The number of distinct types of inventory and that of the customers are the same. Arriving customers are allowed to wait in finite buffers of each category which are reserved for distinct classes of customers except for the most general class, which is provided with an infinite waiting space. The number of servers also equals the number of distinct types of inventory. When items of a particular type arrive in the inventory, the service starts, providing the buffer of customers of the corresponding class is non-empty. The service can be viewed as a selection process with Coxian distributed service times. The system is analyzed using the matrix analytic method and performance measures are obtained. The model is illustrated with suitable numerical examples. Full article

This paper examines the impact of the parameters of the distribution of the time at which a bank’s client defaults on their obligated payments, on the Lundberg adjustment coefficient, the upper and lower bounds of the ruin probability. We study the corresponding ruin probability on the assumption of (i) a phase-type distribution for the time at which default occurs and (ii) an embedding of the stochastic cash flow or the reserves of the bank to the Sparre Andersen model. The exact analytical expression for the ruin probability is not tractable under these assumptions, so Cramér Lundberg bounds types are obtained for the ruin probabilities with concomitant explicit equations for the calculation of the adjustment coefficient. To add some numerical flavour to our results, we provide some numerical illustrations. Full article

Phase-type (PH) distributions are defined as distributions of lifetimes of finite continuous-time Markov processes. Their traditional applications are in queueing, insurance risk, and reliability, but more recently, also in finance and, though to a lesser extent, to life and health insurance. The advantage is that PH distributions form a dense class and that problems having explicit solutions for exponential distributions typically become computationally tractable under PH assumptions. In the first part of this paper, fitting of PH distributions to human lifetimes is considered. The class of generalized Coxian distributions is given special attention. In part, some new software is developed. In the second part, pricing of life insurance products such as guaranteed minimum death benefit and high-water benefit is treated for the case where the lifetime distribution is approximated by a PH distribution and the underlying asset price process is described by a jump diffusion with PH jumps. The expressions are typically explicit in terms of matrix-exponentials involving two matrices closely related to the Wiener-Hopf factorization, for which recently, a Lévy process version has been developed for a PH horizon. The computational power of the method of the approach is illustrated via a number of numerical examples. Full article