Overfitting Bayesian mixture models with an unknown number of components

This paper proposes solutions to three issues pertaining to the estimation of finite mixture models with an unknown number of components: the non-identifiability induced by overfitting the number of components, the mixing limitations of standard Markov Chain Monte Carlo (MCMC) sampling techniques, and the related label switching problem. An overfitting approach is used to estimate the number of components in a finite mixture model via a Zmix algorithm. Zmix provides a bridge between multidimensional samplers and test based estimation methods, whereby priors are chosen to encourage extra groups to have weights approaching zero. MCMC sampling is made possible by the implementation of prior parallel tempering, an extension of parallel tempering. Zmix can accurately estimate the number of components, posterior parameter estimates and allocation probabilities given a sufficiently large sample size. The results will reflect uncertainty in the final model and will report the range of possible candidate models and their respective estimated probabilities from a single run. Label switching is resolved with a computationally light-weight method, Zswitch, developed for overfitted mixtures by exploiting the intuitiveness of allocation-based relabelling algorithms and the precision of label-invariant loss functions. Four simulation studies are included to illustrate Zmix and Zswitch, as well as three case studies from the literature. All methods are available as part of the R package Zmix, which can currently be applied to univariate Gaussian mixture models.

Parameterizing Unconditional Skewness in Models for Financial Time Series

In this paper we consider the third-moment structure of a class of time series models. It is often argued that the marginal distribution of financial time series such as returns is skewed. Therefore it is of importance to know what properties a model should possess if it is to accommodate unconditional skewness. We consider modeling the unconditional mean and variance using models that respond nonlinearly or asymmetrically to shocks. We investigate the implications of these models on the third-moment structure of the marginal distribution as well as conditions under which the unconditional distribution exhibits skewness and nonzero third-order autocovariance structure. In this respect, an asymmetric or nonlinear specification of the conditional mean is found to be of greater importance than the properties of the conditional variance. Several examples are discussed and, whenever possible, explicit analytical expressions provided for all third-order moments and cross-moments. Finally, we introduce a new tool, the shock impact curve, for investigating the impact of shocks on the conditional mean squared error of return series.

Models for engaging public-private partnerships in civil infrastructure projects: A case of ‘having your cake and eating it too’?

Public-Private Partnerships (PPP) are established globally as an important mode of procurement and the features of PPP, not least of which the transfer of risk, appeal to governments and particularly in the current economic climate. There are many other advantages of PPP that are claimed as outweighing the costs of PPP and affording Value for Money (VfM) relative to traditionally financed projects or non-PPP. That said, it is the case that we lack comparative whole-life empirical studies of VfM in PPP and non-PPP. Whilst we await this kind of study, the pace and trajectory of PPP seem set to continue and so in the meantime, the virtues of seeking to improve PPP appear incontrovertible. The decision about which projects, or parts of projects, to offer to the market as a PPP and the decision concerning the allocation or sharing risks as part of engagement of the PPP consortium are among the most fundamental decisions that determine whether PPP deliver VfM. The focus in the paper is on latter decision concerning governments’ attitudes towards risk and more specifically, the effect of this decision on the nature of the emergent PPP consortium, or PPP model, including its economic behavior and outcomes. This paper presents an exploration into the extent to which the seemingly incompatible alternatives of risk allocation and risk sharing, represented by the orthodox/conventional PPP model and the heterodox/alliance PPP model respectively, can be reconciled along with suggestions for new research directions to inform this reconciliation. In so doing, an important step is taken towards charting a path by which governments can harness the relative strengths of both kinds of PPP model.

Combining propensity and influence models for product adoption prediction

This paper studies the problem of selecting users in an online social network for targeted advertising so as to maximize the adoption of a given product. In previous work, two families of models have been considered to address this problem: direct targeting and network-based targeting. The former approach targets users with the highest propensity to adopt the product, while the latter approach targets users with the highest influence potential – that is users whose adoption is most likely to be followed by subsequent adoptions by peers. This paper proposes a hybrid approach that combines a notion of propensity and a notion of influence into a single utility function. We show that targeting a fixed number of high-utility users results in more adoptions than targeting either highly influential users or users with high propensity.

Optimization models for expanding a railway’s theoretical capacity

Changing the topology of a railway network can greatly affect its capacity. Railway networks however can be altered in a multitude of different ways. As each way has significant immediate and long term financial ramifications, it is a difficult task to decide how and where to expand the network. In response some railway capacity expansion models (RCEM) have been developed to help capacity planning activities, and to remove physical bottlenecks in the current railway system. The exact purpose of these models is to decide given a fixed budget, where track duplications and track sub divisions should be made, in order to increase theoretical capacity most. These models are high level and strategic, and this is why increases to the theoretical capacity is concentrated upon. The optimization models have been applied to a case study to demonstrate their application and their worth. The case study evidently shows how automated approaches of this nature could be a formidable alternative to current manual planning techniques and simulation. If the exact effect of track duplications and sub-divisions can be sufficiently approximated, this approach will be very applicable.

Reconciling transport models across scales: The role of volume exclusion

Diffusive transport is a universal phenomenon, throughout both biological and physical sciences, and models of diffusion are routinely used to interrogate diffusion-driven processes. However, most models neglect to take into account the role of volume exclusion, which can significantly alter diffusive transport, particularly within biological systems where the diffusing particles might occupy a significant fraction of the available space. In this work we use a random walk approach to provide a means to reconcile models that incorporate crowding effects on different spatial scales. Our work demonstrates that coarse-grained models incorporating simplified descriptions of excluded volume can be used in many circumstances, but that care must be taken in pushing the coarse-graining process too far.

Models of care in geriatric oncology nursing

Objectives To review models of care for older adults with cancer, with a focus on the role of the oncology nurse in geriatric oncology care. International exemplars of geriatric oncology nursing care are discussed. Data source Published peer reviewed literature, web-based resources, professional society materials, and the authors' experience. Conclusion Nursing care for older patients with cancer is complex and requires integrating knowledge from multiple disciplines that blends the sciences of geriatrics, oncology, and nursing. and which recognizes the dimensions of quality of life. Implications for Nursing Practice: Oncology nurses can benefit from learning key skills of comprehensive geriatric screening and assessment to improve the care they provide for older adults with cancer.

Attributes of clinical role models as described by senior veterinary students in Australia

Role models incite admiration and provide inspiration, contributing to learning as students aspire to emulate their example. The attributes of physician role models for medical trainees are well documented, but they remain largely unexplored in the context of veterinary medical training. The aim of the current study was to describe the attributes that final-year veterinary students (N=213) at the University of Queensland identified when reflecting on their clinical role models. Clinical role model descriptions provided by students were analyzed using concept-mapping software (Leximancer v. 2.25). The most frequent and highly connected concepts used by students when describing their role model(s) included clients, vet, and animal. Role models were described as good communicators who were skilled at managing relationships with clients, patients, and staff. They had exemplary knowledge, skills, and abilities, and they were methodical and conducted well-structured consultations. They were well respected and, in turn, demonstrated respect for clients, colleagues, staff, and students alike. They were also good teachers and able to tailor explanations to suit both clients and students. Findings from this study may serve to assist with faculty development and as a basis for further research in this area.

Eliciting and encoding expert knowledge on variable selection into classical or Bayesian species distribution models

The quality of species distribution models (SDMs) relies to a large degree on the quality of the input data, from bioclimatic indices to environmental and habitat descriptors (Austin, 2002). Recent reviews of SDM techniques, have sought to optimize predictive performance e.g. Elith et al., 2006. In general SDMs employ one of three approaches to variable selection. The simplest approach relies on the expert to select the variables, as in environmental niche models Nix, 1986 or a generalized linear model without variable selection (Miller and Franklin, 2002). A second approach explicitly incorporates variable selection into model fitting, which allows examination of particular combinations of variables. Examples include generalized linear or additive models with variable selection (Hastie et al. 2002); or classification trees with complexity or model based pruning (Breiman et al., 1984, Zeileis, 2008). A third approach uses model averaging, to summarize the overall contribution of a variable, without considering particular combinations. Examples include neural networks, boosted or bagged regression trees and Maximum Entropy as compared in Elith et al. 2006. Typically, users of SDMs will either consider a small number of variable sets, via the first approach, or else supply all of the candidate variables (often numbering more than a hundred) to the second or third approaches. Bayesian SDMs exist, with several methods for eliciting and encoding priors on model parameters (see review in Low Choy et al. 2010). However few methods have been published for informative variable selection; one example is Bayesian trees (O’Leary 2008). Here we report an elicitation protocol that helps makes explicit a priori expert judgements on the quality of candidate variables. This protocol can be flexibly applied to any of the three approaches to variable selection, described above, Bayesian or otherwise. We demonstrate how this information can be obtained then used to guide variable selection in classical or machine learning SDMs, or to define priors within Bayesian SDMs.

Mathematical models of calcium and tight junctions in normal and reconstructed epidermis

This project investigated the calcium distributions of the skin, and the growth patterns of skin substitutes grown in the laboratory, using mathematical models. The research found that the calcium distribution in the upper layer of the skin is controlled by three different mechanisms, not one as previously thought. The research also suggests that tight junctions, which are adhesions between neighbouring skin cells, cannot be solely responsible for the differences in the growth patterns of skin substitutes and normal skin.

Product-library-derived specification parameters in building information models augmentation

This paper conceptualizes a framework for bridging the BIM (building information modelling)-specifications divide through augmenting objects within BIM with specification parameters derived from a product library. We demonstrate how model information, enriched with data at various LODs (levels of development), can evolve simultaneously with design and construction using different representation of a window object embedded in a wall as lifecycle phase exemplars at different levels of granularity. The conceptual standpoint is informed by the need for exploring a methodological approach which extends beyond current limitations of current modelling platforms in enhancing the information content of BIM models. Therefore, this work demonstrates that BIM objects can be augmented with construction specification parameters leveraging product libraries.

Paraxial schematic eye models for 7- and 14-year-old Chinese children

Purpose.: To develop three-surface paraxial schematic eyes with different ages and sexes based on data for 7- and 14-year-old Chinese children from the Anyang Childhood Eye Study. Methods.: Six sets of paraxial schematic eyes, including 7-year-old eyes, 7-year-old male eyes, 7-year-old female eyes, 14-year-old eyes, 14-year-old male eyes, and 14-year-old female eyes, were developed. Both refraction-dependent and emmetropic eye models were developed, with the former using linear dependence of ocular parameters on refraction. Results.: A total of 2059 grade 1 children (boys 58%) and 1536 grade 8 children (boys 49%) were included, with mean age of 7.1 ± 0.4 and 13.7 ± 0.5 years, respectively. Changes in these schematic eyes with aging are increased anterior chamber depth, decreased lens thickness, increased vitreous chamber depth, increased axial length, and decreased lens equivalent power. Male schematic eyes have deeper anterior chamber depth, longer vitreous chamber depth, longer axial length, and lower lens equivalent power than female schematic eyes. Changes in the schematic eyes with positive increase in refraction are decreased anterior chamber depth, increased lens thickness, decreased vitreous chamber depth, decreased axial length, increased corneal radius of curvature, and increased lens power. In general, the emmetropic schematic eyes have biometric parameters similar to those arising from regression fits for the refraction-dependent schematic eyes. Conclusions.: The paraxial schematic eyes of Chinese children may be useful for myopia research and for facilitating comparison with other children with the same or different racial backgrounds and living in different places.

Monitoring healing progression and characterizing the mechanical environment in preclinical models for bone tissue engineering

The treatment of large segmental bone defects remains a significant clinical challenge. Due to limitations surrounding the use of bone grafts, tissue-engineered constructs for the repair of large bone defects could offer an alternative. Before translation of any newly developed tissue engineering (TE) approach to the clinic, efficacy of the treatment must be shown in a validated preclinical large animal model. Currently, biomechanical testing, histology, and microcomputed tomography are performed to assess the quality and quantity of the regenerated bone. However, in vivo monitoring of the progression of healing is seldom performed, which could reveal important information regarding time to restoration of mechanical function and acceleration of regeneration. Furthermore, since the mechanical environment is known to influence bone regeneration, and limb loading of the animals can poorly be controlled, characterizing activity and load history could provide the ability to explain variability in the acquired data sets and potentially outliers based on abnormal loading. Many approaches have been devised to monitor the progression of healing and characterize the mechanical environment in fracture healing studies. In this article, we review previous methods and share results of recent work of our group toward developing and implementing a comprehensive biomechanical monitoring system to study bone regeneration in preclinical TE studies.

Evaluation of k-epsilon and RNG turbulence models for confined swirling and non-swirling flow

In a very recent study [1] the Renormalisation Group (RNG) turbulence model was used to obtain flow predictions in a strongly swirling quarl burner, and was found to perform well in predicting certain features that are not well captured using less sophisticated models of turbulence. The implication is that the RNG approach should provide an economical and reliable tool for the prediction of swirling flows in combustor and furnace geometries commonly encountered in technological applications. To test this hypothesis the present work considers flow in a model furnace for which experimental data is available [2]. The essential features of the flow which differentiate it from the previous study [1] are that the annular air jet entry is relatively narrow and the base wall of the cylindrical furnace is at 90 degrees to the inlet pipe. For swirl numbers of order 1 the resulting flow is highly complex with significant inner and outer recirculation regions. The RNG and standard k-epsilon models are used to model the flow for both swirling and non-swirling entry jets and the results compared with experimental data [2]. Near wall viscous effects are accounted for in both models via the standard wall function formulation [3]. For the RNG model, additional computations with grid placement extending well inside the near wall viscous-affected sublayer are performed in order to assess the low Reynolds number capabilities of the model.

Computation of confined swirling flow using RNG and k-epsilon turbulence models

In this work we numerically model isothermal turbulent swirling flow in a cylindrical burner. Three versions of the RNG k-epsilon model are assessed against performance of the standard k-epsilon model. Sensitivity of numerical predictions to grid refinement, differing convective differencing schemes and choice of (unknown) inlet dissipation rate, were closely scrutinised to ensure accuracy. Particular attention is paid to modelling the inlet conditions to within the range of uncertainty of the experimental data, as model predictions proved to be significantly sensitive to relatively small changes in upstream flow conditions. We also examine the characteristics of the swirl--induced recirculation zone predicted by the models over an extended range of inlet conditions. Our main findings are: - (i) the standard k-epsilon model performed best compared with experiment; - (ii) no one inlet specification can simultaneously optimize the performance of the models considered; - (iii) the RNG models predict both single-cell and double-cell IRZ characteristics, the latter both with and without additional internal stagnation points. The first finding indicates that the examined RNG modifications to the standard k-e model do not result in an improved eddy viscosity based model for the prediction of swirl flows. The second finding suggests that tuning established models for optimal performance in swirl flows a priori is not straightforward. The third finding indicates that the RNG based models exhibit a greater variety of structural behaviour, despite being of the same level of complexity as the standard k-e model. The plausibility of the predicted IRZ features are discussed in terms of known vortex breakdown phenomena.