Marginal reversible jump Markov chain Monte Carlo with application to motor unit number estimation

Motor unit number estimation (MUNE) is a method which aims to provide a quantitative indicator of progression of diseases that lead to loss of motor units, such as motor neurone disease. However the development of a reliable, repeatable and fast real-time MUNE method has proved elusive hitherto. Ridall et al. (2007) implement a reversible jump Markov chain Monte Carlo (RJMCMC) algorithm to produce a posterior distribution for the number of motor units using a Bayesian hierarchical model that takes into account biological information about motor unit activation. However we find that the approach can be unreliable for some datasets since it can suffer from poor cross-dimensional mixing. Here we focus on improved inference by marginalising over latent variables to create the likelihood. In particular we explore how this can improve the RJMCMC mixing and investigate alternative approaches that utilise the likelihood (e.g. DIC (Spiegelhalter et al., 2002)). For this model the marginalisation is over latent variables which, for a larger number of motor units, is an intractable summation over all combinations of a set of latent binary variables whose joint sample space increases exponentially with the number of motor units. We provide a tractable and accurate approximation for this quantity and also investigate simulation approaches incorporated into RJMCMC using results of Andrieu and Roberts (2009).

Arguing the Autopsy : mutual suspicion, jurisdictional confusion and the socially marginal

Vulnerable and marginalised populations are not only over-represented in the criminal justice system, but also in civil jurisdictions like the coronial system. Moreover, many of the personnel who deal with criminal matters, especially in rural and regional areas, are also those who manage the coronial death investigation. This movement back and forth between civil and criminal jurisdictions is difficult for the both professional personnel and the families, but especially for those families who may also have had dealings with these personnel in the criminal justice system, or who present as suspicious due to larger historical and global issues. While coronial legislation now allows families to raise cultural and religious concerns about the process, particularly to do with the autopsy of their loved one, this also requires them to identify themselves to police at the initial stage of the death investigation. This paper, part of a larger body of work on autopsy decision making, discusses the ways in which this information is gathered by police, how it is communicated through the system, the ways in which families are supported through the process, and the difficulties that ensue.

Pseudo-marginal algorithms with multiple CPUs

The emergence of pseudo-marginal algorithms has led to improved computational efficiency for dealing with complex Bayesian models with latent variables. Here an unbiased estimator of the likelihood replaces the true likelihood in order to produce a Bayesian algorithm that remains on the marginal space of the model parameter (with latent variables integrated out), with a target distribution that is still the correct posterior distribution. Very efficient proposal distributions can be developed on the marginal space relative to the joint space of model parameter and latent variables. Thus psuedo-marginal algorithms tend to have substantially better mixing properties. However, for pseudo-marginal approaches to perform well, the likelihood has to be estimated rather precisely. This can be difficult to achieve in complex applications. In this paper we propose to take advantage of multiple central processing units (CPUs), that are readily available on most standard desktop computers. Here the likelihood is estimated independently on the multiple CPUs, with the ultimate estimate of the likelihood being the average of the estimates obtained from the multiple CPUs. The estimate remains unbiased, but the variability is reduced. We compare and contrast two different technologies that allow the implementation of this idea, both of which require a negligible amount of extra programming effort. The superior performance of this idea over the standard approach is demonstrated on simulated data from a stochastic volatility model.

Postcards from somewhere : ‘marginal’ cultural production, creativity and community

This paper focuses on a case study of local postcard production in a rural community in Western Australia. Drawing on in-depth interviews with key producers of these postcards, the analysis presented explores perceptions of and contexts for the emergence of this production, in turn examining the notion of ‘creativity’ articulated and privileged by this cultural work. Connections are identified between the making of postcards, the broader historical field of local cultural work and the construction of community. This, in turn, forms the basis for consideration of the role and relativity of ‘marginality’.

The use of headings and marginal notes in interpreting Queensland legislation : appearances can be deceptive

This article considers the rules relating to the use of marginal notes and headings in interpreting Queensland legislation, both in its original form and in reprinted legislation. It also examines the application of the principles of construction as to the use of section headings in the interpretation of provisions of the Criminal Code 1899 (Qld). Finally, it suggests that amendments should be made to the Acts Interpretation Act 1954 (Qld) in order to clarify the position as to the status of marginal notes and headings in statutory interpretation.

Recursive pathways to marginal likelihood estimation with prior-sensitivity analysis

We investigate the utility to computational Bayesian analyses of a particular family of recursive marginal likelihood estimators characterized by the (equivalent) algorithms known as "biased sampling" or "reverse logistic regression" in the statistics literature and "the density of states" in physics. Through a pair of numerical examples (including mixture modeling of the well-known galaxy dataset) we highlight the remarkable diversity of sampling schemes amenable to such recursive normalization, as well as the notable efficiency of the resulting pseudo-mixture distributions for gauging prior-sensitivity in the Bayesian model selection context. Our key theoretical contributions are to introduce a novel heuristic ("thermodynamic integration via importance sampling") for qualifying the role of the bridging sequence in this procedure, and to reveal various connections between these recursive estimators and the nested sampling technique.

Study on dynamic system optimum assignment to establish marginal time equilibrium

Several analytical methods for Dynamic System Optimum (DSO) assignment have been proposed but they are basically classified into two kinds. This chapter attempts to establish DSO by equilbrating the path dynamic marginal time (DMT). The authors analyze the path DMT for a single path with tandem bottlenecks and showed that the path DMT is not the simple summation of DMT associated with each bottleneck along the path. Next, the authors examined the DMT of several paths passing through a common bottleneck. It is shown that the externality at the bottleneck is shared by the paths in proportion to their demand from the current time until the queue vanishes. This share of the externality is caused by the departure rate shift under first in first out (FIFO) and the externality propagates to the downstream bottlenecks. However, the externalities propagates to the downstream are calculated out if downstream bottlenecks exist. Therefore, the authors concluded that the path DMT can be evaluated without considering the propagation of the externalities, but just as in the evaluation of the path DMT for a single path passing through a series of bottlenecks between the origin and destination. Based on the DMT analysis, the authors finally proposed a heuristic solution algorithm and verified it by comparing the numerical solution with the analytical one.

A pseudo-marginal sequential Monte Carlo algorithm for random effects models in Bayesian sequential design

A computationally efficient sequential Monte Carlo algorithm is proposed for the sequential design of experiments for the collection of block data described by mixed effects models. The difficulty in applying a sequential Monte Carlo algorithm in such settings is the need to evaluate the observed data likelihood, which is typically intractable for all but linear Gaussian models. To overcome this difficulty, we propose to unbiasedly estimate the likelihood, and perform inference and make decisions based on an exact-approximate algorithm. Two estimates are proposed: using Quasi Monte Carlo methods and using the Laplace approximation with importance sampling. Both of these approaches can be computationally expensive, so we propose exploiting parallel computational architectures to ensure designs can be derived in a timely manner. We also extend our approach to allow for model uncertainty. This research is motivated by important pharmacological studies related to the treatment of critically ill patients.

Separating resource rents from intra-marginal rents in fisheries economics survey data

Economic surveys of fisheries are undertaken in several countries as a means of assessing the economic performance of their fisheries. The level of economic profits accruing in the fishery can be estimated from the average economic profits of the boats surveyed. Economic profits consist of two components—resource rent and intra-marginal rent. From a fisheries management perspective, the key indicator of performance is the level of resource rent being generated in the fishery. Consequently, these different components need to be separated out. In this paper, a means of separating out the rent components is identified for a heterogeneous fishery. This is applied to the multi-purpose fleet operating in the English Channel. The paper demonstrates that failing to separate out these two components may result in a misrepresentation of the economic performance of the fishery.

Marginal costs of hospital-acquired conditions : information for priority-setting for patient safety programmes and research

Objective: To estimate the relative inpatient costs of hospital-acquired conditions. Methods: Patient level costs were estimated using computerized costing systems that log individual utilization of inpatient services and apply sophisticated cost estimates from the hospital's general ledger. Occurrence of hospital-acquired conditions was identified using an Australian ‘condition-onset' flag for diagnoses not present on admission. These were grouped to yield a comprehensive set of 144 categories of hospital-acquired conditions to summarize data coded with ICD-10. Standard linear regression techniques were used to identify the independent contribution of hospital-acquired conditions to costs, taking into account the case-mix of a sample of acute inpatients (n = 1,699,997) treated in Australian public hospitals in Victoria (2005/06) and Queensland (2006/07). Results: The most costly types of complications were post-procedure endocrine/metabolic disorders, adding AU$21,827 to the cost of an episode, followed by MRSA (AU$19,881) and enterocolitis due to Clostridium difficile (AU$19,743). Aggregate costs to the system, however, were highest for septicaemia (AU$41.4 million), complications of cardiac and vascular implants other than septicaemia (AU$28.7 million), acute lower respiratory infections, including influenza and pneumonia (AU$27.8 million) and UTI (AU$24.7 million). Hospital-acquired complications are estimated to add 17.3% to treatment costs in this sample. Conclusions: Patient safety efforts frequently focus on dramatic but rare complications with very serious patient harm. Previous studies of the costs of adverse events have provided information on ‘indicators’ of safety problems rather than the full range of hospital-acquired conditions. Adding a cost dimension to priority-setting could result in changes to the focus of patient safety programmes and research. Financial information should be combined with information on patient outcomes to allow for cost-utility evaluation of future interventions.

A preliminary OSL chronology for coastal dunes on Moreton island, Queensland, Australia – Marginal deposits of A large-scale quaternary shelf sediment system

Moreton Island and several other large siliceous sand dune islands and mainland barrier deposits in SE Queensland represent the distal, onshore component of an extensive Quaternary continental shelf sediment system. This sediment has been transported up to 1000 km along the coast and shelf of SE Australia over multiple glacioeustatic sea-level cycles. Stratigraphic relationships and a preliminary Optically Stimulated Luminance (OSL) chronology for Moreton Island indicate a middle Pleistocene age for the large majority of the deposit. Dune units exposed in the centre of the island and on the east coast have OSL ages that indicate deposition occurred between approximately 540 ka and 350 ka BP, and at around 96±10 ka BP. Much of the southern half of the island has a veneer of much younger sediment, with OSL ages of 0.90±0.11 ka, 1.28±0.16 ka, 5.75±0.53 ka and <0.45 ka BP. The younger deposits were partially derived from the reworking of the upper leached zone of the much older dunes. A large parabolic dune at the northern end of the island, OSL age of 9.90±1.0 ka BP, and palaeosol exposures that extend below present sea level suggest the Pleistocene dunes were sourced from shorelines positioned several to tens of metres lower than, and up to few kilometres seaward of the present shoreline. Given the lower gradient of the inner shelf a few km seaward of the island, it seems likely that periods of intermediate sea level (e.g. ~20 m below present) produced strongly positive onshore sediment budgets and the mobilisation of dunes inland to form much of what now comprises Moreton Island. The new OSL ages and comprehensive OSL chronology for the Cooloola deposit, 100 km north of Moreton Island, indicate that the bulk of the coastal dune deposits in SE Queensland were emplaced between approximately 540 ka BP and prior to the Last Interglacial. This chronostratigraphic information improves our fundamental understanding of long-term sediment transport and accumulation on large-scale continental shelf sediment systems.

Accelerating Pseudo-Marginal MCMC using Gaussian Processes

Pseudo-marginal methods such as the grouped independence Metropolis-Hastings (GIMH) and Markov chain within Metropolis (MCWM) algorithms have been introduced in the literature as an approach to perform Bayesian inference in latent variable models. These methods replace intractable likelihood calculations with unbiased estimates within Markov chain Monte Carlo algorithms. The GIMH method has the posterior of interest as its limiting distribution, but suffers from poor mixing if it is too computationally intensive to obtain high-precision likelihood estimates. The MCWM algorithm has better mixing properties, but less theoretical support. In this paper we propose to use Gaussian processes (GP) to accelerate the GIMH method, whilst using a short pilot run of MCWM to train the GP. Our new method, GP-GIMH, is illustrated on simulated data from a stochastic volatility and a gene network model.

A new family of multivariate heavy-tailed distributions with variable marginal amounts of tailweight: Application to robust clustering

We propose a family of multivariate heavy-tailed distributions that allow variable marginal amounts of tailweight. The originality comes from introducing multidimensional instead of univariate scale variables for the mixture of scaled Gaussian family of distributions. In contrast to most existing approaches, the derived distributions can account for a variety of shapes and have a simple tractable form with a closed-form probability density function whatever the dimension. We examine a number of properties of these distributions and illustrate them in the particular case of Pearson type VII and t tails. For these latter cases, we provide maximum likelihood estimation of the parameters and illustrate their modelling flexibility on simulated and real data clustering examples.