In parametrized continuous state-space models, one can obtain estimates of the likelihood of the data for fixed parameters via the Sequential Monte Carlo methodology. Unfortunately, even if the likelihood is continuous in the parameters, the estimates produced by practical particle filters are not, even when common random numbers are used for each filter. This is because the same resampling step which drastically reduces the variance of the estimates also introduces discontinuities in the particles that are selected across filters when the parameters change. When the state variables are univariate, a method exists that gives an estimator of the log-likelihood that is continuous in the parameters. We present a non-trivial generalization of this method using tree-based o(N²) (and as low as O(N log N)) resampling schemes that induce significant correlation amongst the selected particles across filters. In turn, this reduces the variance of the difference between the likelihood evaluated for different values of the parameters and the resulting estimator is considerably smoother than naively running the filters with common random numbers. Importantly, in practice our methods require only a change to the resample operation in the SMC framework without the addition of any extra parameters and can therefore be used for any application in which particle filters are already used. In addition, excepting the optional use of interpolation in the schemes, there are no regularity conditions for their use although certain conditions make them more advantageous. In this thesis, we first introduce the relevant aspects of the SMC methodology to the task of likelihood estimation in continuous state-space models and present an overview of work related to the task of smooth likelihood estimation. Following this, we introduce theoretically correct resampling schemes that cannot be implemented and the practical tree-based resampling schemes that were developed instead. After presenting the performance of our schemes in various applications, we show that two of the schemes are asymptotically consistent with the theoretically correct but unimplementable methods introduced earlier. Finally, we conclude the thesis with a discussion.

Entry into elementary school marks the beginning of a crucial shift in the amount and quality of time that children spend with their peers (Coie & Dodge, 1988). For many 5-year olds, kindergarten provides the opportunity to encounter their first stable peer group. It is in the context of these interactions that children practice essential social skills, as well as develop a capacity to interact with others. For various reasons, however, many children have difficulty gaining acceptance into fundamental peer groups. For these children, the opportunities for peer interactions present in the early school years are limited and often characterized by a high degree of aggressive affect (Coie & Dodge, 1988). Although previous research has reliably identified the individual affective states characteristic of rejected children during a typical peer interaction (Newcomb, Bukowski, & Pattee, 1993), it should be kept in mind that these expressions are embedded within a larger peer context, which plays an important role in how these dynamic processes unfold in real time (O’Connell, Pepler, & Craig, 1999). The purpose of the present study was to explore the application of a dynamic systems (DS) technique, state space grids (SSG), to the study of kindergarten peer processes and their impact on long-term psychopathology. Participants were 267 kindergarten children from a single school serving a predominantly low socioeconomic neighbourhood. In order to examine the social dynamics of interacting triads, moment-to-moment changes in affect were documented. Parent and teacher ratings of child conduct problems were also obtained at four measurement points. Consistent with previous research, both controversial and rejected children were more likely to express aggressive affect. Differential effects across sociometric groups were also replicated for both externalizing and internalizing ratings, where rejected children were found to have significantly higher scores. Extending upon past research, the expression of particular triadic affective states were found to differ significantly across sociometric groups. Furthermore, specific triadic affective states were found to be related to the developmental trajectories of clinical outcomes. Overall, results of the present study extend previous findings on the expression of individual affective states through the application of DS principles and methodology. / Thesis (Master, Psychology) -- Queen's University, 2010-09-20 22:48:51.92

Discrete-Event systems (DES) is a framework in which problems are modelled as finite-state automata and a solution in the form of a supervisory control scheme can be automatically synthesized via an exhaustive search through the state space of the system. Various extensions to the standard DES framework have been introduced to allow it to be applied to a greater variety of problems. When the system in question is very large or varies with time, a limited lookahead policy can be adopted, in which control decisions are made on-the-fly by looking at finite-step projections of the behaviour of the system's underlying automata. This work presents a new approach to limited lookahead supervision which incorporates many of the extensions to DES that are already present in the literature, such as event probability and string desirability. When dealing with a limited lookahead technique, the projected system behaviour is represented as a lookahead tree with some depth limit decided on by the user. It can be difficult to strike a balance between the complexities associated with storing and analyzing the trees and the amount of information available to make decisions, both of which increase with depth. This work also presents a set of methods which are designed to aid in accurately estimating the state space of lookahead trees with the intent of simplifying the process of determining a favourable depth to use. Finally, the approaches introduced herein are applied to a simulation of an infectious disease outbreak, primarily to showcase them in action, but also for the possibility of illuminating any useful information for real-world health units. / Thesis (Master, Computing) -- Queen's University, 2012-01-20 19:35:58.007

With complex systems, monolithic models become impractical and it becomes necessary to model them through subsystems and components. Unless these components and subsystems are structured, exploiting them in a methodical manner to develop a control logic for them also becomes complex. In the previous research, to characterize the input/output behavior of discrete state interacting, systems a condition language framework was defined and algorithms that can automatically generate a controller given the system model and the desired specification using this framework were presented. Though this framework and the control algorithms are ideally suited to simple systems, representation of components with large state spaces requires a more refined approach. In this thesis, we present the modelling framework namely Color condition systems, that compactly represent components with large state spaces. We also present algorithms that can automatically generate a controller that consists of a set of action type taskblocks, given the system model and the desired specification described using color condition systems. The modelling framework and the working of the algorithms are illustrated using figures and comments on the possible ways of optimizing the algorithms are also quoted. Finally, in the appendix, we also present the approach that can be taken to implement a few parts of the algorithm.

In parametrized continuous state-space models, one can obtain estimates of the likelihood of the data for fixed parameters via the Sequential Monte Carlo methodology. Unfortunately, even if the likelihood is continuous in the parameters, the estimates produced by practical particle filters are not, even when common random numbers are used for each filter. This is because the same resampling step which drastically reduces the variance of the estimates also introduces discontinuities in the particles that are selected across filters when the parameters change. When the state variables are univariate, a method exists that gives an estimator of the log-likelihood that is continuous in the parameters. We present a non-trivial generalization of this method using tree-based o(N²) (and as low as O(N log N)) resampling schemes that induce significant correlation amongst the selected particles across filters. In turn, this reduces the variance of the difference between the likelihood evaluated for different values of the parameters and the resulting estimator is considerably smoother than naively running the filters with common random numbers. Importantly, in practice our methods require only a change to the resample operation in the SMC framework without the addition of any extra parameters and can therefore be used for any application in which particle filters are already used. In addition, excepting the optional use of interpolation in the schemes, there are no regularity conditions for their use although certain conditions make them more advantageous. In this thesis, we first introduce the relevant aspects of the SMC methodology to the task of likelihood estimation in continuous state-space models and present an overview of work related to the task of smooth likelihood estimation. Following this, we introduce theoretically correct resampling schemes that cannot be implemented and the practical tree-based resampling schemes that were developed instead. After presenting the performance of our schemes in various applications, we show that two of the schemes are asymptotically consistent with the theoretically correct but unimplementable methods introduced earlier. Finally, we conclude the thesis with a discussion.

Thesis (Ph. D.)--Ohio University, November, 1995. / Title from PDF t.p.

Thesis (Ph.D.)--Physics, Georgia Institute of Technology, 2009. / Committee Chair: Cvitanovic, Predrag; Committee Member: Bracco, Annalisa; Committee Member: Dieci, Luca; Committee Member: Goldman, Daniel; Committee Member: Grigoriev, Roman

Thesis (M. S.)--Mechanical Engineering, Georgia Institute of Technology, 2009. / Committee Chair: Sadegh, Nader; Committee Member: Chen, Xu-Yan; Committee Member: Chen, Ye-Hwa. Part of the SMARTech Electronic Thesis and Dissertation Collection.

Thesis (M.S.)--Rochester Institute of Technology, 1994. / Typescript. Includes bibliographical references (leaves 103-104).

Thesis (Ph.D.) - University of St Andrews, April 2009.