Thesis (Ph. D.)--University of Virginia, 2000. / Spine title: Disruption of inhibition in epilepsy. Includes bibliographical references (p. 186-207). Also available online through Digital Dissertations.

The probabilistic (or quantitative) modal μ-calculus is a fixed-point logic designed for expressing properties of probabilistic labeled transition systems (PLTS’s). Two semantics have been studied for this logic, both assigning to every process state a value in the interval [0, 1] representing the probability that the property expressed by the formula holds at the state. One semantics is denotational and the other is a game semantics, specified in terms of two-player stochastic games. The two semantics have been proved to coincide on all finite PLTS’s. A first contribution of the thesis is to extend this coincidence result to arbitrary PLTS’s. A shortcoming of the probabilistic μ-calculus is the lack of expressiveness required to encode other important temporal logics for PLTS’s such as Probabilistic Computation Tree Logic (PCTL). To address this limitation, we extend the logic with a new pair of operators: independent product and coproduct, and we show that the resulting logic can encode the qualitative fragment of PCTL. Moreover, a further extension of the logic, with the operation of truncated sum and its dual, is expressive enough to encode full PCTL. A major contribution of the thesis is the definition of appropriate game semantics for these extended probabilistic μ-calculi. This relies on the definition of a new class of games, called tree games, which generalize standard 2-player stochastic games. In tree games, a play can be split into concurrent subplays which continue their evolution independently. Surprisingly, this simple device supports the encoding of the whole class of imperfect-information games known as Blackwell games. Moreover, interesting open problems in game theory, such as qualitative determinacy for 2-player stochastic parity games, can be reformulated as determinacy problems for suitable classes of tree games. Our main technical result about tree games is a proof of determinacy for 2-player stochastic metaparity games, which is the class of tree games that we use to give game semantics to the extended probabilistic μ-calculi. In order to cope with measure-theoretic technicalities, the proof is carried out in ZFC set theory extended with Martin’s Axiom at the first uncountable cardinal (MAℵ1). The final result of the thesis shows that the game semantics of the extended logics coincides with the denotational semantics, for arbitrary PLTS’s. However, in contrast to the earlier coincidence result, which is proved in ZFC, the proof of coincidence for the extended calculi is once again carried out in ZFC +MAℵ1.

The main topic of this thesis is how to combine model outputs from deterministic models with measurements from monitoring stations for air pollutants or other meteorological variables. We consider two different approaches to address this particular problem. The first approach is by using the Bayesian Melding (BM) model proposed by Fuentes and Raftery (2005). We successfully implement this model and conduct several simulation studies to examine the performance of this model in different scenarios. We also apply the melding model to the ozone data to show the importance of using the Bayesian melding model to calibrate the model outputs. That is, to adjust the model outputs for the prediction of measurements. Due to the Bayesian framework of the melding model, we can extend it to incorporate other components such as ensemble models, reversible jump MCMC for variable selection. However, the BM model is purely a spatial model and we generally have to deal with space-time dataset in practice. The deficiency of the BM approach leads us to a second approach, an alternative to the BM model, which is a linear mixed model (different from most linear mixed models, the random effects being spatially correlated) with temporally and spatially correlated residuals. We assume the spatial and temporal correlation are separable and use an AR process to model the temporal correlation. We also develop a multivariate version of this model. Both the melding model and linear mixed model are Bayesian hierarchical models, which can better estimate the uncertainties of the estimates and predictions.

The main topic of this thesis is how to combine model outputs from deterministic models with measurements from monitoring stations for air pollutants or other meteorological variables. We consider two different approaches to address this particular problem. The first approach is by using the Bayesian Melding (BM) model proposed by Fuentes and Raftery (2005). We successfully implement this model and conduct several simulation studies to examine the performance of this model in different scenarios. We also apply the melding model to the ozone data to show the importance of using the Bayesian melding model to calibrate the model outputs. That is, to adjust the model outputs for the prediction of measurements. Due to the Bayesian framework of the melding model, we can extend it to incorporate other components such as ensemble models, reversible jump MCMC for variable selection. However, the BM model is purely a spatial model and we generally have to deal with space-time dataset in practice. The deficiency of the BM approach leads us to a second approach, an alternative to the BM model, which is a linear mixed model (different from most linear mixed models, the random effects being spatially correlated) with temporally and spatially correlated residuals. We assume the spatial and temporal correlation are separable and use an AR process to model the temporal correlation. We also develop a multivariate version of this model. Both the melding model and linear mixed model are Bayesian hierarchical models, which can better estimate the uncertainties of the estimates and predictions.

The main topic of this thesis is how to combine model outputs from deterministic models with measurements from monitoring stations for air pollutants or other meteorological variables. We consider two different approaches to address this particular problem. The first approach is by using the Bayesian Melding (BM) model proposed by Fuentes and Raftery (2005). We successfully implement this model and conduct several simulation studies to examine the performance of this model in different scenarios. We also apply the melding model to the ozone data to show the importance of using the Bayesian melding model to calibrate the model outputs. That is, to adjust the model outputs for the prediction of measurements. Due to the Bayesian framework of the melding model, we can extend it to incorporate other components such as ensemble models, reversible jump MCMC for variable selection. However, the BM model is purely a spatial model and we generally have to deal with space-time dataset in practice. The deficiency of the BM approach leads us to a second approach, an alternative to the BM model, which is a linear mixed model (different from most linear mixed models, the random effects being spatially correlated) with temporally and spatially correlated residuals. We assume the spatial and temporal correlation are separable and use an AR process to model the temporal correlation. We also develop a multivariate version of this model. Both the melding model and linear mixed model are Bayesian hierarchical models, which can better estimate the uncertainties of the estimates and predictions. / Science, Faculty of / Statistics, Department of / Graduate

The heightened research activity in the interdisciplinary field of network science can be attributed to the emergence of the social network computer applications. Researchers understood early on that data describing how entities interconnect is highly valuable and that it offers a deeper understanding about the entities themselves. This is why there were so many studies done about various kinds of networks in the last 10-15 years. The study of the networks from the perspective of computer science usually has two objectives. The first objective is to develop statistical mechanisms capable of accurately describing and modeling observed real-world networks. A good fit of such mechanism suggests the correctness of the model's assumptions and leads to better understanding of the network. A second goal is more practical, a well performing model can be used to predict what will happen to the network in the future. Also, such model can be leveraged to use the information gleaned from network to predict what will happen to the networks entities. One important leitmotif of network research and analysis is wide adaptation of log linear models. In this work we apply this philosophy for study and evaluation of log-linear statistical models in various types of networks. We begin with proposal of the new Temporal Exponential Random Graph Model (tERGM) for the analysis and predictions in the binary temporal social networks. We then extended the model for applications in partially observed networks that change over time. Lastly, we generalize the tERGM model to predict the real-valued weighted links in the temporal non-social networks. The log-linear models are not limited to networks that change over time but can also be applied to networks that are static. One such static network is a social network composed of patients undergoing hemodialysis. Hemodialysis is prescribed to people suffering from the end stage renal disease; the treatment necessitates the attendance, on non-changing schedule, of the hemodialysis clinic for a prolonged time period and this is how the social ties are formed. The new log-linear Social Latent Vectors (SLV) model was applied to study such static social networks. The results obtained from SLV experiments suggest that social relationships formed by patients bear influence on individual patients clinical outcome. The study demonstrates how social network analysis can be applied to better understand the network constituents. / Computer and Information Science

Eco-geomorphic interactions occur across a range of spatial and temporal scales from the level of the entire watershed to an individual geomorphic unit within a stream channel. Predicting the mechanisms, rates and timing of sediment production and storage in the landscape are fundamental problems in the watershed sciences. This is of particular concern given that excess sedimentation is considered a major pollutant to aquatic ecosystems. Rates of sediment delivery to stream networks are characteristically unsteady and non-uniform. Because of this, conventional approaches for predicting sediment yield provide incomplete and often inaccurate information. Terrestrial cosmogenic nuclides (TCNs) provide an estimate of spatially averaged rates of sediment yield from 101 to 104 km2 and temporally integrated from 103 to 105 years. Here, I used TCNs to constrain unsteadiness and non-uniformity of sediment yield within specific catchments of the Columbia River Basin (CRB). This is in combination with GIS analysis optically stimulated luminescence (OSL), Carbon-14 (C14) dating of fluvial deposits, and rapid geomorphic assessments. Results showed an order of magnitude spatial variability in the rates of millennial-scale sediment yield at the scale of the entire CRB. At the broadest scale long-term rates of sediment yield generally are poorly predicted from topographic and environmental parameters. A notable exception is the observed positive correlation between mean annual precipitation and sediment yield. Where functional relationships exist, the nature of those relationships are scale and situation-dependent. In addition to the broadest scale, each smaller watershed (e.g., ~ 10 – 2,000 km2) has a distinct geologic, geomorphic, and disturbance history that sets the template for the modern sediment dynamics and the physical aspects of aquatic habitat. Chapter 2 presents results of broad-scale trends while Chapter 3 is comprised of case studies from smaller watersheds. Finally, Chapter 4 explores the relationship between long-term sediment yield and modern channel form.