Modelling the process of learning in economics

Student learning research literature has shown that students' learning approaches are influenced by the learning context (Evans, Kirby, & Fabrigar, 2003). Of the many contextual factors, assessment has been found to have the most important influence on the way students go about learning. For example, assessment that is perceived to required a low level of cognitive abilities will more likely elicit a learning approach that concentrate on reproductive learning activities. Moreover, assessment demand will also interact with learning approach to determine academic performance. In this paper an assessment specific model of learning comprising presage, process and product variables (Biggs, 2001) was proposed and tested against data obtained from a sample of introductory economics students (n=434). The model developed was used to empirically investigate the influence of learning inputs and learning approaches on academic performances across assessment types (essay assignment, multiple choice question exam and exam essay). By including learning approaches in the learning model, the mechanism through which learning inputs determine academic performance was examined. Methodological limitations of the study will also be discussed.

Modelling water droplet movement on a leaf surface

Modelling droplet movement on leaf surfaces is an important component in understanding how water, pesticide or nutrient is absorbed through the leaf surface. A simple mathematical model is proposed in this paper for generating a realistic, or natural looking trajectory of a water droplet traversing a virtual leaf surface. The virtual surface is comprised of a triangular mesh structure over which a hybrid Clough-Tocher seamed element interpolant is constructed from real-life scattered data captured by a laser scanner. The motion of the droplet is assumed to be affected by gravitational, frictional and surface resistance forces and the innovation of our approach is the use of thin-film theory to develop a stopping criterion for the droplet as it moves on the surface. The droplet model is verified and calibrated using experimental measurement; the results are promising and appear to capture reality quite well.

Using accelerometer, high sample rate GPS and magnetometer data to develop a cattle movement and behaviour model

The study described in this paper developed a model of animal movement, which explicitly recognised each individual as the central unit of measure. The model was developed by learning from a real dataset that measured and calculated, for individual cows in a herd, their linear and angular positions and directional and angular speeds. Two learning algorithms were implemented: a Hidden Markov model (HMM) and a long-term prediction algorithm. It is shown that a HMM can be used to describe the animal's movement and state transition behaviour within several “stay” areas where cows remained for long periods. Model parameters were estimated for hidden behaviour states such as relocating, foraging and bedding. For cows’ movement between the “stay” areas a long-term prediction algorithm was implemented. By combining these two algorithms it was possible to develop a successful model, which achieved similar results to the animal behaviour data collected. This modelling methodology could easily be applied to interactions of other animal species.

Submarine dynamic modelling

This paper discusses the development of a dynamic model for a torpedo shaped sub- marine. Expressions for hydrostatic, added mass, hydrodynamic, control surface and pro- peller forces and moments are derived from first principles. Experimental data obtained from flume tests of the submarine are inserted into the model in order to provide computer simulations of the open loop behavior of the system.

Bayesian models for longitudinal data

Longitudinal data, where data are repeatedly observed or measured on a temporal basis of time or age provides the foundation of the analysis of processes which evolve over time, and these can be referred to as growth or trajectory models. One of the traditional ways of looking at growth models is to employ either linear or polynomial functional forms to model trajectory shape, and account for variation around an overall mean trend with the inclusion of random eects or individual variation on the functional shape parameters. The identification of distinct subgroups or sub-classes (latent classes) within these trajectory models which are not based on some pre-existing individual classification provides an important methodology with substantive implications. The identification of subgroups or classes has a wide application in the medical arena where responder/non-responder identification based on distinctly diering trajectories delivers further information for clinical processes. This thesis develops Bayesian statistical models and techniques for the identification of subgroups in the analysis of longitudinal data where the number of time intervals is limited. These models are then applied to a single case study which investigates the neuropsychological cognition for early stage breast cancer patients undergoing adjuvant chemotherapy treatment from the Cognition in Breast Cancer Study undertaken by the Wesley Research Institute of Brisbane, Queensland. Alternative formulations to the linear or polynomial approach are taken which use piecewise linear models with a single turning point, change-point or knot at a known time point and latent basis models for the non-linear trajectories found for the verbal memory domain of cognitive function before and after chemotherapy treatment. Hierarchical Bayesian random eects models are used as a starting point for the latent class modelling process and are extended with the incorporation of covariates in the trajectory profiles and as predictors of class membership. The Bayesian latent basis models enable the degree of recovery post-chemotherapy to be estimated for short and long-term followup occasions, and the distinct class trajectories assist in the identification of breast cancer patients who maybe at risk of long-term verbal memory impairment.

Modelling of inflatable rescue boats (IRBs) in surf conditions to reduce injuries

The Inflatable Rescue Boat (IRB) is arguably the most effective rescue tool used by the Australian surf lifesavers. The exceptional features of high mobility and rapid response have enabled it to become an icon on Australia's popular beaches. However, the IRB's extensive use within an environment that is as rugged as it is spectacular, has led it to become a danger to those who risk their lives to save others. Epidemiological research revealed lower limb injuries to be predominant, particularly the right leg. The common types of injuries were fractures and dislocations, as well as muscle or ligament strains and tears. The concern expressed by Surf Life Saving Queensland (SLSQ) and Surf Life Saving Australia (SLSA) led to a biomechanical investigation into this unique and relatively unresearched field. The aim of the research was to identify the causes of injury and propose processes that may reduce the instances and severity of injury to surf lifesavers during IRB operation. Following a review of related research, a design analysis of the craft was undertaken as an introduction to the craft, its design and uses. The mechanical characteristics of the vessel were then evaluated and the accelerations applied to the crew in the IRB were established through field tests. The data were then combined and modelled in the 3-D mathematical modelling and simulation package, MADYMO. A tool was created to compare various scenarios of boat design and methods of operation to determine possible mechanisms to reduce injuries. The results of this study showed that under simulated wave loading the boats flex around a pivot point determined by the position of the hinge in the floorboard. It was also found that the accelerations experienced by the crew exhibited similar characteristics to road vehicle accidents. Staged simulations indicated the attributes of an optimum foam in terms of thickness and density. Likewise, modelling of the boat and crew produced simulations that predicted realistic crew response to tested variables. Unfortunately, the observed lack of adherence to the SLSA footstrap Standard has impeded successful epidemiological and modelling outcomes. If uniformity of boat setup can be assured then epidemiological studies will be able to highlight the influence of implementing changes to the boat design. In conclusion, the research provided a tool to successfully link the epidemiology and injury diagnosis to the mechanical engineering design through the use of biomechanics. This was a novel application of the mathematical modelling software MADYMO. Other craft can also be investigated in this manner to provide solutions to the problem identified and therefore reduce risk of injury for the operators.

Modelling photochemical production of fine particulates in a toluene/NOx/water vapour system

This work investigates the computer modelling of the photochemical formation of smog products such as ozone and aerosol, in a system containing toluene, NOx and water vapour. In particular, the problem of modelling this process in the Commonwealth Scientific and Industrial Research Organization (CSIRO) smog chambers, which utilize outdoor exposure, is addressed. The primary requirement for such modelling is a knowledge of the photolytic rate coefficients. Photolytic rate coefficients of species other than N02 are often related to JNo2 (rate coefficient for the photolysis ofN02) by a simple factor, but for outdoor chambers, this method is prone to error as the diurnal profiles may not be similar in shape. Three methods for the calculation of diurnal JNo2 are investigated. The most suitable method for incorporation into a general model, is found to be one which determines the photolytic rate coefficients for N02, as well as several other species, from actinic flux, absorption cross section and quantum yields. A computer model was developed, based on this method, to calculate in-chamber photolysis rate coefficients for the CSIRO smog chambers, in which ex-chamber rate coefficients are adjusted by accounting for variation in light intensity by transmittance through the Teflon walls, albedo from the chamber floor and radiation attenuation due to clouds. The photochemical formation of secondary aerosol is investigated in a series of toluene-NOx experiments, which were performed in the CSIRO smog chambers. Three stages of aerosol formation, in plots of total particulate volume versus time, are identified: a delay period in which no significant mass of aerosol is formed, a regime of rapid aerosol formation (regime 1) and a second regime of slowed aerosol formation (regime 2). Two models are presented which were developed from the experimental data. One model is empirically based on observations of discrete stages of aerosol formation and readily allows aerosol growth profiles to be calculated. The second model is based on an adaptation of published toluene photooxidation mechanisms and provides some chemical information about the oxidation products. Both models compare favorably against the experimental data. The gross effects of precursor concentrations (toluene, NOx and H20) and ambient conditions (temperature, photolysis rate) on the formation of secondary aerosol are also investigated, primarily using the mechanism model. An increase in [NOx]o results in increased delay time, rate of aerosol formation in regime 1 and volume of aerosol formed in regime 1. This is due to increased formation of dinitrocresol and furanone products. An increase in toluene results in a decrease in the delay time and an increase in the rate of aerosol formation in regime 1, due to enhanced reactivity from the toluene products, such as the radicals from the photolysis of benzaldehyde. Water vapor has very little effect on the formation of aerosol volume, except that rates are slightly increased due to more OH radicals from reaction with 0(1D) from ozone photolysis. Increased temperature results in increased volume of aerosol formed in regime 1 (increased dinitrocresol formation), while increased photolysis rate results in increased rate of aerosol formation in regime 1. Both the rate and volume of aerosol formed in regime 2 are increased by increased temperature or photolysis rate. Both models indicate that the yield of secondary particulates from hydrocarbons (mass concentration aerosol formed/mass concentration hydrocarbon precursor) is proportional to the ratio [NOx]0/[hydrocarbon]0

Hierarchical models for 2D presence/absence data having ambiguous zeroes: With a biogeographical case study on dingo behaviour

This dissertation is primarily an applied statistical modelling investigation, motivated by a case study comprising real data and real questions. Theoretical questions on modelling and computation of normalization constants arose from pursuit of these data analytic questions. The essence of the thesis can be described as follows. Consider binary data observed on a two-dimensional lattice. A common problem with such data is the ambiguity of zeroes recorded. These may represent zero response given some threshold (presence) or that the threshold has not been triggered (absence). Suppose that the researcher wishes to estimate the effects of covariates on the binary responses, whilst taking into account underlying spatial variation, which is itself of some interest. This situation arises in many contexts and the dingo, cypress and toad case studies described in the motivation chapter are examples of this. Two main approaches to modelling and inference are investigated in this thesis. The first is frequentist and based on generalized linear models, with spatial variation modelled by using a block structure or by smoothing the residuals spatially. The EM algorithm can be used to obtain point estimates, coupled with bootstrapping or asymptotic MLE estimates for standard errors. The second approach is Bayesian and based on a three- or four-tier hierarchical model, comprising a logistic regression with covariates for the data layer, a binary Markov Random field (MRF) for the underlying spatial process, and suitable priors for parameters in these main models. The three-parameter autologistic model is a particular MRF of interest. Markov chain Monte Carlo (MCMC) methods comprising hybrid Metropolis/Gibbs samplers is suitable for computation in this situation. Model performance can be gauged by MCMC diagnostics. Model choice can be assessed by incorporating another tier in the modelling hierarchy. This requires evaluation of a normalization constant, a notoriously difficult problem. Difficulty with estimating the normalization constant for the MRF can be overcome by using a path integral approach, although this is a highly computationally intensive method. Different methods of estimating ratios of normalization constants (N Cs) are investigated, including importance sampling Monte Carlo (ISMC), dependent Monte Carlo based on MCMC simulations (MCMC), and reverse logistic regression (RLR). I develop an idea present though not fully developed in the literature, and propose the Integrated mean canonical statistic (IMCS) method for estimating log NC ratios for binary MRFs. The IMCS method falls within the framework of the newly identified path sampling methods of Gelman & Meng (1998) and outperforms ISMC, MCMC and RLR. It also does not rely on simplifying assumptions, such as ignoring spatio-temporal dependence in the process. A thorough investigation is made of the application of IMCS to the three-parameter Autologistic model. This work introduces background computations required for the full implementation of the four-tier model in Chapter 7. Two different extensions of the three-tier model to a four-tier version are investigated. The first extension incorporates temporal dependence in the underlying spatio-temporal process. The second extensions allows the successes and failures in the data layer to depend on time. The MCMC computational method is extended to incorporate the extra layer. A major contribution of the thesis is the development of a fully Bayesian approach to inference for these hierarchical models for the first time. Note: The author of this thesis has agreed to make it open access but invites people downloading the thesis to send her an email via the 'Contact Author' function.

Modelling and solving train scheduling problems under capacity constraints

Many large coal mining operations in Australia rely heavily on the rail network to transport coal from mines to coal terminals at ports for shipment. Over the last few years, due to the fast growing demand, the coal rail network is becoming one of the worst industrial bottlenecks in Australia. As a result, this provides great incentives for pursuing better optimisation and control strategies for the operation of the whole rail transportation system under network and terminal capacity constraints. This PhD research aims to achieve a significant efficiency improvement in a coal rail network on the basis of the development of standard modelling approaches and generic solution techniques. Generally, the train scheduling problem can be modelled as a Blocking Parallel- Machine Job-Shop Scheduling (BPMJSS) problem. In a BPMJSS model for train scheduling, trains and sections respectively are synonymous with jobs and machines and an operation is regarded as the movement/traversal of a train across a section. To begin, an improved shifting bottleneck procedure algorithm combined with metaheuristics has been developed to efficiently solve the Parallel-Machine Job- Shop Scheduling (PMJSS) problems without the blocking conditions. Due to the lack of buffer space, the real-life train scheduling should consider blocking or hold-while-wait constraints, which means that a track section cannot release and must hold a train until the next section on the routing becomes available. As a consequence, the problem has been considered as BPMJSS with the blocking conditions. To develop efficient solution techniques for BPMJSS, extensive studies on the nonclassical scheduling problems regarding the various buffer conditions (i.e. blocking, no-wait, limited-buffer, unlimited-buffer and combined-buffer) have been done. In this procedure, an alternative graph as an extension of the classical disjunctive graph is developed and specially designed for the non-classical scheduling problems such as the blocking flow-shop scheduling (BFSS), no-wait flow-shop scheduling (NWFSS), and blocking job-shop scheduling (BJSS) problems. By exploring the blocking characteristics based on the alternative graph, a new algorithm called the topological-sequence algorithm is developed for solving the non-classical scheduling problems. To indicate the preeminence of the proposed algorithm, we compare it with two known algorithms (i.e. Recursive Procedure and Directed Graph) in the literature. Moreover, we define a new type of non-classical scheduling problem, called combined-buffer flow-shop scheduling (CBFSS), which covers four extreme cases: the classical FSS (FSS) with infinite buffer, the blocking FSS (BFSS) with no buffer, the no-wait FSS (NWFSS) and the limited-buffer FSS (LBFSS). After exploring the structural properties of CBFSS, we propose an innovative constructive algorithm named the LK algorithm to construct the feasible CBFSS schedule. Detailed numerical illustrations for the various cases are presented and analysed. By adjusting only the attributes in the data input, the proposed LK algorithm is generic and enables the construction of the feasible schedules for many types of non-classical scheduling problems with different buffer constraints. Inspired by the shifting bottleneck procedure algorithm for PMJSS and characteristic analysis based on the alternative graph for non-classical scheduling problems, a new constructive algorithm called the Feasibility Satisfaction Procedure (FSP) is proposed to obtain the feasible BPMJSS solution. A real-world train scheduling case is used for illustrating and comparing the PMJSS and BPMJSS models. Some real-life applications including considering the train length, upgrading the track sections, accelerating a tardy train and changing the bottleneck sections are discussed. Furthermore, the BPMJSS model is generalised to be a No-Wait Blocking Parallel- Machine Job-Shop Scheduling (NWBPMJSS) problem for scheduling the trains with priorities, in which prioritised trains such as express passenger trains are considered simultaneously with non-prioritised trains such as freight trains. In this case, no-wait conditions, which are more restrictive constraints than blocking constraints, arise when considering the prioritised trains that should traverse continuously without any interruption or any unplanned pauses because of the high cost of waiting during travel. In comparison, non-prioritised trains are allowed to enter the next section immediately if possible or to remain in a section until the next section on the routing becomes available. Based on the FSP algorithm, a more generic algorithm called the SE algorithm is developed to solve a class of train scheduling problems in terms of different conditions in train scheduling environments. To construct the feasible train schedule, the proposed SE algorithm consists of many individual modules including the feasibility-satisfaction procedure, time-determination procedure, tune-up procedure and conflict-resolve procedure algorithms. To find a good train schedule, a two-stage hybrid heuristic algorithm called the SE-BIH algorithm is developed by combining the constructive heuristic (i.e. the SE algorithm) and the local-search heuristic (i.e. the Best-Insertion- Heuristic algorithm). To optimise the train schedule, a three-stage algorithm called the SE-BIH-TS algorithm is developed by combining the tabu search (TS) metaheuristic with the SE-BIH algorithm. Finally, a case study is performed for a complex real-world coal rail network under network and terminal capacity constraints. The computational results validate that the proposed methodology would be very promising because it can be applied as a fundamental tool for modelling and solving many real-world scheduling problems.

Monte Carlo modelling of X-ray absorptiometry and its application to body composition studies

This thesis applies Monte Carlo techniques to the study of X-ray absorptiometric methods of bone mineral measurement. These studies seek to obtain information that can be used in efforts to improve the accuracy of the bone mineral measurements. A Monte Carlo computer code for X-ray photon transport at diagnostic energies has been developed from first principles. This development was undertaken as there was no readily available code which included electron binding energy corrections for incoherent scattering and one of the objectives of the project was to study the effects of inclusion of these corrections in Monte Carlo models. The code includes the main Monte Carlo program plus utilities for dealing with input data. A number of geometrical subroutines which can be used to construct complex geometries have also been written. The accuracy of the Monte Carlo code has been evaluated against the predictions of theory and the results of experiments. The results show a high correlation with theoretical predictions. In comparisons of model results with those of direct experimental measurements, agreement to within the model and experimental variances is obtained. The code is an accurate and valid modelling tool. A study of the significance of inclusion of electron binding energy corrections for incoherent scatter in the Monte Carlo code has been made. The results show this significance to be very dependent upon the type of application. The most significant effect is a reduction of low angle scatter flux for high atomic number scatterers. To effectively apply the Monte Carlo code to the study of bone mineral density measurement by photon absorptiometry the results must be considered in the context of a theoretical framework for the extraction of energy dependent information from planar X-ray beams. Such a theoretical framework is developed and the two-dimensional nature of tissue decomposition based on attenuation measurements alone is explained. This theoretical framework forms the basis for analytical models of bone mineral measurement by dual energy X-ray photon absorptiometry techniques. Monte Carlo models of dual energy X-ray absorptiometry (DEXA) have been established. These models have been used to study the contribution of scattered radiation to the measurements. It has been demonstrated that the measurement geometry has a significant effect upon the scatter contribution to the detected signal. For the geometry of the models studied in this work the scatter has no significant effect upon the results of the measurements. The model has also been used to study a proposed technique which involves dual energy X-ray transmission measurements plus a linear measurement of the distance along the ray path. This is designated as the DPA( +) technique. The addition of the linear measurement enables the tissue decomposition to be extended to three components. Bone mineral, fat and lean soft tissue are the components considered here. The results of the model demonstrate that the measurement of bone mineral using this technique is stable over a wide range of soft tissue compositions and hence would indicate the potential to overcome a major problem of the two component DEXA technique. However, the results also show that the accuracy of the DPA( +) technique is highly dependent upon the composition of the non-mineral components of bone and has poorer precision (approximately twice the coefficient of variation) than the standard DEXA measurements. These factors may limit the usefulness of the technique. These studies illustrate the value of Monte Carlo computer modelling of quantitative X-ray measurement techniques. The Monte Carlo models of bone densitometry measurement have:- 1. demonstrated the significant effects of the measurement geometry upon the contribution of scattered radiation to the measurements, 2. demonstrated that the statistical precision of the proposed DPA( +) three tissue component technique is poorer than that of the standard DEXA two tissue component technique, 3. demonstrated that the proposed DPA(+) technique has difficulty providing accurate simultaneous measurement of body composition in terms of a three component model of fat, lean soft tissue and bone mineral,4. and provided a knowledge base for input to decisions about development (or otherwise) of a physical prototype DPA( +) imaging system. The Monte Carlo computer code, data, utilities and associated models represent a set of significant, accurate and valid modelling tools for quantitative studies of physical problems in the fields of diagnostic radiology and radiography.

Real-time performance modelling of a sustained attention to response task

Vigilance declines when exposed to highly predictable and uneventful tasks. Monotonous tasks provide little cognitive and motor stimulation and contribute to human errors. This paper aims to model and detect vigilance decline in real time through participant’s reaction times during a monotonous task. A lab-based experiment adapting the Sustained Attention to Response Task (SART) is conducted to quantify the effect of monotony on overall performance. Then relevant parameters are used to build a model detecting hypovigilance throughout the experiment. The accuracy of different mathematical models are compared to detect in real-time – minute by minute - the lapses in vigilance during the task. We show that monotonous tasks can lead to an average decline in performance of 45%. Furthermore, vigilance modelling enables to detect vigilance decline through reaction times with an accuracy of 72% and a 29% false alarm rate. Bayesian models are identified as a better model to detect lapses in vigilance as compared to Neural Networks and Generalised Linear Mixed Models. This modelling could be used as a framework to detect vigilance decline of any human performing monotonous tasks.

Preliminary modelling outcomes : calculation of holding costs in greenfield residential development

Many of the costs associated with greenfield residential development are apparent and tangible. For example, regulatory fees, government taxes, acquisition costs, selling fees, commissions and others are all relatively easily identified since they represent actual costs incurred at a given point in time. However, identification of holding costs are not always immediately evident since by contrast they characteristically lack visibility. One reason for this is that, for the most part, they are typically assessed over time in an ever-changing environment. In addition, wide variations exist in development pipeline components: they are typically represented from anywhere between a two and over sixteen years time period - even if located within the same geographical region. Determination of the starting and end points, with regards holding cost computation, can also prove problematic. Furthermore, the choice between application of prevailing inflation, or interest rates, or a combination of both over time, adds further complexity. Although research is emerging in these areas, a review of the literature reveals attempts to identify holding cost components are limited. Their quantification (in terms of relative weight or proportionate cost to a development project) is even less apparent; in fact, the computation and methodology behind the calculation of holding costs varies widely and in some instances completely ignored. In addition, it may be demonstrated that ambiguities exists in terms of the inclusion of various elements of holding costs and assessment of their relative contribution. Yet their impact on housing affordability is widely acknowledged to be profound, with their quantification potentially maximising the opportunities for delivering affordable housing. This paper seeks to build on earlier investigations into those elements related to holding costs, providing theoretical modelling of the size of their impact - specifically on the end user. At this point the research is reliant upon quantitative data sets, however additional qualitative analysis (not included here) will be relevant to account for certain variations between expectations and actual outcomes achieved by developers. Although this research stops short of cross-referencing with a regional or international comparison study, an improved understanding of the relationship between holding costs, regulatory charges, and housing affordability results.

Widening the gap between measurement and modelling of secondary organic aerosol properties?

The link between measured sub-saturated hygroscopicity and cloud activation potential of secondary organic aerosol particles produced by the chamber photo-oxidation of α-pinene in the presence or absence of ammonium sulphate seed aerosol was investigated using two models of varying complexity. A simple single hygroscopicity parameter model and a more complex model (incorporating surface effects) were used to assess the detail required to predict the cloud condensation nucleus (CCN) activity from the subsaturated water uptake. Sub-saturated water uptake measured by three hygroscopicity tandem differential mobility analyser (HTDMA) instruments was used to determine the water activity for use in the models. The predicted CCN activity was compared to the measured CCN activation potential using a continuous flow CCN counter. Reconciliation using the more complex model formulation with measured cloud activation could be achieved widely different assumed surface tension behavior of the growing droplet; this was entirely determined by the instrument used as the source of water activity data. This unreliable derivation of the water activity as a function of solute concentration from sub-saturated hygroscopicity data indicates a limitation in the use of such data in predicting cloud condensation nucleus behavior of particles with a significant organic fraction. Similarly, the ability of the simpler single parameter model to predict cloud activation behaviour was dependent on the instrument used to measure sub-saturated hygroscopicity and the relative humidity used to provide the model input. However, agreement was observed for inorganic salt solution particles, which were measured by all instruments in agreement with theory. The difference in HTDMA data from validated and extensively used instruments means that it cannot be stated with certainty the detail required to predict the CCN activity from sub-saturated hygroscopicity. In order to narrow the gap between measurements of hygroscopic growth and CCN activity the processes involved must be understood and the instrumentation extensively quality assured. It is impossible to say from the results presented here due to the differences in HTDMA data whether: i) Surface tension suppression occurs ii) Bulk to surface partitioning is important iii) The water activity coefficient changes significantly as a function of the solute concentration.