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.

Drivers of adoption for successive generation of high-tech products

To understand the diffusion of high technology products such as PCs, digital cameras and DVD players it is necessary to consider the dynamics of successive generations of technology. From the consumer’s perspective, these technology changes may manifest themselves as either a new generation product substituting for the old (for instance digital cameras) or as multiple generations of a single product (for example PCs). To date, research has been confined to aggregate level sales models. These models consider the demand relationship between one generation of a product and a successor generation. However, they do not give insights into the disaggregate-level decisions by individual households – whether to adopt the newer generation, and if so, when. This paper makes two contributions. It is the first large scale empirical study to collect household data for successive generations of technologies in an effort to understand the drivers of adoption. Second, in contrast to traditional analysis in diffusion research that conceptualizes technology substitution as an “adoption of innovation” type process, we propose that from a consumer’s perspective, technology substitution combines elements of both adoption (adopting the new generation technology) and replacement (replacing generation I product with generation II). Key Propositions In some cases, successive generations are clear “substitutes” for the earlier generation (e.g. PCs Pentium I to II to III ). More commonly the new generation II technology is a “partial substitute” for existing generation I technology (e.g. DVD players and VCRs). Some consumers will purchase generation II products as substitutes for their generation I product, while other consumers will purchase generation II products as additional products to be used as well as their generation I product. We propose that substitute generation II purchases combine elements of both adoption and replacement, but additional generation II purchases are solely adoption-driven process. Moreover, drawing on adoption theory consumer innovativeness is the most important consumer characteristic for adoption timing of new products. Hence, we hypothesize consumer innovativeness to influence the timing of both additional and substitute generation II purchases but to have a stronger impact on additional generation II purchases. We further propose that substitute generation II purchases act partially as a replacement purchase for the generation I product. Thus, we hypothesize that households with older generation I products will make substitute generation II purchases earlier. Methods We employ Cox hazard modeling to study factors influencing the timing of a household’s adoption of generation II products. A separate hazard model is conducted for additional and substitute purchases. The age of the generation I product is calculated based on the most recent household purchase of that product. Control variables include size and income of household, age and education of decision-maker. Results and Implications Our preliminary results confirm both our hypotheses. Consumer innovativeness has a strong influence on both additional purchases and substitute purchases. Also consistent with our hypotheses, the age of the generation I product has a dramatic influence for substitute purchases of VCR/DVD players and a strong influence for PCs/notebooks. Yet, also as hypothesized, there was no influence on additional purchases. This implies that there is a clear distinction between additional and substitute purchases of generation II products, each with different drivers. For substitute purchases, product age is a key driver. Therefore marketers of high technology products can utilize data on generation I product age (e.g. from warranty or loyalty programs) to target customers who are more likely to make a purchase.

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.

A cross cultural examination of consumer behaviour and GM food products : results from Australian and South Korean female consumers

The call for the cross cultural examination and validation of commonly accepted relationships within consumer behaviour is strengthening. Consequently, this paper seeks to address this call by examining consumer risk perceptions, reliance on country of origin information and willingness to buy Genetically Modified (GM) food products on Australian and South Korean consumers. Findings indicate a number of cross cultural similarities and differences that have both theoretical and practical implications.