25 research outputs found

    Applications of stochastic simulation in two-stage multiple comparisons with the best problem and time average variance constant estimation

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    In this dissertation, we study two problems. In the first part, we consider the two-stage methods for comparing alternatives using simulation. Suppose there are a finite number of alternatives to compare, with each alternative having an unknown parameter that is the basis for comparison. The parameters are to be estimated using simulation, where the alternatives are simulated independently. We develop two-stage selection and multiple-comparison procedures for simulations under a general framework. The assumptions are that each alternative has a parameter estimation process that satisfies a random- time-change central limit theorem (CLT), and there is a weakly consistent variance estimator (WCVE) for the variance constant appearing in the CLT. The framework encompasses comparing means of independent populations, functions of means, and steady-state means. One problem we consider of considerable practical interest and not handled in previous work on two-stage multiple-comparison procedures is comparing quantiles of alternative populations. We establish the asymptotic validity of our procedures as the prescribed width of the confidence intervals or indifference-zone parameter shrinks to zero. Also, for the steady-state simulation context, we compare our procedures based on WCVEs with techniques that instead use standardized time series methods. In the second part, we propose a new technique of estimating the variance parameter of a wide variety of stochastic processes. This new technique is better than the existing techniques for some standard stochastic processes in terms of bias and variance properties, since it reduces bias at the cost of no significant increase in variance

    Seventh International Workshop on Simulation, 21-25 May, 2013, Department of Statistical Sciences, Unit of Rimini, University of Bologna, Italy. Book of Abstracts

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    Seventh International Workshop on Simulation, 21-25 May, 2013, Department of Statistical Sciences, Unit of Rimini, University of Bologna, Italy. Book of Abstract

    Seventh International Workshop on Simulation, 21-25 May, 2013, Department of Statistical Sciences, Unit of Rimini, University of Bologna, Italy. Book of Abstracts

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    Seventh International Workshop on Simulation, 21-25 May, 2013, Department of Statistical Sciences, Unit of Rimini, University of Bologna, Italy. Book of Abstract

    Bayesian inference for stochastic processes

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    This thesis builds upon two strands of recent research related to conducting Bayesian inference for stochastic processes. Firstly, this thesis will introduce a new residual-bridge proposal for approximately simulating conditioned diffusions formed by applying the modified diffusion bridge approximation of Durham and Gallant, 2002 to the difference between the true diffusion and a second, approximate, diffusion driven by the same Brownian motion. This new proposal attempts to account for volatilities which are not constant and can, therefore, lead to gains in efficiency over recently proposed residual-bridge constructs (Whitaker et al., 2017) in situations where the volatility varies considerably, as is often the case for larger interobservation times and for time-inhomogeneous volatilities. These gains in efficiency are illustrated via a simulation study for three diffusions; the Birth-Death (BD) diffusion, the Lotka-Volterra (LV) diffusion, and a diffusion corresponding to a simple model of gene expression (GE). Secondly, this thesis will introduce two new classes of Markov Chain Monte Carlo samplers, named the Exchangeable Sampler and the Exchangeable Particle Gibbs Sampler, which, at each iteration, use exchangeablility to simulate multiple, weighted proposals whose weights indicate how likely the chain is to move to such a proposal. By generalising the Independence Sampler and the Particle Gibbs Sampler respectively, these new samplers allow for the locality of moves to be controlled by a scaling parameter which can be tuned to optimise the mixing of the resulting MCMC procedure, while still benefiting from the increase in acceptance probability that typically comes with using multiple proposals. These samplers can lead to chains with better mixing properties, and, therefore, to MCMC estimators with smaller variances than their corresponding algorithms based on independent proposals. This improvement in mixing is illustrated, numerically, for both samplers through simulation studies, and, theoretically, for the Exchangeable Sampler through a result which states that, under certain conditions, the Exchangeable Sampler is geometrically ergodic even when the importance weights are unbounded and, hence, in scenarios where the Independence Sampler cannot be geometrically ergodic. To provide guidance in the practical implementation of such samplers, this thesis derives asymptotic expected squared-jump distance results for the Exchangeable Sampler and the Exchangeable Particle Gibbs Sampler. Moreover, simulation studies demonstrate, numerically, how the theory plays out in practice when d is finite

    Advanced Algebraic Concepts for Efficient Multi-Channel Signal Processing

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    Unsere moderne Gesellschaft ist Zeuge eines fundamentalen Wandels in der Art und Weise wie wir mit Technologie interagieren. Geräte werden zunehmend intelligenter - sie verfügen über mehr und mehr Rechenleistung und häufiger über eigene Kommunikationsschnittstellen. Das beginnt bei einfachen Haushaltsgeräten und reicht über Transportmittel bis zu großen überregionalen Systemen wie etwa dem Stromnetz. Die Erfassung, die Verarbeitung und der Austausch digitaler Informationen gewinnt daher immer mehr an Bedeutung. Die Tatsache, dass ein wachsender Anteil der Geräte heutzutage mobil und deshalb batteriebetrieben ist, begründet den Anspruch, digitale Signalverarbeitungsalgorithmen besonders effizient zu gestalten. Dies kommt auch dem Wunsch nach einer Echtzeitverarbeitung der großen anfallenden Datenmengen zugute. Die vorliegende Arbeit demonstriert Methoden zum Finden effizienter algebraischer Lösungen für eine Vielzahl von Anwendungen mehrkanaliger digitaler Signalverarbeitung. Solche Ansätze liefern nicht immer unbedingt die bestmögliche Lösung, kommen dieser jedoch häufig recht nahe und sind gleichzeitig bedeutend einfacher zu beschreiben und umzusetzen. Die einfache Beschreibungsform ermöglicht eine tiefgehende Analyse ihrer Leistungsfähigkeit, was für den Entwurf eines robusten und zuverlässigen Systems unabdingbar ist. Die Tatsache, dass sie nur gebräuchliche algebraische Hilfsmittel benötigen, erlaubt ihre direkte und zügige Umsetzung und den Test unter realen Bedingungen. Diese Grundidee wird anhand von drei verschiedenen Anwendungsgebieten demonstriert. Zunächst wird ein semi-algebraisches Framework zur Berechnung der kanonisch polyadischen (CP) Zerlegung mehrdimensionaler Signale vorgestellt. Dabei handelt es sich um ein sehr grundlegendes Werkzeug der multilinearen Algebra mit einem breiten Anwendungsspektrum von Mobilkommunikation über Chemie bis zur Bildverarbeitung. Verglichen mit existierenden iterativen Lösungsverfahren bietet das neue Framework die Möglichkeit, den Rechenaufwand und damit die Güte der erzielten Lösung zu steuern. Es ist außerdem weniger anfällig gegen eine schlechte Konditionierung der Ausgangsdaten. Das zweite Gebiet, das in der Arbeit besprochen wird, ist die unterraumbasierte hochauflösende Parameterschätzung für mehrdimensionale Signale, mit Anwendungsgebieten im RADAR, der Modellierung von Wellenausbreitung, oder bildgebenden Verfahren in der Medizin. Es wird gezeigt, dass sich derartige mehrdimensionale Signale mit Tensoren darstellen lassen. Dies erlaubt eine natürlichere Beschreibung und eine bessere Ausnutzung ihrer Struktur als das mit Matrizen möglich ist. Basierend auf dieser Idee entwickeln wir eine tensor-basierte Schätzung des Signalraums, welche genutzt werden kann um beliebige existierende Matrix-basierte Verfahren zu verbessern. Dies wird im Anschluss exemplarisch am Beispiel der ESPRIT-artigen Verfahren gezeigt, für die verbesserte Versionen vorgeschlagen werden, die die mehrdimensionale Struktur der Daten (Tensor-ESPRIT), nichzirkuläre Quellsymbole (NC ESPRIT), sowie beides gleichzeitig (NC Tensor-ESPRIT) ausnutzen. Um die endgültige Schätzgenauigkeit objektiv einschätzen zu können wird dann ein Framework für die analytische Beschreibung der Leistungsfähigkeit beliebiger ESPRIT-artiger Algorithmen diskutiert. Verglichen mit existierenden analytischen Ausdrücken ist unser Ansatz allgemeiner, da keine Annahmen über die statistische Verteilung von Nutzsignal und Rauschen benötigt werden und die Anzahl der zur Verfügung stehenden Schnappschüsse beliebig klein sein kann. Dies führt auf vereinfachte Ausdrücke für den mittleren quadratischen Schätzfehler, die Schlussfolgerungen über die Effizienz der Verfahren unter verschiedenen Bedingungen zulassen. Das dritte Anwendungsgebiet ist der bidirektionale Datenaustausch mit Hilfe von Relay-Stationen. Insbesondere liegt hier der Fokus auf Zwei-Wege-Relaying mit Hilfe von Amplify-and-Forward-Relays mit mehreren Antennen, da dieser Ansatz ein besonders gutes Kosten-Nutzen-Verhältnis verspricht. Es wird gezeigt, dass sich die nötige Kanalkenntnis mit einem einfachen algebraischen Tensor-basierten Schätzverfahren gewinnen lässt. Außerdem werden Verfahren zum Finden einer günstigen Relay-Verstärkungs-Strategie diskutiert. Bestehende Ansätze basieren entweder auf komplexen numerischen Optimierungsverfahren oder auf Ad-Hoc-Ansätzen die keine zufriedenstellende Bitfehlerrate oder Summenrate liefern. Deshalb schlagen wir algebraische Ansätze zum Finden der Relayverstärkungsmatrix vor, die von relevanten Systemmetriken inspiriert sind und doch einfach zu berechnen sind. Wir zeigen das algebraische ANOMAX-Verfahren zum Erreichen einer niedrigen Bitfehlerrate und seine Modifikation RR-ANOMAX zum Erreichen einer hohen Summenrate. Für den Spezialfall, in dem die Endgeräte nur eine Antenne verwenden, leiten wir eine semi-algebraische Lösung zum Finden der Summenraten-optimalen Strategie (RAGES) her. Anhand von numerischen Simulationen wird die Leistungsfähigkeit dieser Verfahren bezüglich Bitfehlerrate und erreichbarer Datenrate bewertet und ihre Effektivität gezeigt.Modern society is undergoing a fundamental change in the way we interact with technology. More and more devices are becoming "smart" by gaining advanced computation capabilities and communication interfaces, from household appliances over transportation systems to large-scale networks like the power grid. Recording, processing, and exchanging digital information is thus becoming increasingly important. As a growing share of devices is nowadays mobile and hence battery-powered, a particular interest in efficient digital signal processing techniques emerges. This thesis contributes to this goal by demonstrating methods for finding efficient algebraic solutions to various applications of multi-channel digital signal processing. These may not always result in the best possible system performance. However, they often come close while being significantly simpler to describe and to implement. The simpler description facilitates a thorough analysis of their performance which is crucial to design robust and reliable systems. The fact that they rely on standard algebraic methods only allows their rapid implementation and test under real-world conditions. We demonstrate this concept in three different application areas. First, we present a semi-algebraic framework to compute the Canonical Polyadic (CP) decompositions of multidimensional signals, a very fundamental tool in multilinear algebra with applications ranging from chemistry over communications to image compression. Compared to state-of-the art iterative solutions, our framework offers a flexible control of the complexity-accuracy trade-off and is less sensitive to badly conditioned data. The second application area is multidimensional subspace-based high-resolution parameter estimation with applications in RADAR, wave propagation modeling, or biomedical imaging. We demonstrate that multidimensional signals can be represented by tensors, providing a convenient description and allowing to exploit the multidimensional structure in a better way than using matrices only. Based on this idea, we introduce the tensor-based subspace estimate which can be applied to enhance existing matrix-based parameter estimation schemes significantly. We demonstrate the enhancements by choosing the family of ESPRIT-type algorithms as an example and introducing enhanced versions that exploit the multidimensional structure (Tensor-ESPRIT), non-circular source amplitudes (NC ESPRIT), and both jointly (NC Tensor-ESPRIT). To objectively judge the resulting estimation accuracy, we derive a framework for the analytical performance assessment of arbitrary ESPRIT-type algorithms by virtue of an asymptotical first order perturbation expansion. Our results are more general than existing analytical results since we do not need any assumptions about the distribution of the desired signal and the noise and we do not require the number of samples to be large. At the end, we obtain simplified expressions for the mean square estimation error that provide insights into efficiency of the methods under various conditions. The third application area is bidirectional relay-assisted communications. Due to its particularly low complexity and its efficient use of the radio resources we choose two-way relaying with a MIMO amplify and forward relay. We demonstrate that the required channel knowledge can be obtained by a simple algebraic tensor-based channel estimation scheme. We also discuss the design of the relay amplification matrix in such a setting. Existing approaches are either based on complicated numerical optimization procedures or on ad-hoc solutions that to not perform well in terms of the bit error rate or the sum-rate. Therefore, we propose algebraic solutions that are inspired by these performance metrics and therefore perform well while being easy to compute. For the MIMO case, we introduce the algebraic norm maximizing (ANOMAX) scheme, which achieves a very low bit error rate, and its extension Rank-Restored ANOMAX (RR-ANOMAX) that achieves a sum-rate close to an upper bound. Moreover, for the special case of single antenna terminals we derive the semi-algebraic RAGES scheme which finds the sum-rate optimal relay amplification matrix based on generalized eigenvectors. Numerical simulations evaluate the resulting system performance in terms of bit error rate and system sum rate which demonstrates the effectiveness of the proposed algebraic solutions

    NASA thesaurus. Volume 2: Access vocabulary

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    The access vocabulary, which is essentially a permuted index, provides access to any word or number in authorized postable and nonpostable terms. Additional entries include postable and nonpostable terms, other word entries and pseudo-multiword terms that are permutations of words that contain words within words. The access vocabulary contains almost 42,000 entries that give increased access to the hierarchies in Volume 1 - Hierarchical Listing

    NASA thesaurus. Volume 2: Access vocabulary

    Get PDF
    The Access Vocabulary, which is essentially a permuted index, provides access to any word or number in authorized postable and nonpostable terms. Additional entries include postable and nonpostable terms, other word entries, and pseudo-multiword terms that are permutations of words that contain words within words. The Access Vocabulary contains 40,738 entries that give increased access to the hierarchies in Volume 1 - Hierarchical Listing

    Abstract Central Limit Theorems for Permuted Regenerative Estimators

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    We prove strong laws of large numbers and central limit theorems for some permuted estimators from regenerative simulations. These limit theorems provide the basis for constructing asymptoti-cally valid confidence intervals for the permuted estimators
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