A Markov chain model for the early stochastic phase of the transmission of an infectious pathogen is studied, investigating its properties in the case of an isolated population and of two coupled populations with explicit movement of infectious individuals. Travel was found to play a role in the early development and spread of an infectious disease, particularly in the case of differing basic reproduction numbers in the connected locations. / February 2017

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Diss. Stockholm : Handelshögskolan, 2006.

Determining safe yield of an existing water supply is a basic aspect of water supply planning. Where water is withdrawn from a river directly without any storage, the withdrawal is constrained by the worst drought flow in the river. There is no flexibility for operational adjustments other than implementing conservation measures. Where there is a storage reservoir, yields higher than the flow in the source stream can be maintained for a period of time by releasing the water in storage. The determination of safe yield in this situation requires elaborate computation. This thesis presents a synthesis of methods of drought flow analysis and yield estimation. The yield depends on both the magnitude of the deficit and its temporal distribution. A new Markov chain analysis for assessing frequencies of annual flows is proposed. The Markov chain results compare very well with the empirical data analysis. Another advantage of the Markov chain analysis is that both high and low flows are considered simultaneously; no separate analyses for the lower and upper tails of the distribution are necessary. The temporal distribution of drought flows is considered with the aid of the generalized bootstrap method, time series analysis, and cluster sequencing of worsening droughts called Waitt's procedure. The methods are applied to drought inflows for three different water supply reservoirs in Spotsylvania County, Virginia, and different yield estimates are obtained. / Master of Science

Bayesian analysis is definitely different from the classic statistical methods. Although, both of them use subjective ideas, it is used in the selection of models in the classic statistical methods, rather than as an explicit part in Bayesian models, which allows the combination of subjective ideas with the data collected, update the prior information and improve inferences. Drastic growth of Bayesian applications indicates it becomes more and more popular, because the advent of computational methods (e.g., MCMC) renders sophisticated analysis. In Bayesian framework, the flexibility and generality allows it to cope with very complex problems. One big obstacle in earlier Bayesian analysis is how to sample from the usually complex posterior distribution. With modern techniques and fast-developed computation capacity, we now have tools to solve this problem. We discuss Acceptance-Rejection sampling, importance sampling and then the MCMC methods. Metropolis-Hasting algorithm, as a very versatile, efficient and powerful simulation technique to construct a Markov Chain, borrows the idea from the well-known acceptance-rejection sampling to generate candidates that are either accepted or rejected, but then retains the current values when rejection takes place (1). A special case of Metropolis-Hasting algorithm is Gibbs Sampler. When dealing with high dimensional problems, Gibbs Sampler doesn’t require a decent proposal distribution. It generates the Markov Chain through univariate conditional probability distribution, which greatly simplifies problems. We illustrate the use of those approaches with examples (with R codes) to provide a thorough review. Those basic methods have variants to deal with different situations. And they are building blocks for more advanced problems. This report is not a tutorial for statistics or the software R. The author assumes that readers are familiar with basic statistical concepts and common R statements. If needed, a detailed instruction of R programming can be found in the Comprehensive R Archive Network (CRAN): http://cran.R-project.org / text

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This thesis is concerned with the utilisation of spatial information in processing of high-frequency sidescan SONAR imagery, and particularly in how such information can be used in developing techniques to assist in mapping functions. Survey applications aim to generate maps of the seabed, but are time consuming and expensive; automatic processing is required to improve efficiency. Current techniques have had some success, but utilise little of the available spatial information. Previously, inclusion of such knowledge was prohibitively expensive; recent improvements in numerical simulations techniques has reduced the costs involved. This thesis attempts to exploit these improvements into a method for including spatial information in SONAR processing and in general to image and signal analysis. Bayesian techniques for inclusion of prior knowledge and structuring complex problems are developed and applied to problems of texture segmentation, object detection and parameter extraction. It is shown through experiments on groundtruth and real datasets that the inclusion of spatial context can be very effective in improving poor techniques or, conversely in allowing simpler techniques to be used with the same objective outcome (with obvious computational advantages). The thesis also considers some of the implementation problems with the techniques used, and develops simple modifications to improve common algorithms.

The Intelligent Transportation System (ITS) is a cooperative system that relies on reliable and robust communication schemes among vehicles and between vehicles and their surroundings. The main objective of the ITS is to ensure the safety of vehicle drivers and pedestrians. It provides an efficient and reliable transportation system that enhances traffic management, reduces congestion time, enables smooth traffic re-routing, and avoids economic losses. An essential part of the ITS is the Vehicular Ad hoc Network (VANET). VANET enables the setup of Vehicle-to-Vehicle (V2V) as well as Vehicle-to-Infrastructure (V2I) communication platforms: the two key components in the ITS. The de-facto standard used in wireless V2V and V2I communication applications is the Dedicated Short Range Communication (DSRC). The protocol that defines the specifications for the Medium Access Control (MAC) layer and the physical layer in the DSRC is the IEEE 802.11p protocol. The IEEE 802.11p protocol and its Enhanced Distributed Channel Access (EDCA) mechanism are the main focus of this thesis. Our main objective is to develop new IEEE 802.11p-based protocol for V2V and V2I communication systems, to improve the performance of safety-related applications. These applications are of paramount importance in ITS, because their goal is to decrease the rate of vehicle collisions, and hence reduce the enormous costs associated with them. In fact, large percentage of vehicle collisions can be easily avoided with the exchange of relevant information between vehicles and the Road Side Units (RSUs) installed on the sides of the roads. In this thesis, we propose various enhancements to the IEEE 802.11p protocol to improve its performance by lowering the average end-to-end delay and increasing the average network throughput. We introduce multiple adaptive algorithms to promote the QoS support across all the Access Categories (AC) in IEEE 802.11p. We propose two adaptive backoff algorithms and two algorithms that adaptively change the values of the Arbitrary Inter-Frame Space (AIFS). Then we extend our model to be applied in a large-scale vehicular network. In this context, a multi-layer cluster-based architecture is adopted, and two new distributed time synchronization mechanisms are developed.