Using Bayesian methods for the estimation of uncertainty in complex statistical models

The research objectives of this thesis were to contribute to Bayesian statistical methodology by contributing to risk assessment statistical methodology, and to spatial and spatio-temporal methodology, by modelling error structures using complex hierarchical models. Specifically, I hoped to consider two applied areas, and use these applications as a springboard for developing new statistical methods as well as undertaking analyses which might give answers to particular applied questions. Thus, this thesis considers a series of models, firstly in the context of risk assessments for recycled water, and secondly in the context of water usage by crops. The research objective was to model error structures using hierarchical models in two problems, namely risk assessment analyses for wastewater, and secondly, in a four dimensional dataset, assessing differences between cropping systems over time and over three spatial dimensions. The aim was to use the simplicity and insight afforded by Bayesian networks to develop appropriate models for risk scenarios, and again to use Bayesian hierarchical models to explore the necessarily complex modelling of four dimensional agricultural data. The specific objectives of the research were to develop a method for the calculation of credible intervals for the point estimates of Bayesian networks; to develop a model structure to incorporate all the experimental uncertainty associated with various constants thereby allowing the calculation of more credible credible intervals for a risk assessment; to model a single day’s data from the agricultural dataset which satisfactorily captured the complexities of the data; to build a model for several days’ data, in order to consider how the full data might be modelled; and finally to build a model for the full four dimensional dataset and to consider the timevarying nature of the contrast of interest, having satisfactorily accounted for possible spatial and temporal autocorrelations. This work forms five papers, two of which have been published, with two submitted, and the final paper still in draft. The first two objectives were met by recasting the risk assessments as directed, acyclic graphs (DAGs). In the first case, we elicited uncertainty for the conditional probabilities needed by the Bayesian net, incorporated these into a corresponding DAG, and used Markov chain Monte Carlo (MCMC) to find credible intervals, for all the scenarios and outcomes of interest. In the second case, we incorporated the experimental data underlying the risk assessment constants into the DAG, and also treated some of that data as needing to be modelled as an ‘errors-invariables’ problem [Fuller, 1987]. This illustrated a simple method for the incorporation of experimental error into risk assessments. In considering one day of the three-dimensional agricultural data, it became clear that geostatistical models or conditional autoregressive (CAR) models over the three dimensions were not the best way to approach the data. Instead CAR models are used with neighbours only in the same depth layer. This gave flexibility to the model, allowing both the spatially structured and non-structured variances to differ at all depths. We call this model the CAR layered model. Given the experimental design, the fixed part of the model could have been modelled as a set of means by treatment and by depth, but doing so allows little insight into how the treatment effects vary with depth. Hence, a number of essentially non-parametric approaches were taken to see the effects of depth on treatment, with the model of choice incorporating an errors-in-variables approach for depth in addition to a non-parametric smooth. The statistical contribution here was the introduction of the CAR layered model, the applied contribution the analysis of moisture over depth and estimation of the contrast of interest together with its credible intervals. These models were fitted using WinBUGS [Lunn et al., 2000]. The work in the fifth paper deals with the fact that with large datasets, the use of WinBUGS becomes more problematic because of its highly correlated term by term updating. In this work, we introduce a Gibbs sampler with block updating for the CAR layered model. The Gibbs sampler was implemented by Chris Strickland using pyMCMC [Strickland, 2010]. This framework is then used to consider five days data, and we show that moisture in the soil for all the various treatments reaches levels particular to each treatment at a depth of 200 cm and thereafter stays constant, albeit with increasing variances with depth. In an analysis across three spatial dimensions and across time, there are many interactions of time and the spatial dimensions to be considered. Hence, we chose to use a daily model and to repeat the analysis at all time points, effectively creating an interaction model of time by the daily model. Such an approach allows great flexibility. However, this approach does not allow insight into the way in which the parameter of interest varies over time. Hence, a two-stage approach was also used, with estimates from the first-stage being analysed as a set of time series. We see this spatio-temporal interaction model as being a useful approach to data measured across three spatial dimensions and time, since it does not assume additivity of the random spatial or temporal effects.

The moral economy of social media

In this chapter we take a high-level view of social media, focusing not on specific applications, domains, websites, or technologies, but instead our interest is in the forms of engagement that social media engender. This is not to suggest that all social media are the same, or even that everyone’s experience with any particular medium or technology is the same. However, we argue common issues arise that characterize social media in a broad sense, and provide a different analytic perspective than we would gain from looking at particular systems or applications. We do not take the perspective that social life merely happens “within” such systems, nor that social life “shapes” such systems, but rather these systems provide a site for the production of social and cultural reality – that media are always already social and the engagement with, in, and through media of all sorts is a thoroughly social phenomenon. Accordingly, in this chapter, we examine two phenomena concurrently: social life seen through the lens of social media, and social media seen through the lens of social life. In particular, we want to understand the ways that a set of broad phenomena concerning forms of participation in social life is articulated in the domain of social media. As a conceptual entry-point, we use the notion of the “moral economy” as a means to open up the domain of inquiry. We first discuss the notion of the “moral economy” as it has been used by a number of social theorists, and then identify a particular set of conceptual concerns that we suggest link it to the phenomena of social networking in general. We then discuss a series of examples drawn from a range of studies to elaborate and ground this conceptual framework in empirical data. This leads us to a broader consideration of audiences and publics in social media that, we suggest, holds important lessons for how we treat social media analytically.

Bayesian mixtures for modelling complex medical data : a case study in Parkinson’s disease

Mixture models are a flexible tool for unsupervised clustering that have found popularity in a vast array of research areas. In studies of medicine, the use of mixtures holds the potential to greatly enhance our understanding of patient responses through the identification of clinically meaningful clusters that, given the complexity of many data sources, may otherwise by intangible. Furthermore, when developed in the Bayesian framework, mixture models provide a natural means for capturing and propagating uncertainty in different aspects of a clustering solution, arguably resulting in richer analyses of the population under study. This thesis aims to investigate the use of Bayesian mixture models in analysing varied and detailed sources of patient information collected in the study of complex disease. The first aim of this thesis is to showcase the flexibility of mixture models in modelling markedly different types of data. In particular, we examine three common variants on the mixture model, namely, finite mixtures, Dirichlet Process mixtures and hidden Markov models. Beyond the development and application of these models to different sources of data, this thesis also focuses on modelling different aspects relating to uncertainty in clustering. Examples of clustering uncertainty considered are uncertainty in a patient’s true cluster membership and accounting for uncertainty in the true number of clusters present. Finally, this thesis aims to address and propose solutions to the task of comparing clustering solutions, whether this be comparing patients or observations assigned to different subgroups or comparing clustering solutions over multiple datasets. To address these aims, we consider a case study in Parkinson’s disease (PD), a complex and commonly diagnosed neurodegenerative disorder. In particular, two commonly collected sources of patient information are considered. The first source of data are on symptoms associated with PD, recorded using the Unified Parkinson’s Disease Rating Scale (UPDRS) and constitutes the first half of this thesis. The second half of this thesis is dedicated to the analysis of microelectrode recordings collected during Deep Brain Stimulation (DBS), a popular palliative treatment for advanced PD. Analysis of this second source of data centers on the problems of unsupervised detection and sorting of action potentials or "spikes" in recordings of multiple cell activity, providing valuable information on real time neural activity in the brain.

The Prehistory of Potyviruses: Their Initial Radiation Was during the Dawn of Agriculture

Background: Potyviruses are found world wide, are spread by probing aphids and cause considerable crop damage. Potyvirus is one of the two largest plant virus genera and contains about 15% of all named plant virus species. When and why did the potyviruses become so numerous? Here we answer the first question and discuss the other. Methods and Findings: We have inferred the phylogenies of the partial coat protein gene sequences of about 50 potyviruses, and studied in detail the phylogenies of some using various methods and evolutionary models. Their phylogenies have been calibrated using historical isolation and outbreak events: the plum pox virus epidemic which swept through Europe in the 20th century, incursions of potyviruses into Australia after agriculture was established by European colonists, the likely transport of cowpea aphid-borne mosaic virus in cowpea seed from Africa to the Americas with the 16th century slave trade and the similar transport of papaya ringspot virus from India to the Americas. Conclusions/Significance: Our studies indicate that the partial coat protein genes of potyviruses have an evolutionary rate of about 1.1561024 nucleotide substitutions/site/year, and the initial radiation of the potyviruses occurred only about 6,600 years ago, and hence coincided with the dawn of agriculture. We discuss the ways in which agriculture may have triggered the prehistoric emergence of potyviruses and fostered their speciation.

Fathers' rights groups : demographic correlates and impact on custody policy

This article combines information from fathers' rights Web sites with demographic, historical, and other information to provide an empirically based analysis of fathers' rights advocacy in the United States. Content analysis discerns three factors that are central to the groups' rhetoric: representing domestic violence allegations as false, promoting presumptive joint custody and decreasing child support, and portraying women as perpetrators of domestic abuse. Fathers' rights organizations and themes are examined in relation to state-level demographics and custody policy. The implications of fathers' rights activism for battered women and their children are explored.

A home-based progressive resistance exercise programme for patients with venous leg ulcers : a feasibility study

This study aimed to assess the feasibility of a home-based exercise program and examine the effects on the healing rates of venous leg ulcers. A 12 –week randomised controlled trial was conducted investigating the effects of an exercise intervention compared to a usual care group. Participants in both groups (n = 13) had active venous ulceration and were treated in a metropolitan hospital outpatients clinic in Australia. Data were collected on recruitment from medical records, clinical assessment and questionnaires. Follow-up data on progress in healing and treatments were collected fortnightly for 12 weeks. Calf muscle pump function data were collected at baseline and 12 weeks from recruitment. Range of ankle motion data were collected at baseline, 6 and 12 weeks from recruitment. This pilot study indicated that the intervention was feasible. Clinical significance was observed in the intervention group with a 32% greater decrease in ulcer size (p=0.34) than the control group, and a 10% (p=0.74) improvement in the number of participants healed in the intervention group compared to the control group. Significant differences between groups over time were observed in calf muscle pump function parameters; (ejection fraction [p = 0.05]; residual volume fraction [p = 0.04]) and range of ankle motion (p = 0.01). This pilot study is one of the first studies to examine and measure clinical healing rates for participants involved in a home-based progressive resistance exercise program. Further research is warranted with a larger multi-site study.

Effect of Fe3O4 addition on removal of ammonium by zeolite NaA

Magnetic zeolite NaA with different Fe3O4 loadings was prepared by hydrothermal synthesis based on metakaolin and Fe3O4. The effect of added Fe3O4 on the removal of ammonium by zeolite NaA was investigated by varying the Fe3O4 loading, pH, adsorption temperature, initial concentration, adsorption time. Langmuir, Freundlich, and pseudo-second-order modeling were used to describe the nature and mechanism of ammonium ion exchange using both zeolite and magnetic zeolite. Thermodynamic parameters such as change in Gibbs free energy, enthalpy and entropy were calculated. The results show that all the selected factors affect the ammonium ion exchange by zeolite and magnetic zeolite, however, the added Fe3O4 apparently does not affect the ion exchange performance of zeolite to the ammonium ion. Freundlich model provides a better description of the adsorption process than Langmuir model. Moreover, kinetic analysis indicates the exchange of ammonium on the two materials follows a pseudosecond-order model. Thermodynamic analysis makes it clear that the adsorption process of ammonium is spontaneous and exothermic. Regardless of kinetic or thermodynamic analysis, all the results suggest that no considerable effect on the adsorption of the ammonium ion by zeolite is found after the addition of Fe3O4. According to the results, magnetic zeolite NaA can be used for the removal of ammonium due to the good adsorption performance and easy separation method from aqueous solution.

The effect of surface tension and kinetic undercooling on a radially-symmetric melting problem

The addition of surface tension to the classical Stefan problem for melting a sphere causes the solution to blow up at a finite time before complete melting takes place. This singular behaviour is characterised by the speed of the solid-melt interface and the flux of heat at the interface both becoming unbounded in the blow-up limit. In this paper, we use numerical simulation for a particular energy-conserving one-phase version of the problem to show that kinetic undercooling regularises this blow-up, so that the model with both surface tension and kinetic undercooling has solutions that are regular right up to complete melting. By examining the regime in which the dimensionless kinetic undercooling parameter is small, our results demonstrate how physically realistic solutions to this Stefan problem are consistent with observations of abrupt melting of nanoscaled particles.

Genus Umbravirus

The practical need to partition the world of viruses into distinguishable, universally agreed upon entities is the ultimate justification for developing a virus classification system. The Author of this Book is Andrew MQ King, Elliot Lefkowitz, Eric B. Carstens, Michael J. Adams Since 1971, the International Committee on Taxonomy of Viruses (ICTV) operating on behalf of the world community of virologists has taken on the task of developing a single, universal taxonomic scheme for all viruses infecting animals (vertebrate, invertebrates, and protozoa), plants (higher plants and algae), fungi, bacteria, and archaea.

Carrot mottle mimic virus (CMoMV): A second umbravirus associated with carrot motley dwarf disease recognised by nucleic acid hybridisation

Carrot mottle umbravirus (CMoV) has always been found co-infecting plants with carrot red leaf luteovirus (CRLV) and in carrot (Daucus carota) these co-infections are associated with carrot motley dwarf disease (CMD). CMD occurs wherever carrots are grown. Hence, CMoV was believed to have a corresponding global distribution. However, little or no hybridisation was detected between cDNA generated from the sequenced Australian isolate of CMoV (CMoV-A) and RNA from the much studied Scottish isolate of CMoV (CMoV-S). A weak hybridisation signal was obtained using cDNA to a conserved part of the RNA-dependent RNA polymerase gene of CMoV-A, but when cDNAs to other parts of the CMoV-A genome were used as probes there was no detectable hybridisation with CMoV-S RNA. This lack of hybridisation suggests that the two virus isolates have relatively divergent genomes and that they should be regarded as distinct virus species. Both viruses are transmitted by Cavariella aegopodii, but only with the help of CRLV, and they yield almost identical double-stranded RNA profiles. For these reasons, we propose that the CMoV isolate from Australia be renamed carrot mottle mimic umbravirus (CMoMV). cDNA to CMoMV RNA hybridised with RNA from an isolate from New Zealand, whereas cDNA to CMoV-S RNA hybridised with RNA from isolates from England and Morocco but not to RNA from the isolate from New Zealand. Although preliminary, these data suggest that CMoV and CMoMV may have different global distributions.

Comparison of promoters and selectable marker genes for use in Indica rice transformation

The effectiveness of different promoters for use in Indica rice transformation was compared. Plasmids encoding the Escherichia coli uidA (gus) gene under the control of CaMV 35S, Emu, Act1 or Ubi1 promoters were delivered into cell suspension cultures by particle bombardment. Transient gene expression, 48 h after delivery, was greatest from plasmids utilising the constitutive promoters, Act1 and Ubi1. Gene expression in stably transformed tissue was examined by bombarding embryogenic Indica rice calli with a pUbil-gus plasmid and a plasmid containing either the selectable marker gene, hph, which confers hygromycin resistance, or bar, which confers resistance to the herbicide phosphinothricin (BASTA) each under the control of the CaMV 35S, Emu, Act1 or the Ubi1 promoters. The bombarded calli were placed on the appropriate selection media and stained for GUS activity at 1 day, 3 weeks and 5 weeks after shooting. Callus bombarded with the pUbi1-hph or the pEmu-hph constructs gave a dramatic increase in the size of the GUS staining areas with time. No such increase in the size of GUS staining areas was observed in calli co-bombarded with pUbi1-gus and any of the bar containing constructs. Co-bombardment of calli with either the pEmu-hph or pUbi1-hph construct and a virus minor coat protein (cp) gene construct resulted in many fertile transgenic Indica rice plants, containing one to eight copies of both the hph and cp genes. These genes were stably inherited by the T 1 generation.

Genome segment 5 of rice ragged stunt virus encodes a virion protein

The complete nucleotide sequence of the genome segment 5 (S5) of a Thai isolate of rice ragged stunt virus (RRSV) was determined. The 2682 nucleotide sequence contains a single long open reading frame capable of encoding a polypeptide with a molecular mass of ~91 kDa. Polypeptides encoded by various truncated cDNAs of S5 were expressed using the pGEX fusion protein vector and the highest level of fusion protein was obtained from a construct encoding a hydrophilic region of S5 protein. Antibodies raised against this fusion protein recognized a minor polypeptide, with a molecular mass of ~ 91 kDa, that was present in purified preparations of RRSV particles, infected insect vectors and infected rice plants. This indicates that RRSV S5 encodes a minor structural protein. Comparing the RRSV S5 sequence with sequences of other reo-viruses did not reveal any significant sequence similarities.