Seeing the Wood for the Trees: A Critical Evaluation of Methods to Estimate the Parameters of Stochastic Differential Equations

Maximum-likelihood estimates of the parameters of stochastic differential equations are consistent and asymptotically efficient, but unfortunately difficult to obtain if a closed-form expression for the transitional probability density function of the process is not available. As a result, a large number of competing estimation procedures have been proposed. This article provides a critical evaluation of the various estimation techniques. Special attention is given to the ease of implementation and comparative performance of the procedures when estimating the parameters of the Cox–Ingersoll–Ross and Ornstein–Uhlenbeck equations respectively.

The contribution of maize cropping in the Midwest USA to global warming: A regional estimate

Agricultural soils emit about 50% of the global flux of N2O attributable to human influence, mostly in response to nitrogen fertilizer use. Recent evidence that the relationship between N2O fluxes and N-fertilizer additions to cereal maize are non-linear provides an opportunity to estimate regional N2O fluxes based on estimates of N application rates rather than as a simple percentage of N inputs as used by the Intergovernmental Panel on Climate Change (IPCC). We combined a simple empirical model of N2O production with the SOCRATES soil carbon dynamics model to estimate N2O and other sources of Global Warming Potential (GWP) from cereal maize across 19,000 cropland polygons in the North Central Region (NCR) of the US over the period 1964–2005. Results indicate that the loading of greenhouse gases to the atmosphere from cereal maize production in the NCR was 1.7 Gt CO2e, with an average 268 t CO2e produced per tonne of grain. From 1970 until 2005, GHG emissions per unit product declined on average by 2.8 t CO2e ha−1 annum−1, coinciding with a stabilisation in N application rate and consistent increases in grain yield from the mid-1970’s. Nitrous oxide production from N fertilizer inputs represented 59% of these emissions, soil C decline (0–30 cm) represented 11% of total emissions, with the remaining 30% (517 Mt) from the combustion of fuel associated with farm operations. Of the 126 Mt of N fertilizer applied to cereal maize from 1964 to 2005, we estimate that 2.2 Mt N was emitted as N2O when using a non-linear response model, equivalent to 1.75% of the applied N.

On the optimality of sample-based estimates of the expectation of the empirical minimizer

We study sample-based estimates of the expectation of the function produced by the empirical minimization algorithm. We investigate the extent to which one can estimate the rate of convergence of the empirical minimizer in a data dependent manner. We establish three main results. First, we provide an algorithm that upper bounds the expectation of the empirical minimizer in a completely data-dependent manner. This bound is based on a structural result due to Bartlett and Mendelson, which relates expectations to sample averages. Second, we show that these structural upper bounds can be loose, compared to previous bounds. In particular, we demonstrate a class for which the expectation of the empirical minimizer decreases as O(1/n) for sample size n, although the upper bound based on structural properties is Ω(1). Third, we show that this looseness of the bound is inevitable: we present an example that shows that a sharp bound cannot be universally recovered from empirical data.

The Bayesian conditional independence model for measurement error: applications in ecology

The measurement error model is a well established statistical method for regression problems in medical sciences, although rarely used in ecological studies. While the situations in which it is appropriate may be less common in ecology, there are instances in which there may be benefits in its use for prediction and estimation of parameters of interest. We have chosen to explore this topic using a conditional independence model in a Bayesian framework using a Gibbs sampler, as this gives a great deal of flexibility, allowing us to analyse a number of different models without losing generality. Using simulations and two examples, we show how the conditional independence model can be used in ecology, and when it is appropriate.

Error analysis and attitude observability of a monocular GPS/visual odometry integrated navigation filter

In this paper, we present a method for the recovery of position and absolute attitude (including pitch, roll and yaw) using a novel fusion of monocular Visual Odometry and GPS measurements in a similar manner to a classic loosely-coupled GPS/INS error state navigation filter. The proposed filter does not require additional restrictions or assumptions such as platform-specific dynamics, map-matching, feature-tracking, visual loop-closing, gravity vector or additional sensors such as an IMU or magnetic compass. An observability analysis of the proposed filter is performed, showing that the scale factor, position and attitude errors are fully observable under acceleration that is non-parallel to velocity vector in the navigation frame. The observability properties of the proposed filter are demonstrated using numerical simulations. We conclude the article with an implementation of the proposed filter using real flight data collected from a Cessna 172 equipped with a downwards-looking camera and GPS, showing the feasibility of the algorithm in real-world conditions.

Performance control of distributed generation using digital estimation of signal parameters

The Queensland University of Technology (QUT) allows the presentation of a thesis for the Degree of Doctor of Philosophy in the format of published or submitted papers, where such papers have been published, accepted or submitted during the period of candidature. This thesis is composed of seven published/submitted papers, of which one has been published, three accepted for publication and the other three are under review. This project is financially supported by an Australian Research Council (ARC) Discovery Grant with the aim of proposing strategies for the performance control of Distributed Generation (DG) system with digital estimation of power system signal parameters. Distributed Generation (DG) has been recently introduced as a new concept for the generation of power and the enhancement of conventionally produced electricity. Global warming issue calls for renewable energy resources in electricity production. Distributed generation based on solar energy (photovoltaic and solar thermal), wind, biomass, mini-hydro along with use of fuel cell and micro turbine will gain substantial momentum in the near future. Technically, DG can be a viable solution for the issue of the integration of renewable or non-conventional energy resources. Basically, DG sources can be connected to local power system through power electronic devices, i.e. inverters or ac-ac converters. The interconnection of DG systems to power system as a compensator or a power source with high quality performance is the main aim of this study. Source and load unbalance, load non-linearity, interharmonic distortion, supply voltage distortion, distortion at the point of common coupling in weak source cases, source current power factor, and synchronism of generated currents or voltages are the issues of concern. The interconnection of DG sources shall be carried out by using power electronics switching devices that inject high frequency components rather than the desired current. Also, noise and harmonic distortions can impact the performance of the control strategies. To be able to mitigate the negative effect of high frequency and harmonic as well as noise distortion to achieve satisfactory performance of DG systems, new methods of signal parameter estimation have been proposed in this thesis. These methods are based on processing the digital samples of power system signals. Thus, proposing advanced techniques for the digital estimation of signal parameters and methods for the generation of DG reference currents using the estimates provided is the targeted scope of this thesis. An introduction to this research – including a description of the research problem, the literature review and an account of the research progress linking the research papers – is presented in Chapter 1. One of the main parameters of a power system signal is its frequency. Phasor Measurement (PM) technique is one of the renowned and advanced techniques used for the estimation of power system frequency. Chapter 2 focuses on an in-depth analysis conducted on the PM technique to reveal its strengths and drawbacks. The analysis will be followed by a new technique proposed to enhance the speed of the PM technique while the input signal is free of even-order harmonics. The other techniques proposed in this thesis as the novel ones will be compared with the PM technique comprehensively studied in Chapter 2. An algorithm based on the concept of Kalman filtering is proposed in Chapter 3. The algorithm is intended to estimate signal parameters like amplitude, frequency and phase angle in the online mode. The Kalman filter is modified to operate on the output signal of a Finite Impulse Response (FIR) filter designed by a plain summation. The frequency estimation unit is independent from the Kalman filter and uses the samples refined by the FIR filter. The frequency estimated is given to the Kalman filter to be used in building the transition matrices. The initial settings for the modified Kalman filter are obtained through a trial and error exercise. Another algorithm again based on the concept of Kalman filtering is proposed in Chapter 4 for the estimation of signal parameters. The Kalman filter is also modified to operate on the output signal of the same FIR filter explained above. Nevertheless, the frequency estimation unit, unlike the one proposed in Chapter 3, is not segregated and it interacts with the Kalman filter. The frequency estimated is given to the Kalman filter and other parameters such as the amplitudes and phase angles estimated by the Kalman filter is taken to the frequency estimation unit. Chapter 5 proposes another algorithm based on the concept of Kalman filtering. This time, the state parameters are obtained through matrix arrangements where the noise level is reduced on the sample vector. The purified state vector is used to obtain a new measurement vector for a basic Kalman filter applied. The Kalman filter used has similar structure to a basic Kalman filter except the initial settings are computed through an extensive math-work with regards to the matrix arrangement utilized. Chapter 6 proposes another algorithm based on the concept of Kalman filtering similar to that of Chapter 3. However, this time the initial settings required for the better performance of the modified Kalman filter are calculated instead of being guessed by trial and error exercises. The simulations results for the parameters of signal estimated are enhanced due to the correct settings applied. Moreover, an enhanced Least Error Square (LES) technique is proposed to take on the estimation when a critical transient is detected in the input signal. In fact, some large, sudden changes in the parameters of the signal at these critical transients are not very well tracked by Kalman filtering. However, the proposed LES technique is found to be much faster in tracking these changes. Therefore, an appropriate combination of the LES and modified Kalman filtering is proposed in Chapter 6. Also, this time the ability of the proposed algorithm is verified on the real data obtained from a prototype test object. Chapter 7 proposes the other algorithm based on the concept of Kalman filtering similar to those of Chapter 3 and 6. However, this time an optimal digital filter is designed instead of the simple summation FIR filter. New initial settings for the modified Kalman filter are calculated based on the coefficients of the digital filter applied. Also, the ability of the proposed algorithm is verified on the real data obtained from a prototype test object. Chapter 8 uses the estimation algorithm proposed in Chapter 7 for the interconnection scheme of a DG to power network. Robust estimates of the signal amplitudes and phase angles obtained by the estimation approach are used in the reference generation of the compensation scheme. Several simulation tests provided in this chapter show that the proposed scheme can very well handle the source and load unbalance, load non-linearity, interharmonic distortion, supply voltage distortion, and synchronism of generated currents or voltages. The purposed compensation scheme also prevents distortion in voltage at the point of common coupling in weak source cases, balances the source currents, and makes the supply side power factor a desired value.

The effect of simulated astigmatic refractive error on reading performance

Background: Few studies have specifically investigated the functional effects of uncorrected astigmatism on measures of reading fluency. This information is important to provide evidence for the development of clinical guidelines for the correction of astigmatism. Methods: Participants included 30 visually normal, young adults (mean age 21.7 ± 3.4 years). Distance and near visual acuity and reading fluency were assessed with optimal spectacle correction (baseline) and for two levels of astigmatism, 1.00DC and 2.00DC, at two axes (90° and 180°) to induce both against-the-rule (ATR) and with-the-rule (WTR) astigmatism. Reading and eye movement fluency were assessed using standardized clinical measures including the test of Discrete Reading Rate (DRR), the Developmental Eye Movement (DEM) test and by recording eye movement patterns with the Visagraph (III) during reading for comprehension. Results: Both distance and near acuity were significantly decreased compared to baseline for all of the astigmatic lens conditions (p < 0.001). Reading speed with the DRR for N16 print size was significantly reduced for the 2.00DC ATR condition (a reduction of 10%), while for smaller text sizes reading speed was reduced by up to 24% for the 1.00DC ATR and 2.00DC condition in both axis directions (p<0.05). For the DEM, sub-test completion speeds were significantly impaired, with the 2.00DC condition affecting both vertical and horizontal times and the 1.00DC ATR condition affecting only horizontal times (p<0.05). Visagraph reading eye movements were not significantly affected by the induced astigmatism. Conclusions: Induced astigmatism impaired performance on selected tests of reading fluency, with ATR astigmatism having significantly greater effects on performance than did WTR, even for relatively small amounts of astigmatic blur of 1.00DC. These findings have implications for the minimal prescribing criteria for astigmatic refractive errors.

Adaptive cache aware multiprocessor scheduling framework

Computer resource allocation represents a significant challenge particularly for multiprocessor systems, which consist of shared computing resources to be allocated among co-runner processes and threads. While an efficient resource allocation would result in a highly efficient and stable overall multiprocessor system and individual thread performance, ineffective poor resource allocation causes significant performance bottlenecks even for the system with high computing resources. This thesis proposes a cache aware adaptive closed loop scheduling framework as an efficient resource allocation strategy for the highly dynamic resource management problem, which requires instant estimation of highly uncertain and unpredictable resource patterns. Many different approaches to this highly dynamic resource allocation problem have been developed but neither the dynamic nature nor the time-varying and uncertain characteristics of the resource allocation problem is well considered. These approaches facilitate either static and dynamic optimization methods or advanced scheduling algorithms such as the Proportional Fair (PFair) scheduling algorithm. Some of these approaches, which consider the dynamic nature of multiprocessor systems, apply only a basic closed loop system; hence, they fail to take the time-varying and uncertainty of the system into account. Therefore, further research into the multiprocessor resource allocation is required. Our closed loop cache aware adaptive scheduling framework takes the resource availability and the resource usage patterns into account by measuring time-varying factors such as cache miss counts, stalls and instruction counts. More specifically, the cache usage pattern of the thread is identified using QR recursive least square algorithm (RLS) and cache miss count time series statistics. For the identified cache resource dynamics, our closed loop cache aware adaptive scheduling framework enforces instruction fairness for the threads. Fairness in the context of our research project is defined as a resource allocation equity, which reduces corunner thread dependence in a shared resource environment. In this way, instruction count degradation due to shared cache resource conflicts is overcome. In this respect, our closed loop cache aware adaptive scheduling framework contributes to the research field in two major and three minor aspects. The two major contributions lead to the cache aware scheduling system. The first major contribution is the development of the execution fairness algorithm, which degrades the co-runner cache impact on the thread performance. The second contribution is the development of relevant mathematical models, such as thread execution pattern and cache access pattern models, which in fact formulate the execution fairness algorithm in terms of mathematical quantities. Following the development of the cache aware scheduling system, our adaptive self-tuning control framework is constructed to add an adaptive closed loop aspect to the cache aware scheduling system. This control framework in fact consists of two main components: the parameter estimator, and the controller design module. The first minor contribution is the development of the parameter estimators; the QR Recursive Least Square(RLS) algorithm is applied into our closed loop cache aware adaptive scheduling framework to estimate highly uncertain and time-varying cache resource patterns of threads. The second minor contribution is the designing of a controller design module; the algebraic controller design algorithm, Pole Placement, is utilized to design the relevant controller, which is able to provide desired timevarying control action. The adaptive self-tuning control framework and cache aware scheduling system in fact constitute our final framework, closed loop cache aware adaptive scheduling framework. The third minor contribution is to validate this cache aware adaptive closed loop scheduling framework efficiency in overwhelming the co-runner cache dependency. The timeseries statistical counters are developed for M-Sim Multi-Core Simulator; and the theoretical findings and mathematical formulations are applied as MATLAB m-file software codes. In this way, the overall framework is tested and experiment outcomes are analyzed. According to our experiment outcomes, it is concluded that our closed loop cache aware adaptive scheduling framework successfully drives co-runner cache dependent thread instruction count to co-runner independent instruction count with an error margin up to 25% in case cache is highly utilized. In addition, thread cache access pattern is also estimated with 75% accuracy.

Thresholds for error probability measures of business process models

The quality of conceptual business process models is highly relevant for the design of corresponding information systems. In particular, a precise measurement of model characteristics can be beneficial from a business perspective, helping to save costs thanks to early error detection. This is just as true from a software engineering point of view. In this latter case, models facilitate stakeholder communication and software system design. Research has investigated several proposals as regards measures for business process models, from a rather correlational perspective. This is helpful for understanding, for example size and complexity as general driving forces of error probability. Yet, design decisions usually have to build on thresholds, which can reliably indicate that a certain counter-action has to be taken. This cannot be achieved only by providing measures; it requires a systematic identification of effective and meaningful thresholds. In this paper, we derive thresholds for a set of structural measures for predicting errors in conceptual process models. To this end, we use a collection of 2,000 business process models from practice as a means of determining thresholds, applying an adaptation of the ROC curves method. Furthermore, an extensive validation of the derived thresholds was conducted by using 429 EPC models from an Australian financial institution. Finally, significant thresholds were adapted to refine existing modeling guidelines in a quantitative way.

Error correction in second language writing : teachers’ beliefs, practices, and students’ preferences

Error correction is perhaps the most widely used method for responding to student writing. While various studies have investigated the effectiveness of providing error correction, there has been relatively little research incorporating teachers' beliefs, practices, and students' preferences in written error correction. The current study adopted features of an ethnographic research design in order to explore the beliefs and practices of ESL teachers, and investigate the preferences of L2 students regarding written error correction in the context of a language institute situated in the Brisbane metropolitan district. In this study, two ESL teachers and two groups of adult intermediate L2 students were interviewed and observed. The beliefs and practices of the teachers were elicited through interviews and classroom observations. The preferences of L2 students were elicited through focus group interviews. Responses of the participants were encoded and analysed. Results of the teacher interviews showed that teachers believe that providing written error correction has advantages and disadvantages. Teachers believe that providing written error correction helps students improve their proof-reading skills in order to revise their writing more efficiently. However, results also indicate that providing written error correction is very time consuming. Furthermore, teachers prefer to provide explicit written feedback strategies during the early stages of the language course, and move to a more implicit strategy of providing written error correction in order to facilitate language learning. On the other hand, results of the focus group interviews suggest that students regard their teachers' practice of written error correction as important in helping them locate their errors and revise their writing. However, students also feel that the process of providing written error correction is time consuming. Nevertheless, students want and expect their teachers to provide written feedback because they believe that the benefits they gain from receiving feedback on their writing outweigh the apparent disadvantages of their teachers' written error correction strategies.

Can partial coherence interferometry be used to determine retinal shape?

Purpose: To determine likely errors in estimating retinal shape using partial coherence interferometric instruments when no allowance is made for optical distortion. Method: Errors were estimated using Gullstrand’s No. 1 schematic eye and variants which included a 10 D axial myopic eye, an emmetropic eye with a gradient-index lens, and a 10.9 D accommodating eye with a gradient-index lens. Performance was simulated for two commercial instruments, the IOLMaster (Carl Zeiss Meditec) and the Lenstar LS 900 (Haag-Streit AG). The incident beam was directed towards either the centre of curvature of the anterior cornea (corneal-direction method) or the centre of the entrance pupil (pupil-direction method). Simple trigonometry was used with the corneal intercept and the incident beam angle to estimate retinal contour. Conics were fitted to the estimated contours. Results: The pupil-direction method gave estimates of retinal contour that were much too flat. The cornea-direction method gave similar results for IOLMaster and Lenstar approaches. The steepness of the retinal contour was slightly overestimated, the exact effects varying with the refractive error, gradient index and accommodation. Conclusion: These theoretical results suggest that, for field angles ≤30º, partial coherence interferometric instruments are of use in estimating retinal shape by the corneal-direction method with the assumptions of a regular retinal shape and no optical distortion. It may be possible to improve on these estimates out to larger field angles by using optical modeling to correct for distortion.