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.

Methods used in cross-cultural comparisons of psychological symptoms and their determinants

This paper is the second in a series of reviews of cross-cultural studies of menopausal symptoms. The goal of this review is to compare and contrast methods which have been previously utilized in Cross-Cultural Midlife Women's Health Studies with a view to (1) identifying the challenges in measurement across cultures in psychological symptoms and (2) suggesting a set of unified questions and tools that can be used in future research in this area. This review also aims to examine the determinants of psychological symptoms and how those determinants were measured. The review included eight studies that explicitly compared symptoms in different countries or different ethnic groups in the same country and included: Australian/Japanese Midlife Women's Health Study (AJMWHS), Decisions At Menopause Study (DAMeS), Four Major Ethnic Groups (FMEG), Hilo Women's Health Survey (HWHS), Penn Ovarian Aging Study (POAS), Study of Women's Health Across the Nation (SWAN), Women's Health in Midlife National Study (WHiMNS), and the Women's International Study of Health and Sexuality (WISHeS). This review concludes that mental morbidity does affect vasomotor symptom prevalence across cultures and therefore should be measured. Based on the review of these eight studies it is recommended that the following items be included when measuring psychological symptoms across cultures, feeling tense or nervous, sleeping difficulty, difficulty in concentrating, depressed and irritability along with the CES-D Scale, and the Perceived Stress Scale. The measurement of these symptoms will provide an evidence based approach when forming any future menopause symptom list and allow for comparisons across studies.

Seasonality of suicide in Shandong China, 1991–2009 : associations with gender, age, area and methods of suicide

Backgrounds Whether suicide in China has significant seasonal variations is unclear. The aim of this study is to examine the seasonality of suicide in Shandong China and to assess the associations of suicide seasonality with gender, residence, age and methods of suicide. Methods Three types of tests (Chi-square, Edwards' T and Roger's Log method) were used to detect the seasonality of the suicide data extracted from the official mortality data of Shandong Disease Surveillance Point (DSP) system. Peak/low ratios (PLRs) and 95% confidence intervals (CIs) were calculated to indicate the magnitude of seasonality. Results A statistically significant seasonality with a single peak in suicide rates in spring and early summer, and a dip in winter was observed, which remained relatively consistent over years. Regardless of gender, suicide seasonality was more pronounced in rural areas, younger age groups and for non-violent methods, in particular, self-poisoning by pesticide. Conclusions There are statistically significant seasonal variations of completed suicide for both men and women in Shandong, China. Differences exist between residence (urban/rural), age groups and suicide methods. Results appear to support a sociological explanation of suicide seasonality.

Numerical methods for solving a two-dimensional variable-order anomalous subdiffusion equation

Anomalous subdiffusion equations have in recent years received much attention. In this paper, we consider a two-dimensional variable-order anomalous subdiffusion equation. Two numerical methods (the implicit and explicit methods) are developed to solve the equation. Their stability, convergence and solvability are investigated by the Fourier method. Moreover, the effectiveness of our theoretical analysis is demonstrated by some numerical examples. © 2011 American Mathematical Society.

The SAGE Handbook of Criminological Research Methods

Conducting research into crime and criminal justice carries unique challenges. This Handbook focuses on the application of 'methods' to address the core substantive questions that currently motivate contemporary criminological research. It maps a canon of methods that are more elaborated than in most other fields of social science, and the intellectual terrain of research problems with which criminologists are routinely confronted. Drawing on exemplary studies, chapters in each section illustrate the techniques (qualitative and quantitative) that are commonly applied in empirical studies, as well as the logic of criminological enquiry. Organized into five sections, each prefaced by an editorial introduction, the Handbook covers: • Crime and Criminals • Contextualizing Crimes in Space and Time: Networks, Communities and Culture • Perceptual Dimensions of Crime • Criminal Justice Systems: Organizations and Institutions • Preventing Crime and Improving Justice Edited by leaders in the field of criminological research, and with contributions from internationally renowned experts, The SAGE Handbook of Criminological Research Methods is set to become the definitive resource for postgraduates, researchers and academics in criminology, criminal justice, policing, law, and sociology.

Foundations of International Climate Law : Objectives, principles and methods

This chapter explores the objectives, principle and methods of climate law. The United Nations Framework Convention on Climate Change (UNFCCC) lays the foundations of the international regime by setting out its ultimate objectives in Article 2, the key principles in Article 3, and the methods of the regime in Article 4. The ultimate objective of the regime – to avoid dangerous anthropogenic interference – is examined and assessments of the Intergovernmental Panel on Climate Change (IPCC) are considered when seeking to understand the definition of this concept. The international environmental principles of: state sovereignty and responsibility, preventative action, cooperation, sustainable development, precaution, polluter pays and common but differentiated responsibility are then examined and their incorporation within the international climate regime instruments evaluated. This is followed by an examination of the methods used by the mitigation and adaptation regimes in seeking to achieve the objective of the UNFCCC. Methods of the mitigation regime include: domestic implementation of policies, setting of standards and targets and allocation of rights, use of flexibility mechanisms, and reporting. While it is noted that methods of the adaptation regime are still evolving, the latter includes measures such as impact assessments, national adaptation plans and the provision of funding.

Numerical methods for strong solutions of stochastic differential equations : an overview

This paper gives a review of recent progress in the design of numerical methods for computing the trajectories (sample paths) of solutions to stochastic differential equations. We give a brief survey of the area focusing on a number of application areas where approximations to strong solutions are important, with a particular focus on computational biology applications, and give the necessary analytical tools for understanding some of the important concepts associated with stochastic processes. We present the stochastic Taylor series expansion as the fundamental mechanism for constructing effective numerical methods, give general results that relate local and global order of convergence and mention the Magnus expansion as a mechanism for designing methods that preserve the underlying structure of the problem. We also present various classes of explicit and implicit methods for strong solutions, based on the underlying structure of the problem. Finally, we discuss implementation issues relating to maintaining the Brownian path, efficient simulation of stochastic integrals and variable-step-size implementations based on various types of control.

Frontier Techniques for Measuring and Estimating Airport Efficiency : An Empirical Review with Practical Guidelines for Analysis and Future Research

Airport efficiency is important because it has a direct impact on customer safety and satisfaction and therefore the financial performance and sustainability of airports, airlines, and affiliated service providers. This is especially so in a world characterized by an increasing volume of both domestic and international air travel, price and other forms of competition between rival airports, airport hubs and airlines, and rapid and sometimes unexpected changes in airline routes and carriers. It also reflects expansion in the number of airports handling regional, national, and international traffic and the growth of complementary airport facilities including industrial, commercial, and retail premises. This has fostered a steadily increasing volume of research aimed at modeling and providing best-practice measures and estimates of airport efficiency using mathematical and econometric frontiers. The purpose of this chapter is to review these various methods as they apply to airports throughout the world. Apart from discussing the strengths and weaknesses of the different approaches and their key findings, the paper also examines the steps faced by researchers as they move through the modeling process in defining airport inputs and outputs and the purported efficiency drivers. Accordingly, the chapter provides guidance to those conducting empirical research on airport efficiency and serves as an aid for aviation regulators and airport operators among others interpreting airport efficiency research outcomes.

Nutrition screening and assessment in Parkinson's disease : a comparison of methods

Background & Aims Nutrition screening and assessment enable early identification of malnourished people and those at risk of malnutrition. Appropriate assessment tools assist with informing and monitoring nutrition interventions. Tool choice needs to be appropriate to the population and setting. Methods Community-dwelling people with Parkinson’s disease (>18 years) were recruited. Body mass index (BMI) was calculated from weight and height. Participants were classified as underweight according to World Health Organisation (WHO) (≤18.5kg/m2) and age specific (<65 years,≤18.5kg/m2; ≥65 years,≤23.5kg/m2) cut-offs. The Mini-Nutritional Assessment (MNA) screening (MNA-SF) and total assessment scores were calculated. The Patient-Generated Subjective Global Assessment (PG-SGA), including the Subjective Global Assessment (SGA), was performed. Sensitivity, specificity, positive predictive value, negative predictive value and weighted kappa statistic of each of the above compared to SGA were determined. Results Median age of the 125 participants was 70.0(35-92) years. Age-specific BMI (Sn 68.4%, Sp 84.0%) performed better than WHO (Sn 15.8%, Sp 99.1%) categories. MNA-SF performed better (Sn 94.7%, Sp 78.3%) than both BMI categorisations for screening purposes. MNA had higher specificity but lower sensitivity than PG-SGA (MNA Sn 84.2%, Sp 87.7%; PG-SGA Sn 100.0%, Sp 69.8%). Conclusions BMI lacks sensitivity to identify malnourished people with Parkinson’s disease and should be used with caution. The MNA-SF may be a better screening tool in people with Parkinson’s disease. The PG-SGA performed well and may assist with informing and monitoring nutrition interventions. Further research should be conducted to validate screening and assessment tools in Parkinson’s disease.  

Terrorism risk, resilience and volatility : a comparison of terrorism patterns in three Southeast Asian countries

Objective This article explores patterns of terrorist activity over the period from 2000 through 2010 across three target countries: Indonesia, the Philippines and Thailand. Methods We use self-exciting point process models to create interpretable and replicable metrics for three key terrorism concepts: risk, resilience and volatility, as defined in the context of terrorist activity. Results Analysis of the data shows significant and important differences in the risk, volatility and resilience metrics over time across the three countries. For the three countries analysed, we show that risk varied on a scale from 0.005 to 1.61 “expected terrorist attacks per day”, volatility ranged from 0.820 to 0.994 “additional attacks caused by each attack”, and resilience, as measured by the number of days until risk subsides to a pre-attack level, ranged from 19 to 39 days. We find that of the three countries, Indonesia had the lowest average risk and volatility, and the highest level of resilience, indicative of the relatively sporadic nature of terrorist activity in Indonesia. The high terrorism risk and low resilience in the Philippines was a function of the more intense, less clustered pattern of terrorism than what was evident in Indonesia. Conclusions Mathematical models hold great promise for creating replicable, reliable and interpretable “metrics” to key terrorism concepts such as risk, resilience and volatility.

A discussion of “Estimating the historical and future probabilities of large terrorist events'' by Aaron Clauset and Ryan Woodard

The terrorist attacks in the United States on September 11, 2001 appeared to be a harbinger of increased terrorism and violence in the 21st century, bringing terrorism and political violence to the forefront of public discussion. Questions about these events abound, and “Estimating the Historical and Future Probabilities of Large Scale Terrorist Event” [Clauset and Woodard (2013)] asks specifically, “how rare are large scale terrorist events?” and, in general, encourages discussion on the role of quantitative methods in terrorism research and policy and decision-making. Answering the primary question raises two challenges. The first is identify- ing terrorist events. The second is finding a simple yet robust model for rare events that has good explanatory and predictive capabilities. The challenges of identifying terrorist events is acknowledged and addressed by reviewing and using data from two well-known and reputable sources: the Memorial Institute for the Prevention of Terrorism-RAND database (MIPT-RAND) [Memorial Institute for the Prevention of Terrorism] and the Global Terror- ism Database (GTD) [National Consortium for the Study of Terrorism and Responses to Terrorism (START) (2012), LaFree and Dugan (2007)]. Clauset and Woodard (2013) provide a detailed discussion of the limitations of the data and the models used, in the context of the larger issues surrounding terrorism and policy.

Quantitative and qualitative impairments in semantic fluency, but not phonetic fluency, as a potential risk factor for Alzheimer's disease

Qualitative aspects of verbal fluency may be more useful in discerning the precise cause of any quantitative deficits in phonetic or category fluency, especially in the case of mild cognitive impairment (MCI), a possible intermediate stage between normal performance and Alzheimer's disease (AD). The aim of this study was to use both quantitative and qualitative (switches and clusters) methods to compare the phonetic and category verbal fluency performance of elderly adults with no cognitive impairment (n = 51), significant memory impairment (n = 16), and AD (n = 16). As expected, the AD group displayed impairments in all quantitative and qualitative measures of the two fluency tasks relative to their age- and education-matched peers. By contrast, the amnestic MCI group produced fewer animal names on the semantic fluency task than controls and showed normal performance on the phonetic fluency task. The MCI group's inferior category fluency performance was associated with a deficit in their category-switching rate rather than word cluster size. Overall, the results indicate that a semantic measure such as category fluency when used in conjunction with a test of episodic memory may increase the sensitivity for detecting preclinical AD. Future research using external cues and other measures of set shifting capacity may assist in clarifying the origin of the amnestic MCI-specific category-switching deficiency. Copyright

Agent-based simulation as a component of mixed methods in entrepreneurship research

As a new research method supplementing the existing qualitative and quantitative approaches, agent-based modelling and simulation (ABMS) may fit well within the entrepreneurship field because the core concepts and basic premises of entrepreneurship coincide with the characteristics of ABMS (McKelvey, 2004; Yang & Chandra, 2013). Agent-based simulation is a simulation method based on agent-based models. The agentbased models are composed of heterogeneous agents and their behavioural rules. By repeatedly carrying out agent-based simulations on a computer, the simulations reproduce each agent’s behaviour, their interactive process, and the emerging macroscopic phenomenon according to the flow of time. Using agent-based simulations, researchers may investigate temporal or dynamic effects of each agent’s behaviours.

Comparison of nitrogen fertilization methods and rates for subsurface drip irrigated corn in the semi-arid Great Plains

In semi-arid areas such as western Nebraska, interest in subsurface drip irrigation (SDI) for corn is increasing due to restricted irrigation allocations. However, crop response quantification to nitrogen (N) applications with SDI and the environmental benefits of multiple in-season (IS) SDI N applications instead of a single early-season (ES) surface application are lacking. The study was conducted in 2004, 2005, and 2006 at the University of Nebraska-Lincoln West Central Research and Extension Center in North Platte, Nebraska, comparing two N application methods (IS and ES) and three N rates (128, 186, and 278 kg N ha(-1)) using a randomized complete block design with four replications. No grain yield or biomass response was observed in 2004. In 2005 and 2006, corn grain yield and biomass production increased with increasing N rates, and the IS treatment increased grain yield, total N uptake, and gross return after N application costs (GRN) compared to the ES treatment. Chlorophyll meter readings taken at the R3 corn growth stage in 2006 showed that less N was supplied to the plant with ES compared to the IS treatment. At the end of the study, soil NO3-N masses in the 0.9 to 1.8 m depth were greater under the IS treatment compared to the ES treatment. Results suggested that greater losses of NO3-N below the root zone under the ES treatment may have had a negative effect on corn production. Under SDI systems, fertigating a recommended N rate at various corn growth stages can increase yields, GRN, and reduce NO3-N leaching in soils compared to concentrated early-season applications.