Design of experiments for bivariate binary responses modelled by Copula functions

Optimal design for generalized linear models has primarily focused on univariate data. Often experiments are performed that have multiple dependent responses described by regression type models, and it is of interest and of value to design the experiment for all these responses. This requires a multivariate distribution underlying a pre-chosen model for the data. Here, we consider the design of experiments for bivariate binary data which are dependent. We explore Copula functions which provide a rich and flexible class of structures to derive joint distributions for bivariate binary data. We present methods for deriving optimal experimental designs for dependent bivariate binary data using Copulas, and demonstrate that, by including the dependence between responses in the design process, more efficient parameter estimates are obtained than by the usual practice of simply designing for a single variable only. Further, we investigate the robustness of designs with respect to initial parameter estimates and Copula function, and also show the performance of compound criteria within this bivariate binary setting.

Krylov subspace approximations for the exponential Euler method: Error estimates and the harmonic Ritz approximant

We study Krylov subspace methods for approximating the matrix-function vector product φ(tA)b where φ(z) = [exp(z) - 1]/z. This product arises in the numerical integration of large stiff systems of differential equations by the Exponential Euler Method, where A is the Jacobian matrix of the system. Recently, this method has found application in the simulation of transport phenomena in porous media within mathematical models of wood drying and groundwater flow. We develop an a posteriori upper bound on the Krylov subspace approximation error and provide a new interpretation of a previously published error estimate. This leads to an alternative Krylov approximation to φ(tA)b, the so-called Harmonic Ritz approximant, which we find does not exhibit oscillatory behaviour of the residual error.

Optimistic linear programming gives logarithmic regret for irreducible MDPs

We present an algorithm called Optimistic Linear Programming (OLP) for learning to optimize average reward in an irreducible but otherwise unknown Markov decision process (MDP). OLP uses its experience so far to estimate the MDP. It chooses actions by optimistically maximizing estimated future rewards over a set of next-state transition probabilities that are close to the estimates, a computation that corresponds to solving linear programs. We show that the total expected reward obtained by OLP up to time T is within C(P) log T of the reward obtained by the optimal policy, where C(P) is an explicit, MDP-dependent constant. OLP is closely related to an algorithm proposed by Burnetas and Katehakis with four key differences: OLP is simpler, it does not require knowledge of the supports of transition probabilities, the proof of the regret bound is simpler, but our regret bound is a constant factor larger than the regret of their algorithm. OLP is also similar in flavor to an algorithm recently proposed by Auer and Ortner. But OLP is simpler and its regret bound has a better dependence on the size of the MDP.

Evaluating multivariate volatility forecasts : how effective are statistical and economic loss functions?

Multivariate volatility forecasts are an important input in many financial applications, in particular portfolio optimisation problems. Given the number of models available and the range of loss functions to discriminate between them, it is obvious that selecting the optimal forecasting model is challenging. The aim of this thesis is to thoroughly investigate how effective many commonly used statistical (MSE and QLIKE) and economic (portfolio variance and portfolio utility) loss functions are at discriminating between competing multivariate volatility forecasts. An analytical investigation of the loss functions is performed to determine whether they identify the correct forecast as the best forecast. This is followed by an extensive simulation study examines the ability of the loss functions to consistently rank forecasts, and their statistical power within tests of predictive ability. For the tests of predictive ability, the model confidence set (MCS) approach of Hansen, Lunde and Nason (2003, 2011) is employed. As well, an empirical study investigates whether simulation findings hold in a realistic setting. In light of these earlier studies, a major empirical study seeks to identify the set of superior multivariate volatility forecasting models from 43 models that use either daily squared returns or realised volatility to generate forecasts. This study also assesses how the choice of volatility proxy affects the ability of the statistical loss functions to discriminate between forecasts. Analysis of the loss functions shows that QLIKE, MSE and portfolio variance can discriminate between multivariate volatility forecasts, while portfolio utility cannot. An examination of the effective loss functions shows that they all can identify the correct forecast at a point in time, however, their ability to discriminate between competing forecasts does vary. That is, QLIKE is identified as the most effective loss function, followed by portfolio variance which is then followed by MSE. The major empirical analysis reports that the optimal set of multivariate volatility forecasting models includes forecasts generated from daily squared returns and realised volatility. Furthermore, it finds that the volatility proxy affects the statistical loss functions’ ability to discriminate between forecasts in tests of predictive ability. These findings deepen our understanding of how to choose between competing multivariate volatility forecasts.

Linear models for endocytic transformations from live cell imaging

Endocytosis is the process by which cells internalise molecules including nutrient proteins from the extracellular media. In one form, macropinocytosis, the membrane at the cell surface ruffles and folds over to give rise to an internalised vesicle. Negatively charged phospholipids within the membrane called phosphoinositides then undergo a series of transformations that are critical for the correct trafficking of the vesicle within the cell, and which are often pirated by pathogens such as Salmonella. Advanced fluorescent video microscopy imaging now allows the detailed observation and quantification of these events in live cells over time. Here we use these observations as a basis for building differential equation models of the transformations. An initial investigation of these interactions was modelled with reaction rates proportional to the sum of the concentrations of the individual constituents. A first order linear system for the concentrations results. The structure of the system enables analytical expressions to be obtained and the problem becomes one of determining the reaction rates which generate the observed data plots. We present results with reaction rates which capture the general behaviour of the reactions so that we now have a complete mathematical model of phosphoinositide transformations that fits the experimental observations. Some excellent fits are obtained with modulated exponential functions; however, these are not solutions of the linear system. The question arises as to how the model may be modified to obtain a system whose solution provides a more accurate fit.

Representational change and strategy use in children's number line estimation during the first years of primary school

Background: The objective of this study was to scrutinize number line estimation behaviors displayed by children in mathematics classrooms during the first three years of schooling. We extend existing research by not only mapping potential logarithmic-linear shifts but also provide a new perspective by studying in detail the estimation strategies of individual target digits within a number range familiar to children. Methods: Typically developing children (n = 67) from Years 1 – 3 completed a number-to-position numerical estimation task (0-20 number line). Estimation behaviors were first analyzed via logarithmic and linear regression modeling. Subsequently, using an analysis of variance we compared the estimation accuracy of each digit, thus identifying target digits that were estimated with the assistance of arithmetic strategy. Results: Our results further confirm a developmental logarithmic-linear shift when utilizing regression modeling; however, uniquely we have identified that children employ variable strategies when completing numerical estimation, with levels of strategy advancing with development. Conclusion: In terms of the existing cognitive research, this strategy factor highlights the limitations of any regression modeling approach, or alternatively, it could underpin the developmental time course of the logarithmic-linear shift. Future studies need to systematically investigate this relationship and also consider the implications for educational practice.

Event-related brain potentials dissociate the developmental time-course of automatic numerical magnitude analysis and cognitive control functions during the first three years of primary school

In this study we set out to dissociate the developmental time course of automatic symbolic number processing and cognitive control functions in grade 1-3 British primary school children. Event-related potential (ERP) and behavioral data were collected in a physical size discrimination numerical Stroop task. Task-irrelevant numerical information was processed automatically already in grade 1. Weakening interference and strengthening facilitation indicated the parallel development of general cognitive control and automatic number processing. Relationships among ERP and behavioral effects suggest that control functions play a larger role in younger children and that automaticity of number processing increases from grade 1 to 3.

Structural damage detection using frequency response functions and neural networks

This paper illustrates the damage identification and condition assessment of a three story bookshelf structure using a new frequency response functions (FRFs) based damage index and Artificial Neural Networks (ANNs). A major obstacle of using measured frequency response function data is a large size input variables to ANNs. This problem is overcome by applying a data reduction technique called principal component analysis (PCA). In the proposed procedure, ANNs with their powerful pattern recognition and classification ability were used to extract damage information such as damage locations and severities from measured FRFs. Therefore, simple neural network models are developed, trained by Back Propagation (BP), to associate the FRFs with the damage or undamaged locations and severity of the damage of the structure. Finally, the effectiveness of the proposed method is illustrated and validated by using the real data provided by the Los Alamos National Laboratory, USA. The illustrated results show that the PCA based artificial Neural Network method is suitable and effective for damage identification and condition assessment of building structures. In addition, it is clearly demonstrated that the accuracy of proposed damage detection method can also be improved by increasing number of baseline datasets and number of principal components of the baseline dataset.

Structural damage identification with noise polluted Frequency Response Functions (FRFs)

Damage detection in structures has become increasingly important in recent years. While a number of damage detection and localization methods have been proposed, very few attempts have been made to explore the structure damage with noise polluted data which is unavoidable effect in real world. The measurement data are contaminated by noise because of test environment as well as electronic devices and this noise tend to give error results with structural damage identification methods. Therefore it is important to investigate a method which can perform better with noise polluted data. This paper introduces a new damage index using principal component analysis (PCA) for damage detection of building structures being able to accept noise polluted frequency response functions (FRFs) as input. The FRF data are obtained from the function datagen of MATLAB program which is available on the web site of the IASC-ASCE (International Association for Structural Control– American Society of Civil Engineers) Structural Health Monitoring (SHM) Task Group. The proposed method involves a five-stage process: calculation of FRFs, calculation of damage index values using proposed algorithm, development of the artificial neural networks and introducing damage indices as input parameters and damage detection of the structure. This paper briefly describes the methodology and the results obtained in detecting damage in all six cases of the benchmark study with different noise levels. The proposed method is applied to a benchmark problem sponsored by the IASC-ASCE Task Group on Structural Health Monitoring, which was developed in order to facilitate the comparison of various damage identification methods. The illustrated results show that the PCA-based algorithm is effective for structural health monitoring with noise polluted FRFs which is of common occurrence when dealing with industrial structures.

Quantitative studies of lower motor neuron degeneration in amyotrophic lateral sclerosis : Evidence for exponential decay of motor unit numbers and greatest rate of loss at the site of onset

Objective: To use our Bayesian method of motor unit number estimation (MUNE) to evaluate lower motor neuron degeneration in ALS. Methods: In subjects with ALS we performed serial MUNE studies. We examined the repeatability of the test and then determined whether the loss of MUs was fitted by an exponential or Weibull distribution. Results: The decline in motor unit (MU) numbers was well-fitted by an exponential decay curve. We calculated the half life of MUs in the abductor digiti minimi (ADM), abductor pollicis brevis (APB) and/or extensor digitorum brevis (EDB) muscles. The mean half life of the MUs of ADM muscle was greater than those of the APB or EDB muscles. The half-life of MUs was less in the ADM muscle of subjects with upper limb than in those with lower limb onset. Conclusions: The rate of loss of lower motor neurons in ALS is exponential, the motor units of the APB decay more quickly than those of the ADM muscle and the rate of loss of motor units is greater at the site of onset of disease. Significance: This shows that the Bayesian MUNE method is useful in following the course and exploring the clinical features of ALS. 2012 International Federation of Clinical Neurophysiology.

A variable-stepsize Jacobian-free exponential integrator for simulating transport in heterogeneous porous media : application to wood drying

A Jacobian-free variable-stepsize method is developed for the numerical integration of the large, stiff systems of differential equations encountered when simulating transport in heterogeneous porous media. Our method utilises the exponential Rosenbrock-Euler method, which is explicit in nature and requires a matrix-vector product involving the exponential of the Jacobian matrix at each step of the integration process. These products can be approximated using Krylov subspace methods, which permit a large integration stepsize to be utilised without having to precondition the iterations. This means that our method is truly "Jacobian-free" - the Jacobian need never be formed or factored during the simulation. We assess the performance of the new algorithm for simulating the drying of softwood. Numerical experiments conducted for both low and high temperature drying demonstrates that the new approach outperforms (in terms of accuracy and efficiency) existing simulation codes that utilise the backward Euler method via a preconditioned Newton-Krylov strategy.

A comparison of safety climate and safety outcomes between construction and resource functions in a large case study organisation

The research described in this paper forms part of an in-depth investigation of safety culture in one of Australia’s largest construction companies. The research builds on a previous qualitative study with organisational safety leaders and further investigates how safety culture is perceived and experienced by organisational members, as well as how this relates to their safety behaviour and related outcomes at work. Participants were 2273 employees of the case study organisation, with 689 from the Construction function and 1584 from the Resources function. The results of several analyses revealed some interesting organisational variance on key measures. Specifically, the Construction function scored significantly higher on all key measures: safety climate, safety motivation, safety compliance, and safety participation. The results are discussed in terms of relevance in an applied research context.