A fully Bayesian approach to inference for Coxian phase-type distributions with covariate dependent mean

Phase-type distributions represent the time to absorption for a finite state Markov chain in continuous time, generalising the exponential distribution and providing a flexible and useful modelling tool. We present a new reversible jump Markov chain Monte Carlo scheme for performing a fully Bayesian analysis of the popular Coxian subclass of phase-type models; the convenient Coxian representation involves fewer parameters than a more general phase-type model. The key novelty of our approach is that we model covariate dependence in the mean whilst using the Coxian phase-type model as a very general residual distribution. Such incorporation of covariates into the model has not previously been attempted in the Bayesian literature. A further novelty is that we also propose a reversible jump scheme for investigating structural changes to the model brought about by the introduction of Erlang phases. Our approach addresses more questions of inference than previous Bayesian treatments of this model and is automatic in nature. We analyse an example dataset comprising lengths of hospital stays of a sample of patients collected from two Australian hospitals to produce a model for a patient's expected length of stay which incorporates the effects of several covariates. This leads to interesting conclusions about what contributes to length of hospital stay with implications for hospital planning. We compare our results with an alternative classical analysis of these data.

Power law distributions in pattern dynamics of attacker-defender dyads in the team sport of Rugby Union : phenomena in a region of self-organized criticality?

In the region of self-organized criticality (SOC) interdependency between multi-agent system components exists and slight changes in near-neighbor interactions can break the balance of equally poised options leading to transitions in system order. In this region, frequency of events of differing magnitudes exhibits a power law distribution. The aim of this paper was to investigate whether a power law distribution characterized attacker-defender interactions in team sports. For this purpose we observed attacker and defender in a dyadic sub-phase of rugby union near the try line. Videogrammetry was used to capture players’ motion over time as player locations were digitized. Power laws were calculated for the rate of change of players’ relative position. Data revealed that three emergent patterns from dyadic system interactions (i.e., try; unsuccessful tackle; effective tackle) displayed a power law distribution. Results suggested that pattern forming dynamics dyads in rugby union exhibited SOC. It was concluded that rugby union dyads evolve in SOC regions suggesting that players’ decisions and actions are governed by local interactions rules.

Uncertainty budget in the measurement of typical airborne number, surface area and mass particle distributions

The effects of particulate matter on environment and public health have been widely studied in recent years. A number of studies in the medical field have tried to identify the specific effect on human health of particulate exposure, but agreement amongst these studies on the relative importance of the particles’ size and its origin with respect to health effects is still lacking. Nevertheless, air quality standards are moving, as the epidemiological attention, towards greater focus on the smaller particles. Current air quality standards only regulate the mass of particulate matter less than 10 μm in aerodynamic diameter (PM10) and less than 2.5 μm (PM2.5). The most reliable method used in measuring Total Suspended Particles (TSP), PM10, PM2.5 and PM1 is the gravimetric method since it directly measures PM concentration, guaranteeing an effective traceability to international standards. This technique however, neglects the possibility to correlate short term intra-day variations of atmospheric parameters that can influence ambient particle concentration and size distribution (emission strengths of particle sources, temperature, relative humidity, wind direction and speed and mixing height) as well as human activity patterns that may also vary over time periods considerably shorter than 24 hours. A continuous method to measure the number size distribution and total number concentration in the range 0.014 – 20 μm is the tandem system constituted by a Scanning Mobility Particle Sizer (SMPS) and an Aerodynamic Particle Sizer (APS). In this paper, an uncertainty budget model of the measurement of airborne particle number, surface area and mass size distributions is proposed and applied for several typical aerosol size distributions. The estimation of such an uncertainty budget presents several difficulties due to i) the complexity of the measurement chain, ii) the fact that SMPS and APS can properly guarantee the traceability to the International System of Measurements only in terms of number concentration. In fact, the surface area and mass concentration must be estimated on the basis of separately determined average density and particle morphology. Keywords: SMPS-APS tandem system, gravimetric reference method, uncertainty budget, ultrafine particles.

The efficacy of the Sortino ratio and other benchmarked performance measures under skewed return distributions

This paper will investigate the suitability of existing performance measures under the assumption of a clearly defined benchmark. A range of measures are examined including the Sortino Ratio, the Sharpe Selection ratio (SSR), the Student’s t-test and a decay rate measure. A simulation study is used to assess the power and bias of these measures based on variations in sample size and mean performance of two simulated funds. The Sortino Ratio is found to be the superior performance measure exhibiting more power and less bias than the SSR when the distribution of excess returns are skewed.

Poisson, Poisson-gamma and zero-inflated regression models of motor vehicle crashes: balancing statistical fit and theory

There has been considerable research conducted over the last 20 years focused on predicting motor vehicle crashes on transportation facilities. The range of statistical models commonly applied includes binomial, Poisson, Poisson-gamma (or negative binomial), zero-inflated Poisson and negative binomial models (ZIP and ZINB), and multinomial probability models. Given the range of possible modeling approaches and the host of assumptions with each modeling approach, making an intelligent choice for modeling motor vehicle crash data is difficult. There is little discussion in the literature comparing different statistical modeling approaches, identifying which statistical models are most appropriate for modeling crash data, and providing a strong justification from basic crash principles. In the recent literature, it has been suggested that the motor vehicle crash process can successfully be modeled by assuming a dual-state data-generating process, which implies that entities (e.g., intersections, road segments, pedestrian crossings, etc.) exist in one of two states—perfectly safe and unsafe. As a result, the ZIP and ZINB are two models that have been applied to account for the preponderance of “excess” zeros frequently observed in crash count data. The objective of this study is to provide defensible guidance on how to appropriate model crash data. We first examine the motor vehicle crash process using theoretical principles and a basic understanding of the crash process. It is shown that the fundamental crash process follows a Bernoulli trial with unequal probability of independent events, also known as Poisson trials. We examine the evolution of statistical models as they apply to the motor vehicle crash process, and indicate how well they statistically approximate the crash process. We also present the theory behind dual-state process count models, and note why they have become popular for modeling crash data. A simulation experiment is then conducted to demonstrate how crash data give rise to “excess” zeros frequently observed in crash data. It is shown that the Poisson and other mixed probabilistic structures are approximations assumed for modeling the motor vehicle crash process. Furthermore, it is demonstrated that under certain (fairly common) circumstances excess zeros are observed—and that these circumstances arise from low exposure and/or inappropriate selection of time/space scales and not an underlying dual state process. In conclusion, carefully selecting the time/space scales for analysis, including an improved set of explanatory variables and/or unobserved heterogeneity effects in count regression models, or applying small-area statistical methods (observations with low exposure) represent the most defensible modeling approaches for datasets with a preponderance of zeros

Further notes on the application of zero-inflated models in highway safety

The intent of this note is to succinctly articulate additional points that were not provided in the original paper (Lord et al., 2005) and to help clarify a collective reluctance to adopt zero-inflated (ZI) models for modeling highway safety data. A dialogue on this important issue, just one of many important safety modeling issues, is healthy discourse on the path towards improved safety modeling. This note first provides a summary of prior findings and conclusions of the original paper. It then presents two critical and relevant issues: the maximizing statistical fit fallacy and logic problems with the ZI model in highway safety modeling. Finally, we provide brief conclusions.

Perfusion model system to generate engineered grafts with controlled cellular distributions

Engineered tissue grafts, which mimic the spatial variations of cell density and extracellular matrix present in native tissues, could facilitate more efficient tissue regeneration and integration. We previously demonstrated that cells could be uniformly seeded throughout a 3D scaffold having a random pore architecture using a perfusion bioreactor2. In this work, we aimed to generate 3D constructs with defined cell distributions based on rapid prototyped scaffolds manufactured with a controlled gradient in porosity. Computational models were developed to assess the influence of fluid flow, associated with pore architecture and perfusion regime, on the resulting cell distribution.