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 impact of surgical ward nurses practicing respiratory assessment on positive patient outcomes

Objective: A literature review to examine the incorporation of respiratory assessment into everyday surgical nursing practice; possible barriers to this; and the relationship to patient outcomes. Primary argument: Escalating demands on intensive care beds have led to highly dependent patients being cared for in general surgical ward areas. This change in patient demographics has meant the knowledge and skills required of registered nurses in these areas has expanded exponentially. The literature supported the notion that postoperative monitoring of vital signs should include the fundamental assessment of respiratory rate; depth and rhythm; work of breathing; use of accessory muscles and symmetrical chest movement; as well as auscultation of lung fields using a stethoscope. Early intervention in response to changes in a patient's respiratory health status impacts positively on patient health outcomes. Substantial support exists for the contention that technologically adept nurses who also possess competent respiratory assessment skills make a difference to respiratory care. Conclusions: Sub-clinical respiratory problems have been demonstrated to contribute to adverse events. There is a paucity of research knowledge as to whether respiratory education programs and associated inservice make a difference to nursing clinical practice. Similarly, the implications for associated respiratory educational needs are not well documented, nor has a research base been sufficiently developed to guide nursing practice. Further research has the potential to influence the future role and function of the registered nurse by determining the importance of respiratory education programs on post-operative patient outcomes.

The influence of teachers’ expectations

As teachers and educators understand, just because you want a student to learn something or perform well doesn’t mean that they always will! Often we focus on what the student is doing or not doing correctly – “Why can’t they just…?”. However, if we only focus on reasons that are external to us, we may miss important opportunities to reflect on how our own behaviour might influence our students’ performance.

The art of the positive pas de deux : putting positive psychology into dance!

Performance psychology has more recently included a focus on applied practice within the performing arts, and specifically the dance industry. Whilst the use of psychology within this field has been occurring for a number of years, it has primarily taken its cues from the area of sport psychology or clinical psychology when dealing with ‘problems’ (e.g. eating disorders). What has been evident with the more recent introduction of positive psychology concepts with this population is the observed responsiveness from dancers towards a strengths-based approach. The aim of the inclusion of these frameworks has been to assist in increasing the empowerment, personal responsibility and effectiveness of the dancers’ psychological preparation and skills in the area of performance – whether on stage or off.

Seixas family papers, undated, 1746-1911, 1926, 1939.

The collection contains items relating to individual members of the family as well as the Seixas family in general. Included are papers of the following persons: Isaac Mendes Seixas (1708/9-1780/1), a copy of A voyage to Hudson's--Bay, by Henry Ellis, inscribed with his name on the title page, along with additional inscriptions on the end papers (1748); and a daily prayer book printed in Amsterdam (title page missing), with an inscription on the first page indicating that the book was owned by Seixas in 1758/9, and subsequently by his grandson, Theodore J. Seixas, in 1816/17.

Towards understanding the mixing characteristics of turbulent buoyant flows

This work proposes a new simulation methodology in which variable density turbulent flows can be studied in the context of a mixing layer with or without the presence of gravity. Specifically, this methodology is developed to probe the nature of non-buoyantly-driven (i.e. isotropically-driven) or buoyantly-driven mixing deep inside a mixing layer. Numerical forcing methods are incorporated into both the velocity and scalar fields, which extends the length of time over which mixing physics can be studied. The simulation framework is designed to allow for independent variation of four non-dimensional parameters, including the Reynolds, Richardson, Atwood, and Schmidt numbers. Additionally, the governing equations are integrated in such a way to allow for the relative magnitude of buoyant energy production and non-buoyant energy production to be varied.

The computational requirements needed to implement the proposed configuration are presented. They are justified in terms of grid resolution, order of accuracy, and transport scheme. Canonical features of turbulent buoyant flows are reproduced as validation of the proposed methodology. These features include the recovery of isotropic Kolmogorov scales under buoyant and non-buoyant conditions, the recovery of anisotropic one-dimensional energy spectra under buoyant conditions, and the preservation of known statistical distributions in the scalar field, as found in other DNS studies.

This simulation methodology is used to perform a parametric study of turbulent buoyant flows to discern the effects of varying the Reynolds, Richardson, and Atwood numbers on the resulting state of mixing. The effects of the Reynolds and Atwood numbers are isolated by looking at two energy dissipation rate conditions under non-buoyant (variable density) and constant density conditions. The effects of Richardson number are isolated by varying the ratio of buoyant energy production to total energy production from zero (non-buoyant) to one (entirely buoyant) under constant Atwood number, Schmidt number, and energy dissipation rate conditions. It is found that the major differences between non-buoyant and buoyant turbulent flows are contained in the transfer spectrum and longitudinal structure functions, while all other metrics are largely similar (e.g. energy spectra, alignment characteristics of the strain-rate tensor). Also, despite the differences noted between fully buoyant and non-buoyant turbulent fields, the scalar field, in all cases, is unchanged by these. The mixing dynamics in the scalar field are found to be insensitive to the source of turbulent kinetic energy production (non-buoyant vs. buoyant).

The growth of brown trout

An article discussing the factors affecting the rate of growth of brown trout, detailing the research udnertaken at Wray Castle, designed to clarify the influencing factors in different waters and investigate what would be required to increase their size. The article considers factors such as alkalinity, total hardness, the presence of coarse fish in the waterbodies and competition for food. Previous work undertaken on brown trout in Ireland by other authors is reviewed. A figure showing average growth rate of brown trout in five lakes, as determined from their scales (Lough Derg, Windermere, Loch Leven, Ullswater, Haweswater).

The food of coarse fish

Remarkably little has been published on the feeding habits of the non-salmonid fishes of British fresh waters. The following report briefly summarizes the results obtained from the examination of the stomach contents of some 2,700 fish, belonging to 19 species, which were obtained during 1939. The results of all examinations of gut contents were analysed, species by species, upon a simple basis of the presence of different types of food. Foodstuffs were divided up into six main categories— fish, molluscs, insects, crustaceans, higher plants together with filamentous algae, and diatoms—and the occurrence of members of any of these categories was recorded for each fish.

Pela criança, para a família: a intervenção científica no espaço privado através do Serviço de Ortofrenia e Higiene mental (1934-1939)

Afirmar a sociedade brasileira nos quadros da modernidade foi o anseio de intelectuais de campos variados no contexto das décadas iniciais do século XX. Neste cenário, a educação era considerada uma via possível para promover mudanças de hábitos, conformando a população a partir dos referenciais modernos. Se a escola assumiu papel de destaque por ser um espaço a partir do qual seria possível educar a infância, a importância de outras instâncias educativas também era considerada, dentre as quais, destacamos a família, pensada como espaço fundamental de socialização. A educação ministrada no espaço privado deveria, no entanto, ser consoante com os ideais preconizados à época, para isso fazia-se necessário intervir sobre ele, educando os agentes do seu interior. Neste estudo, analisamos as ações encaminhadas pelo Serviço de Ortofrenia e Higiene Mental (SOHM), que funcionou no Rio de Janeiro, então Distrito Federal, no período de 1934 a 1939. Este Serviço, chefiado por Arthur Ramos, visava prevenir e corrigir os problemas dos escolares, considerando as relações culturais e sociais importantes para uma compreensão global destes indivíduos. Como as relações familiares e o espaço doméstico eram aspectos a serem conhecidos e modificados quando necessário e, como os pais eram chamados a colaborar com as ações do Serviço de formas diversas, buscamos analisar estratégias variadas destinadas a intervir no espaço doméstico, focalizando as prescrições voltadas a este e alguns aspectos da dinâmica estabelecida nas relações entre as famílias e a escola, através do SOHM.

The suppression of Ge-132 on the Maillard reaction of BSA by fluorescence spectrum

The fluorescences of BSA and glycosylated BSA were observed respectively. The lambda(cm) of BSA was 340 nm; while the lambda(cm) of glycosylated BSA was 436 nm. Because the fluorescence spectra of them were different greatly, we can observe the suppression of Ge-132 on the Maillard reaction of BSA without any interference of itself. It was showed that the fluorescence intensity of glycosylated BSA increased continuously with the cultured time, Ge-132 may suppress the Maillard reaction of BSA greatly, and the suppressing efficicency would be 32 %. The key site of the Maillard reaction of BSA is free amino groups of alanine residues on N-terminal amino group, besides the epsilon-amino groups of intrachain Lysine residues.