Notes on the hydrology of the Waikato River

The catchment area of the Waikato River is 5,500 square miles. If its source is accepted as being the Upper Waikato, then its distance to the sea at Port Waikato including its journey through Lake Taupo is 266 miles. It rises, together with the Whangaehu, the Rangitikei and the Wanganui, between the volcanic region of Ruapehu 9,000 ft. above sea level and the Kaimanawa Ranges 5,000 ft. above sea level. The river flows northwards for 34 miles into Lake Taupo, losing its identity into the Tongariro for the last 26 miles to the lake. It emerges from Lake Taupo resuming its proper name and, still flowing northwards, passes for more than 100 miles through a series of lakes formed by hydroelectric dams to Cambridge. From here it continues through a deeply incised channel to Ngaruawahia where it is joined by its major tributary, the Waipa River. From Ngaruawahia to the mouth, a distance of 60 miles, shallow lakes and peat swamps predominate on both sides of the river, many of them protected and drained and developed into rich dairy farms. From Mercer, 35 miles downstream of Ngaruawahia, where slight tidal effects are discernable at low flows, the river changes its general northerly direction to a westerly one and, still 9 miles from the mouth, enters the delta. Here it is fragmented into many channels before emptying into the broad expanse of Maioro Bay and finally emerges by two fairly narrow channels into the sea on the west coast, 25 miles south of Manukau Heads

Rethinking Metacognitive Intervention: A Scaffolded Exam Wrapper Strategy

Students lack the behaviors and strategies that support success in postsecondary environments, which has led one-third of all college students to enroll in remedial courses (Bowen, Chingos, & McPherson, 2009). One particular executive function that low-achieving students are often without is metacognition, or thinking about thinking. Traditional models of education in the United States do not teach students how to analyze their performance even though metacognition is linked to improved academic performance (Young & Fry, 2008). This work presents a scaffolded metacognitive strategy to help low-achieving students improve their metacognitive skillfulness and examination performance

Bayesian sequential experimental design for binary response data with application to electromyographic experiments

We develop a sequential Monte Carlo approach for Bayesian analysis of the experimental design for binary response data. Our work is motivated by surface electromyographic (SEMG) experiments, which can be used to provide information about the functionality of subjects' motor units. These experiments involve a series of stimuli being applied to a motor unit, with whether or not the motor unit res for each stimulus being recorded. The aim is to learn about how the probability of ring depends on the applied stimulus (the so-called stimulus response curve); One such excitability parameter is an estimate of the stimulus level for which the motor unit has a 50% chance of ring. Within such an experiment we are able to choose the next stimulus level based on the past observations. We show how sequential Monte Carlo can be used to analyse such data in an online manner. We then use the current estimate of the posterior distribution in order to choose the next stimulus level. The aim is to select a stimulus level that mimimises the expected loss. We will apply this loss function to the estimates of target quantiles from the stimulus-response curve. Through simulation we show that this approach is more ecient than existing sequential design methods for choosing the stimulus values. If applied in practice, it could more than halve the length of SEMG experiments

Motor unit number estimation via sequential Monte Carlo

A change in the number of motor units that operate a particular muscle is an important indicator for the progress of a neuromuscular disease and the efficacy of a therapy. Inference for realistic statistical models of the typical data produced when testing muscle function is difficult, and estimating the number of motor units is an ongoing statistical challenge. We consider a set of models for the data, each with a different number of working motor units, and present a novel method for Bayesian inference based on sequential Monte Carlo. This provides estimates of the marginal likelihood and, hence, a posterior probability for each model. Implementing this approach in practice requires a sequential Monte Carlo method that has excellent computational and Monte Carlo properties. We achieve this by benefiting from the model's conditional independence structure, where, given knowledge of which motor units fired as a result of a particular stimulus, parameters that specify the size of each unit's response are independent of the parameters defining the probability that a unit will respond at all. The scalability of our methodology relies on the natural conjugacy structure that we create for the former and an enforced, approximate, conjugate structure for the latter. A simulation study demonstrates the accuracy of our method, and inferences are consistent across two different datasets arising from the same rat tibial muscle

Biomarkers in motor neuron disease: A state of the art review

Motor neuron disease can be viewed as an umbrella term describing a heterogeneous group of conditions, all of which are relentlessly progressive and ultimately fatal. The average life expectancy is 2 years, but with a broad range of months to decades. Biomarker research deepens disease understanding through exploration of pathophysiological mechanisms which, in turn, highlights targets for novel therapies. It also allows differentiation of the disease population into sub-groups, which serves two general purposes: (a) provides clinicians with information to better guide their patients in terms of disease progression, and (b) guides clinical trial design so that an intervention may be shown to be effective if population variation is controlled for. Biomarkers also have the potential to provide monitoring during clinical trials to ensure target engagement. This review highlights biomarkers that have emerged from the fields of systemic measurements including biochemistry (blood, cerebrospinal fluid, and urine analysis); imaging and electrophysiology, and gives examples of how a combinatorial approach may yield the best results. We emphasize the importance of systematic sample collection and analysis, and the need to correlate biomarker findings with detailed phenotype and genotype data

Motor Unit Number Estimation - A Bayesian Approach

All muscle contractions are dependent on the functioning of motor units. In diseases such as amyotrophic lateral sclerosis (ALS), progressive loss of motor units leads to gradual paralysis. A major difficulty in the search for a treatment for these diseases has been the lack of a reliable measure of disease progression. One possible measure would be an estimate of the number of surviving motor units. Despite over 30 years of motor unit number estimation (MUNE), all proposed methods have been met with practical and theoretical objections. Our aim is to develop a method of MUNE that overcomes these objections. We record the compound muscle action potential (CMAP) from a selected muscle in response to a graded electrical stimulation applied to the nerve. As the stimulus increases, the threshold of each motor unit is exceeded, and the size of the CMAP increases until a maximum response is obtained. However, the threshold potential required to excite an axon is not a precise value but fluctuates over a small range leading to probabilistic activation of motor units in response to a given stimulus. When the threshold ranges of motor units overlap, there may be alternation where the number of motor units that fire in response to the stimulus is variable. This means that increments in the value of the CMAP correspond to the firing of different combinations of motor units. At a fixed stimulus, variability in the CMAP, measured as variance, can be used to conduct MUNE using the "statistical" or the "Poisson" method. However, this method relies on the assumptions that the numbers of motor units that are firing probabilistically have the Poisson distribution and that all single motor unit action potentials (MUAP) have a fixed and identical size. These assumptions are not necessarily correct. We propose to develop a Bayesian statistical methodology to analyze electrophysiological data to provide an estimate of motor unit numbers. Our method of MUNE incorporates the variability of the threshold, the variability between and within single MUAPs, and baseline variability. Our model not only gives the most probable number of motor units but also provides information about both the population of units and individual units. We use Markov chain Monte Carlo to obtain information about the characteristics of individual motor units and about the population of motor units and the Bayesian information criterion for MUNE. We test our method of MUNE on three subjects. Our method provides a reproducible estimate for a patient with stable but severe ALS. In a serial study, we demonstrate a decline in the number of motor unit numbers with a patient with rapidly advancing disease. Finally, with our last patient, we show that our method has the capacity to estimate a larger number of motor units

2003 Membership Survey: The Report

The Queensland Law Society survey of members provides a snapshot of the Queensland legal profession in 2003 including perceptions from within the profession as to discrimination and other factors affecting their workforce. The survey was an initiative of the Equalising Opportunities Committee of the Queensland Law Society and was distributed with the membership renewal forms in early 2003. This report tabulates and analyses the main findings

Bayesian Latent Variable Models for Biostatistical Applications

In this thesis we develop several kinds of latent variable models in order to address three types of bio-statistical problem. The three problems are the treatment effect of carcinogens on tumour development, spatial interactions between plant species and motor unit number estimation (MUNE). The three types of data looked at are: highly heterogeneous longitudinal count data, quadrat counts of species on a rectangular lattice and lastly, electrophysiological data consisting of measurements of compound muscle action potential (CMAP) area and amplitude. Chapter 1 sets out the structure and the development of ideas presented in this thesis from the point of view of: model structure, model selection, and efficiency of estimation. Chapter 2 is an introduction to the relevant literature that has in influenced the development of this thesis. In Chapter 3 we use the EM algorithm for an application of an autoregressive hidden Markov model to describe longitudinal counts. The data is collected from experiments to test the effect of carcinogens on tumour growth in mice. Here we develop forward and backward recursions for calculating the likelihood and for estimation. Chapter 4 is the analysis of a similar kind of data using a more sophisticated model, incorporating random effects, but estimation this time is conducted from the Bayesian perspective. Bayesian model selection is also explored. In Chapter 5 we move to the two dimensional lattice and construct a model for describing the spatial interaction of tree types. We also compare the merits of directed and undirected graphical models for describing the hidden lattice. Chapter 6 is the application of a Bayesian hierarchical model (MUNE), where the latent variable this time is multivariate Gaussian and dependent on a covariate, the stimulus. Model selection is carried out using the Bayes Information Criterion (BIC). In Chapter 7 we approach the same problem by using the reversible jump methodology (Green, 1995) where this time we use a dual Gaussian-Binary representation of the latent data. We conclude in Chapter 8 with suggestions for the direction of new work. In this thesis, all of the estimation carried out on real data has only been performed once we have been satisfied that estimation is able to retrieve the parameters from simulated data. Keywords: Amyotrophic lateral sclerosis (ALS), carcinogens, hidden Markov models (HMM), latent variable models, longitudinal data analysis, motor unit disease (MND), partially ordered Markov models (POMMs), the pseudo auto- logistic model, reversible jump, spatial interactions