The widespread use of ordinary differential equation (ODE) models has long been underrepresented in the statistical literature. The most common methods for estimating parameters from ODE models are nonlinear least squares and an MCMC based method. Both of these methods depend on a likelihood involving the numerical solution to the ODE. The challenge faced by these methods is parameter spaces that are difficult to navigate, exacerbated by the wide variety of behaviours that a single ODE model can produce with respect to small changes in parameter values. / In this work, two competing methods, generalized profile estimation and Bayesian collocation tempering are described. Both of these methods use a basis expansion to approximate the ODE solution in the likelihood, where the shape of the basis expansion, or data smooth, is guided by the ODE model. This approximation to the ODE, smooths out the likelihood surface, reducing restrictions on parameter movement. / Generalized Profile Estimation maximizes the profile likelihood for the ODE parameters while profiling out the basis coefficients of the data smooth. The smoothing parameter determines the balance between fitting the data and the ODE model, and consequently is used to build a parameter cascade, reducing the dimension of the estimation problem. Generalized profile estimation is described with under a constraint to ensure the smooth follows known behaviour such as monotonicity or non-negativity. / Bayesian collocation tempering, uses a sequence posterior densities with smooth approximations to the ODE solution. The level of the approximation is determined by the value of the smoothing parameter, which also determines the level of smoothness in the likelihood surface. In an algorithm similar to parallel tempering, parallel MCMC chains are run to sample from the sequence of posterior densities, while allowing ODE parameters to swap between chains. This method is introduced and tested against a variety of alternative Bayesian models, in terms of posterior variance and rate of convergence. / The performance of generalized profile estimation and Bayesian collocation tempering are tested and compared using simulated data sets from the FitzHugh-Nagumo ODE system and real data from nylon production dynamics.

Hierarchical task decompositions play an essential role in the design of complex simulation and decision systems, such as the ones that arise in video games. Game designers find it very natural to adopt a divide-and-conquer philosophy of specifying hierarchical policies, where decision modules can be constructed somewhat independently. The process of choosing the parameters of these modules manually is typically lengthy and tedious. The hierarchical reinforcement learning (HRL) field has produced elegant ways of decomposing policies and value functions using semi-Markov decision processes. However, there is still a lack of demonstrations in larger nonlinear systems with discrete and continuous variables. To narrow this gap between industrial practices and academic ideas, we address the problem of designing efficient algorithms to facilitate the deployment of HRL ideas in more realistic settings. In particular, we propose Bayesian active learning methods to learn the relevant aspects of either policies or value functions by focusing on the most relevant parts of the parameter and state spaces respectively. To demonstrate the scalability of our solution, we have applied it to The Open Racing Car Simulator (TORCS), a 3D game engine that implements complex vehicle dynamics. The environment is a large topological map roughly based on downtown Vancouver, British Columbia. Higher level abstract tasks are also learned in this process using a model-based extension of the MAXQ algorithm. Our solution demonstrates how HRL can be scaled to large applications with complex, discrete and continuous non-linear dynamics.

The need of today�s society for new technology has resulted in the development of a growing number of software systems. Developing a software system is a complex endeavour that requires a large amount of time. This amount of time is referred to as software development effort. Software development effort is the sum of hours spent by all individuals involved. Therefore, it is not equal to the duration of the development. Accurate prediction of the effort at an early stage of development is an important factor in the successful completion of a software system, since it enables the developing organization to allocate and manage their resource effectively. However, for many software systems, accurately predicting the effort is a challenge. Hence, a model that assists in the prediction is of active interest to software practitioners and researchers alike. Software development effort varies depending on many variables that are specific to the system, its developmental environment and the organization in which it is being developed. An accurate model for predicting software development effort can often be built specifically for the target system and its developmental environment. A local dataset of similar systems to the target system, developed in a similar environment, is then used to calibrate the model. However, such a dataset often consists of fewer than 10 software systems, causing a serious problem in the prediction, since predictive accuracy of existing models deteriorates as the size of the dataset decreases. This research addressed this problem with a new approach using Bayesian statistics. This particular approach was chosen, since the predictive accuracy of a Bayesian statistical model is not so dependent on a large dataset as other models. As the size of the dataset decreases to fewer than 10 software systems, the accuracy deterioration of the model is expected to be less than that of existing models. The Bayesian statistical model can also provide additional information useful for predicting software development effort, because it is also capable of selecting important variables from multiple candidates. In addition, it is parametric and produces an uncertainty estimate. This research developed new Bayesian statistical models for predicting software development effort. Their predictive accuracy was then evaluated in four case studies using different datasets, and compared with other models applicable to the same small dataset. The results have confirmed that the best new models are not only accurate but also consistently more accurate than their regression counterpart, when calibrated with fewer than 10 systems. They can thus replace the regression model when using small datasets. Furthermore, one case study has shown that the best new models are more accurate than a simple model that predicts the effort by calculating the average value of the calibration data. Two case studies has also indicated that the best new models can be more accurate for some software systems than a case-based reasoning model. Since the case studies provided sufficient empirical evidence that the new models are generally more accurate than existing models compared, in the case of small datasets, this research has produced a methodology for predicting software development effort using the new models.

An important mechanism during nervous system development is the guidance of axons by chemical gradients. The structure responsible for responding to chemical cues in the embryonic environment is the axonal growth cone -- a structure combining sensory and motor functions to direct axon growth. In this thesis, we develop a series of mathematical models for the gradient-based guidance of axonal growth cones, based on the idea that growth cones might be optimised for such a task. In particular, we study axon guidance from the framework of Bayesian decision theory, an approach that has recently proved to be very successful in understanding higher level sensory processing problems. We build our models in complexity, beginning with a one-dimensional array of chemoreceptors simply trying to decide whether an external gradient points to the right or the left. Even with this highly simplified model, we can obtain a good fit of theory to experiment. Furthermore, we find that the information a growth cone can obtain about the locations of its receptors has a strong influence on the functional dependence of gradient sensing performance on average concentration. We find that the shape of the sensitivity curve is robust to changes in the precise inference strategy used to determine gradient detection, and depends only on the information the growth cone can obtain about the locations of its receptors. We then consider the optimal distribution of guidance cues for guidance over long range, and find that the same upper limit on guidance distance is reached regardless of whether only bound, or only unbound receptors signal. We also discuss how information from multiple cues ought to be combined for optimal guidance. In chapters 5 and 6, we extend our model to two-dimensions, and to explicitly include temporal dynamics. The two-dimensional case yields results which are essentially equivalent to the one dimensional model. In contrast, explicitly including temporal dynamics in our leads to some significant departures from the one-dimensional and two-dimensional models, depending on the timescales over which various processes operate. Overall, we suggest that decision theory, in addition to providing a useful normative approach to studying growth cone chemotaxis, might provide a framework for understanding some of the biochemical pathways involved in growth cone chemotaxis, and in the chemotaxis of other eukaryotic cells.

Thesis (M.S.)--Ohio University, August, 2007. / Title from PDF t.p. Includes bibliographical references.

Thesis (Ph. D.)--University of Nevada, Reno, 2006. / "August, 2006." Includes bibliographical references (leaves 124-135). Online version available on the World Wide Web.

Thesis (Ph. D.)--Ohio State University, 2007. / Title from first page of PDF file. Includes bibliographical references (p. 168-180).

Thesis (Ph. D.)--Brigham Young University. Dept. of Computer Science, 2007. / Includes bibliographical references (p. 203-209).

Univ., Diss.--Utrecht.

Thesis (Ph.D.)--Michigan State University. Dept. of Statistics, 2008. / Title from PDF t.p. (viewed on Mar. 27, 2009) Includes bibliographical references (p.114-122). Also issued in print.