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.

Analysis of the distribution of the number of bidders in construction contract auctions

The number of bidders, N, involved in a construction procurement auction is known to have an important effect on the value of the lowest bid and the mark up applied by bidders. In practice, for example, it is important for a bidder to have a good estimate of N when bidding for a current contract. One approach, instigated by Friedman in 1956, is to make such an estimate by statistical analysis and modelling. Since then, however, finding a suitable model for N has been an enduring problem for researchers and, despite intensive research activity in the subsequent thirty years little progress has been made - due principally to the absence of new ideas and perspectives. This paper resumes the debate by checking old assumptions, providing new evidence relating to concomitant variables and proposing a new model. In doing this and in order to assure universality, a novel approach is developed and tested by using a unique set of twelve construction tender databases from four continents. This shows the new model provides a significant advancement on previous versions. Several new research questions are also posed and other approaches identified for future study.

Towards an understanding of the information dynamics of the handover process in aged care settings: A prerequisite for the safe and effective use of ICT

Background Poor clinical handover has been associated with inaccurate clinical assessment and diagnosis, delays in diagnosis and test ordering, medication errors and decreased patient satisfaction in the acute care setting. Research on the handover process in the residential aged care sector is very limited. Purpose The aims of this study were to: (i) Develop an in-depth understanding of the handover process in aged care by mapping all the key activities and their information dynamics, (ii) Identify gaps in information exchange in the handover process and analyze implications for resident safety, (iii) Develop practical recommendations on how information communication technology (ICT) can improve the process and resident safety. Methods The study was undertaken at a large metropolitan facility in NSW with more than 300 residents and a staff including 55 registered nurses (RNs) and 146 assistants in nursing (AINs). A total of 3 focus groups, 12 interviews and 3 observation sessions were conducted over a period from July to October 2010. Process mapping was undertaken by translating the qualitative data via a five-category code book that was developed prior to the analysis. Results Three major sub-processes were identified and mapped. The three major stages are Handover process (HOP) I “Information gathering by RN”, HOP II “Preparation of preliminary handover sheet” and HOP III “Execution of handover meeting”. Inefficient processes were identified in relation to the handover including duplication of information, utilization of multiple communication modes and information sources, and lack of standardization. Conclusion By providing a robust process model of handover this study has made two critical contributions to research in aged care: (i) a means to identify important, possibly suboptimal practices; and (ii) valuable evidence to plan and improve ICT implementation in residential aged care. The mapping of this process enabled analysis of gaps in information flow and potential impacts on resident safety. In addition it offers the basis for further studies into a process that, despite its importance for securing resident safety and continuity of care, lacks research.

Counting the cost: Estimating the number of deaths among recently released prisoners in Australia

TO THE EDITOR: Kinner and colleagues described the high proportion of deaths among recently released prisoners in Australia...

A semi-analytical solution for multilayer diffusion in a composite medium consisting of a large number of layers

Diffusion in a composite slab consisting of a large number of layers provides an ideal prototype problem for developing and analysing two-scale modelling approaches for heterogeneous media. Numerous analytical techniques have been proposed for solving the transient diffusion equation in a one-dimensional composite slab consisting of an arbitrary number of layers. Most of these approaches, however, require the solution of a complex transcendental equation arising from a matrix determinant for the eigenvalues that is difficult to solve numerically for a large number of layers. To overcome this issue, in this paper, we present a semi-analytical method based on the Laplace transform and an orthogonal eigenfunction expansion. The proposed approach uses eigenvalues local to each layer that can be obtained either explicitly, or by solving simple transcendental equations. The semi-analytical solution is applicable to both perfect and imperfect contact at the interfaces between adjacent layers and either Dirichlet, Neumann or Robin boundary conditions at the ends of the slab. The solution approach is verified for several test cases and is shown to work well for a large number of layers. The work is concluded with an application to macroscopic modelling where the solution of a fine-scale multilayered medium consisting of two hundred layers is compared against an “up-scaled” variant of the same problem involving only ten layers.