To evaluate the expectation of a simple function with respect to a complicated multivariate density Monte Carlo integration has become the main technique. Gibbs sampling and importance sampling are the most popular methods for this task. In this contribution we propose a new simple general purpose importance sampling procedure. In a simulation study we compare the performance of this method with the performance of Gibbs sampling and of importance sampling using a vector of independent variates. It turns out that the new procedure is much better than independent importance sampling; up to dimension five it is also better than Gibbs sampling. The simulation results indicate that for higher dimensions Gibbs sampling is superior. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

To improve product quality and reduce cost, batch production is often implemented in many exible manufacturing systems. However, the current literature does not provide any method to analyze the quality performance in a flexible manufacturing system with batch production. In this research, we present an analytical method with closed-form formula to evaluate the quality performance in such systems. Based on the model, we discover and investigate monotonic and non-monotonic properties in quality to provide practical guidance for operation management. To improve product quality, we introduce the notions of quality improvability with respect to product sequencing. In addition, we develop the indicators for quality improvability based on the data available on the factory floor rather than complicated calculations. We define the bottleneck sequence and bottleneck transition as the ones that impede quality in the strongest manner, investigate the sensitivity of quality performance with respect to sequences and transitions, and propose quality bottleneck sequence and transition indicators based on the measured data. Finally, we provide a case study at an automotive paint shop to show how this method is applied to improve paint quality. Moreover, we explore a potential application to reduce energy consumption and atmospheric emissions at automotive paint shops. By selecting appropriate batch and sequence policies, the paint quality can be improved and repaints can be reduced so that less material and energy will be consumed, and less atmospheric emissions will be generated. It is shown that such scheduling and control method can lead to significant energy savings and emission reduction with no extra investment nor changes to existing painting processes. The successful development of such method would open up a new area in manufacturing systems research and contribute to establish a solid foundation for an integrated study on productivity, quality and exibility. In addition, it will provide production engineers and operation managers a quantitative tool for continuous improvement on product quality in flexible manufacturing environment

Many recent research results have concluded that the multiple-input multiple-output (MIMO) wireless communication architecture is a promising approach to achieve high bandwidth efficiencies. MIMO wireless channels can be simply defined as a link for which both the transmitting and receiving ends are equipped with multiple antenna elements. This advanced communication technology has the potential to resolve the bottleneck in traffic capacity for future wireless networks. Applying MIMO techniques to mobile communication systems, the problem of channel fading between the transmitters and receivers, which results in received signal strength fluctuations, is inevitable. The time-varying nature of the mobile channel affects various aspects of receiver design. This thesis provides some analytical methodologies to investigate the variation of MIMO eigenmodes. Although the scope is largely focussed on the temporal variation in this thesis, our results are also extended to frequency variation. Accurate analytical approximations for the level crossing rate (LCR) and average fade duration (AFD) of the MIMO eigenmodes in an independent, identically distributed (i.i.d.) flat-fading channel are derived. Furthermore, since several channel metrics (such as the total power gain, eigenvalue spread, capacity and Demmel condition number) are all related to the eigenmodes, we also derive their LCRs and AFDs using a similar approach. The effectiveness of our method lies in the fact that the eigenvalues and corresponding channel metrics can be well approximated by gamma or Gaussian variables. Our results provide a comprehensive, closed-form analysis for the temporal behavior of MIMO channel metrics that is simple, robust and rapid to compute. An alternative simplified formula for the LCR for MIMO eigenmodes is also presented with applications to different types of autocorrelation functions (ACF). Our analysis has been verified via Monte Carlo computer simulations. The joint probability density function (PDF) for the eigenvalues of a complex Wishart matrix and a perturbed version of it are also derived in this thesis. The latter version can be used to model channel estimation errors and variations over time or frequency. Using this PDF, the probabilities of adaptation error (PAE) due to feedback delay in some adaptive MIMO schemes are evaluated. In particular, finite state Markov chains (FSMC) have been used to model rate-feedback system and dual-mode antenna selection schemes. The PDF is also applied to investigate MIMO systems that merge singular value decomposition (SVD)-based transceiver structure and adaptive modulation. A FSMC is constructed to investigate the modulation state entering rates (MSER), the average stay duration (ASD), and the effects of feedback delay on the accuracy of modulation state selection in mobile radio systems. The system performance of SVD-based transceivers is closely related to the quality of the channel information at both ends of the link. Hence, we examine the effect of feedback time delay, which causes the transmitter to use outdated channel information in time-varying fading channels. In this thesis, we derive an analytical expression for the instantaneous signal to interference plus noise ratio (SINR) of eigenmode transmission with a feedback time delay. Moreover, this expression implies some novel metrics that gauge the system performance sensitivity to time-variations of the steering vectors (eigenvectors of the channel correlation matrix) at the transmitter. Finally, the fluctuation of the channel in the frequency domain is of interest. This is motivated by adaptive orthogonal frequency division multiplexing (OFDM) systems where the signalling parameters per subcarriers are assigned in accordance with some channel quality metrics. A Gaussian distribution has been suggested to approximate the number of subcarriers using certain signalling modes (such as outage/transmission and diversity/multiplexing), as well as the total data rates, per OFDM realization. Additionally, closed-form LCRs for the channel gains (including the individual eigenmode gains) over frequency are also derived for both single-input single-output (SISO) and MIMO-OFDM systems. The corresponding results for the average fade bandwidth (AFB) follow trivially, These results may be useful for system design, for example by calculating the feedback overheads based on subcarrier aggregation.

Using an extensive cross-section of US corporate CDS this paper offers an economic understanding of implied loss given default (LGD) and jumps in default risk. We formulate and underpin empirical stylized facts about CDS spreads, which are then reproduced in our affine intensity-based jump-diffusion model. Implied LGD is well identified, with obligors possessing substantial tangible assets expected to recover more. Sudden increases in the default risk of investment-grade obligors are higher relative to speculative grade. The probability of structural migration to default is low for investment-grade and heavily regulated obligors because investors fear distress rather through rare but devastating events. (authors' abstract)

This paper compares the performance of Bayesian variable selection approaches for spatial autoregressive models. We present two alternative approaches which can be implemented using Gibbs sampling methods in a straightforward way and allow us to deal with the problem of model uncertainty in spatial autoregressive models in a flexible and computationally efficient way. In a simulation study we show that the variable selection approaches tend to outperform existing Bayesian model averaging techniques both in terms of in-sample predictive performance and computational efficiency. (authors' abstract) / Series: Department of Economics Working Paper Series

Understanding demographic and disease processes in wildlife populations tends to be hampered by incomplete observations which can include significant errors. Models provide useful insights into the potential impacts of key processes and the value of such models greatly improves through integration with available data in a way that includes all sources of stochasticity and error. To date, the impact on disease of spatial and social structures observed in wildlife populations has not been widely addressed in modelling. I model the joint effects of differential fecundity and spatial heterogeneity on demography and disease dynamics, using a stochastic description of births, deaths, social-geographic migration, and disease transmission. A small set of rules governs the rates of births and movements in an environment where individuals compete for improved fecundity. This results in realistic population structures which, depending on the mode of disease transmission can have a profound effect on disease persistence and therefore has an impact on disease control strategies in wildlife populations. I also apply a simple model with births, deaths and disease events to the long-term observations of TB (Mycobacterium bovis) in badgers in Woodchester Park. The model is a continuous time, discrete state space Markov chain and is fitted to the data using an implementation of Bayesian parameter inference with an event-based likelihood. This provides a flexible framework to combine data with expert knowledge (in terms of model structure and prior distributions of parameters) and allows us to quantify the model parameters and their uncertainties. Ecological observations tend to be restricted in terms of scope and spatial temporal coverage and estimates are also affected by trapping efficiency and disease test sensitivity. My method accounts for such limitations as well as the stochastic nature of the processes. I extend the likelihood function by including an error term that depends on the difference between observed and inferred state space variables. I also demonstrate that the estimates improve by increasing observation frequency, combining the likelihood of more than one group and including variation of parameter values through the application of hierarchical priors.

Markov Chain Monte Carlo (MCMC) is a technique for sampling from a target probability distribution, and has risen in importance as faster computing hardware has made possible the exploration of hitherto difficult distributions. Unfortunately, this powerful technique is often misapplied by poor selection of transition kernel for the Markov chain that is generated by the simulation. Some kernels are used without being checked against the convergence requirements for MCMC (total balance and ergodicity), but in this work we prove the existence of a simple proxy for total balance that is not as demanding as detailed balance, the most widely used standard. We show that, for discrete-state MCMC, that if a transition kernel is equivalent when it is “reversed” and applied to data which is also “reversed”, then it satisfies total balance. We go on to prove that the sequential single-variable update Metropolis kernel, where variables are simply updated in order, does indeed satisfy total balance for many discrete target distributions, such as the Ising model with uniform exchange constant. Also, two well-known papers by Gelman, Roberts, and Gilks (GRG)[1, 2] have proposed the application of the results of an interesting mathematical proof to the realistic optimization of Markov Chain Monte Carlo computer simulations. In particular, they advocated tuning the simulation parameters to select an acceptance ratio of 0.234 . In this paper, we point out that although the proof is valid, its result’s application to practical computations is not advisable, as the simulation algorithm considered in the proof is so inefficient that it produces very poor results under all circumstances. The algorithm used by Gelman, Roberts, and Gilks is also shown to introduce subtle time-dependent correlations into the simulation of intrinsically independent variables. These correlations are of particular interest since they will be present in all simulations that use multi-dimensional MCMC moves.

It is suggested to discriminate between different state space models for a given time series by means of a Bayesian approach which chooses the model that minimizes the expected loss. Practical implementation of this procedures requires a fully Bayesian analysis for both the state vector and the unknown hyperparameters which is carried out by Markov chain Monte Carlo methods. Application to some non-standard situations such as testing hypotheses on the boundary of the parameter space, discriminating non-nested models and discrimination of more than two models is discussed in detail. (author's abstract) / Series: Forschungsberichte / Institut für Statistik

By equipping vehicles with the on-board wireless facility, the newly emerged vehicular networking targets to provision the broadband serves to vehicles. As such, a variety of novel and exciting applications can be provided to vehicular users to enhance their road safety and travel comfort, and finally raise a complete change to their on-road life. As the content distribution and media/video streaming, such as Youtube, Netflix, nowadays have become the most popular Internet applications, to enable the efficient content distribution and audio/video streaming services is thus of the paramount importance to the success of the vehicular networking. This, however, is fraught with fundamental challenges due to the distinguished natures of vehicular networking. On one hand, the vehicular communication is challenged by the spotty and volatile wireless connections caused by the high mobility of vehicles. This makes the download performance of connections very unstable and dramatically change over time, which directly threats to the on-top media applications. On the other hand, a vehicular network typically involves an extremely large-scale node population (e.g., hundreds or thousandths of vehicles in a region) with intense spatial and temporal variations across the network geometry at different times. This dictates any designs to be scalable and fully distributed which should not only be resilient to the network dynamics, but also provide the guaranteed quality-of-service (QoS) to users. The purpose of this dissertation is to address the challenges of the vehicular networking imposed by its intrinsic dynamic and large-scale natures, and build the efficient, scalable and, more importantly, practical systems to enable the cost-effective and QoS guaranteed content distribution and media streaming services to vehicular users. Note that to effective- ly deliver the content from the remote Internet to in-motion vehicles, it typically involves three parts as: 1.) an infrastructure grid of gateways which behave as the data depots or injection points of Internet contents and services to vehicles, 2.) protocol at gateways which schedules the bandwidth resource at gateways and coordinates the parallel transmissions to different vehicles, and 3.) the end-system control mechanism at receivers which adapts the receiver’s content download/playback strategy based on the available network throughput to provide users with the desired service experience. With above three parts in mind, the entire research work in this dissertation casts a systematic view to address each part in one topic with: 1.) design of large-scale cost-effective content distribution infrastructure, 2.) MAC (media access control) performance evaluation and channel time scheduling, and 3.) receiver adaptation and adaptive playout in dynamic download environment. In specific, in the first topic, we propose a practical solution to form a large-scale and cost-effective content distribution infrastructure in the city. We argue that a large-scale infrastructure with the dedicated resources, including storage, computing and communication capacity, is necessary for the vehicular network to become an alternative of 3G/4G cellular network as the dominating approach of ubiquitous content distribution and data services to vehicles. On addressing this issue, we propose a fully distributed scheme to form a large-scale infrastructure by the contributions of individual entities in the city, such as grocery stores, movie theaters, etc. That is to say, the installation and maintenance costs are shared by many individuals. In this topic, we explain the design rationale on how to motivate individuals to contribute, and specify the detailed design of the system, which is embodied with distributed protocols and performance evaluation. The second topic investigates on the MAC throughput performance of the vehicle-to- infrastructure (V2I) communications when vehicles drive through RSUs, namely drive-thru Internet. Note that with a large-scale population of fast-motion nodes contending the chan- nel for transmissions, the MAC performance determines the achievable nodal throughput and is crucial to the on-top applications. In this topic, using a simple yet accurate Marko- vian model, we first show the impacts of mobility (characterized by node velocity and moving directions) on the nodal and system throughput performance, respectively. Based on this analysis, we then propose three enhancement schemes to timely adjust the MAC parameters in tune with the vehicle mobility to achieve the maximal the system throughput. The last topic investigates on the end-system design to deliver the user desired media streaming services in the vehicular environment. In specific, the vehicular communications are notoriously known for the intermittent connectivity and dramatically varying throughput. Video streaming on top of vehicular networks therefore inevitably suffers from the severe network dynamics, resulting in the frequent jerkiness or even freezing video playback. To address this issue, an analytical model is first developed to unveil the impacts of network dynamics on the resultant video performance to users in terms of video start-up delay and smoothness of playback. Based on the analysis, the adaptive playout buffer mechanism is developed to adapt the video playback strategy at receivers towards the user-defined video quality. The proposals developed in the three topics are validated with the extensive and high fidelity simulations. We believe that our analysis developed in the dissertation can provide insightful lights on understanding the fundamental performance of the vehicular content distribution networks from the aspects of session-level download performance in urban vehicular networks (topic 1), MAC throughput performance (topic 2), and user perceived media quality (topic 3). The protocols developed in the three topics, respectively, offer practical and efficient solutions to build and optimize the vehicular content distribution networks.

The majority of this thesis is concerned with the development of efficient and robust numerical methods based on adaptive algebraic multigrid to compute the stationary distribution of Markov chains. It is shown that classical algebraic multigrid techniques can be applied in an exact interpolation scheme framework to compute the stationary distribution of irreducible, homogeneous Markov chains. A quantitative analysis shows that algebraically smooth multiplicative error is locally constant along strong connections in a scaled system operator, which suggests that classical algebraic multigrid coarsening and interpolation can be applied to the class of nonsymmetric irreducible singular M-matrices with zero column sums. Acceleration schemes based on fine-level iterant recombination, and over-correction of the coarse-grid correction are developed to improve the rate of convergence and scalability of simple adaptive aggregation multigrid methods for Markov chains. Numerical tests over a wide range of challenging nonsymmetric test problems demonstrate the effectiveness of the proposed multilevel method and the acceleration schemes. This thesis also investigates the application of adaptive algebraic multigrid techniques for computing the canonical decomposition of higher-order tensors. The canonical decomposition is formulated as a least squares optimization problem, for which local minimizers are computed by solving the first-order optimality equations. The proposed multilevel method consists of two phases: an adaptive setup phase that uses a multiplicative correction scheme in conjunction with bootstrap algebraic multigrid interpolation to build the necessary operators on each level, and a solve phase that uses additive correction cycles based on the full approximation scheme to efficiently obtain an accurate solution. The alternating least squares method, which is a standard one-level iterative method for computing the canonical decomposition, is used as the relaxation scheme. Numerical tests show that for certain test problems arising from the discretization of high-dimensional partial differential equations on regular lattices the proposed multilevel method significantly outperforms the standard alternating least squares method when a high level of accuracy is required.