Generalised Bayesian matrix factorisation models

Factor analysis and related models for probabilistic matrix factorisation are of central importance to the unsupervised analysis of data, with a colourful history more than a century long. Probabilistic models for matrix factorisation allow us to explore the underlying structure in data, and have relevance in a vast number of application areas including collaborative filtering, source separation, missing data imputation, gene expression analysis, information retrieval, computational finance and computer vision, amongst others. This thesis develops generalisations of matrix factorisation models that advance our understanding and enhance the applicability of this important class of models. The generalisation of models for matrix factorisation focuses on three concerns: widening the applicability of latent variable models to the diverse types of data that are currently available; considering alternative structural forms in the underlying representations that are inferred; and including higher order data structures into the matrix factorisation framework. These three issues reflect the reality of modern data analysis and we develop new models that allow for a principled exploration and use of data in these settings. We place emphasis on Bayesian approaches to learning and the advantages that come with the Bayesian methodology. Our port of departure is a generalisation of latent variable models to members of the exponential family of distributions. This generalisation allows for the analysis of data that may be real-valued, binary, counts, non-negative or a heterogeneous set of these data types. The model unifies various existing models and constructs for unsupervised settings, the complementary framework to the generalised linear models in regression. Moving to structural considerations, we develop Bayesian methods for learning sparse latent representations. We define ideas of weakly and strongly sparse vectors and investigate the classes of prior distributions that give rise to these forms of sparsity, namely the scale-mixture of Gaussians and the spike-and-slab distribution. Based on these sparsity favouring priors, we develop and compare methods for sparse matrix factorisation and present the first comparison of these sparse learning approaches. As a second structural consideration, we develop models with the ability to generate correlated binary vectors. Moment-matching is used to allow binary data with specified correlation to be generated, based on dichotomisation of the Gaussian distribution. We then develop a novel and simple method for binary PCA based on Gaussian dichotomisation. The third generalisation considers the extension of matrix factorisation models to multi-dimensional arrays of data that are increasingly prevalent. We develop the first Bayesian model for non-negative tensor factorisation and explore the relationship between this model and the previously described models for matrix factorisation.Supported by a Commonwealth Scholarship awarded by the Commonwealth Scholarship and Fellowship Programme (CSFP) [Award number ZACS-2207-363] Supported by award from the National Research Foundation, South Africa (NRF) [Award number SFH2007072200001

Fiscal News, Uncertainty, and the Business Cycle

The recent "Great Recession" has thrown macroeconomic research into a state of disarray and has clearly shown the need to go beyond traditional business cycle explanations. However, many of the recently proposed business cycle explanations rely on factors that are not directly observed by the econometrician. One promising way to deal with this issue of unobserved state variables has been the use of structural estimation. The present work contributes to the literature on non-traditional business cycle explanations by using structural macroeconomic modeling and structural estimation to analyze the role of fiscal news (Chapter 1), policy risk (Chapter 2), and terms of trade uncertainty (Chapter 3) for explaining macroeconomic fluctuations. Chapter 1 investigates the role of news about fiscal policy, and in particular the anticipation of tax rate changes, for macroeconomic fluctuations in the United States. To deal with the problem that news shocks are not observed by the econometrician, we resort to structural estimation of a New Keynesian DSGE model. We find that while fiscal policy accounts for 12 to 20 percent of output variance at business cycle frequencies, the anticipated components hardly matter for explaining fluctuations of real variables. In contrast, anticipated capital tax shocks do explain a sizable part of inflation and nominal interest rate fluctuations, accounting for 5 to 15 percent of their total variance. Consistent with earlier studies, we find that news shocks account for 20 percent of output variance, driven by news about stationary TFP and non-stationary investment-specific technology. Chapter 2 analyzes the role of policy risk in explaining business cycle fluctuations by using an estimated New Keynesian model featuring policy risk as well as uncertainty about technology. To deal with the unobserved state "uncertainty", we directly measure uncertainty from aggregate time series by structurally estimating a stochastic volatility model using Sequential Monte Carlo Methods. While we find considerable evidence of policy risk in the data, we show that the "pure uncertainty"-effect of policy risk is unlikely to play a major role in business cycle fluctuations. In the estimated model, output effects are relatively small due to i) dampening general equilibrium effects that imply a low amplification and ii) counteracting partial effects of uncertainty. Chapter 3 analyzes the effects of terms of trade uncertainty on Chilean business cycles through the lens of a small open economy DSGE model. My findings are fourfold. First, there is considerable evidence for time-varying terms of trade uncertainty in the Chilean data, with the variance of terms of trade shocks more than doubling in a short period of time. Second, I show that the ex-ante and ex-post effects of increased terms of trade uncertainty can account for about one fifth of Chilean output fluctuations at business cycle frequencies. Third, I find that a two-standard deviation terms of trade risk shock, i.e. a 54 percent increase in uncertainty, leads to a 0.1 percent drop in output. The fact that terms of trade uncertainty more than doubled during the recent commodities boom suggests that the contribution of terms of trade risk during this more recent period may have been substantial. Finally, I show that the economic mechanisms that attenuated the negative output effects of uncertainty in Chapter 2 also dampen the negative impact of terms of trade uncertainty

Efficient algorithms for arbitrary sample rate conversion with application to wave field synthesis

Arbitrary sample rate conversion (ASRC) is used in many fields of digital signal processing to alter the sampling rate of discrete-time signals by arbitrary, potentially time-varying ratios. This thesis investigates efficient algorithms for ASRC and proposes several improvements. First, closed-form descriptions for the modified Farrow structure and Lagrange interpolators are derived that are directly applicable to algorithm design and analysis. Second, efficient implementation structures for ASRC algorithms are investigated. Third, this thesis considers coefficient design methods that are optimal for a selectable error norm and optional design constraints. Finally, the performance of different algorithms is compared for several performance metrics. This enables the selection of ASRC algorithms that meet the requirements of an application with minimal complexity. Wave field synthesis (WFS), a high-quality spatial sound reproduction technique, is the main application considered in this work. For WFS, sophisticated ASRC algorithms improve the quality of moving sound sources. However, the improvements proposed in this thesis are not limited to WFS, but applicable to general-purpose ASRC problems.Verfahren zur unbeschränkten Abtastratenwandlung (arbitrary sample rate conversion,ASRC) ermöglichen die Änderung der Abtastrate zeitdiskreter Signale um beliebige, zeitvarianteVerhältnisse. ASRC wird in vielen Anwendungen digitaler Signalverarbeitung eingesetzt.In dieser Arbeit wird die Verwendung von ASRC-Verfahren in der Wellenfeldsynthese(WFS), einem Verfahren zur hochqualitativen, räumlich korrekten Audio-Wiedergabe, untersucht.Durch ASRC-Algorithmen kann die Wiedergabequalität bewegter Schallquellenin WFS deutlich verbessert werden. Durch die hohe Zahl der in einem WFS-Wiedergabesystembenötigten simultanen ASRC-Operationen ist eine direkte Anwendung hochwertigerAlgorithmen jedoch meist nicht möglich.Zur Lösung dieses Problems werden verschiedene Beiträge vorgestellt. Die Komplexitätder WFS-Signalverarbeitung wird durch eine geeignete Partitionierung der ASRC-Algorithmensignifikant reduziert, welche eine effiziente Wiederverwendung von Zwischenergebnissenermöglicht. Dies erlaubt den Einsatz hochqualitativer Algorithmen zur Abtastratenwandlungmit einer Komplexität, die mit der Anwendung einfacher konventioneller ASRCAlgorithmenvergleichbar ist. Dieses Partitionierungsschema stellt jedoch auch zusätzlicheAnforderungen an ASRC-Algorithmen und erfordert Abwägungen zwischen Performance-Maßen wie der algorithmischen Komplexität, Speicherbedarf oder -bandbreite.Zur Verbesserung von Algorithmen und Implementierungsstrukturen für ASRC werdenverschiedene Maßnahmen vorgeschlagen. Zum Einen werden geschlossene, analytischeBeschreibungen für den kontinuierlichen Frequenzgang verschiedener Klassen von ASRCStruktureneingeführt. Insbesondere für Lagrange-Interpolatoren, die modifizierte Farrow-Struktur sowie Kombinationen aus Überabtastung und zeitkontinuierlichen Resampling-Funktionen werden kompakte Darstellungen hergeleitet, die sowohl Aufschluss über dasVerhalten dieser Filter geben als auch eine direkte Verwendung in Design-Methoden ermöglichen.Einen zweiten Schwerpunkt bildet das Koeffizientendesign für diese Strukturen, insbesonderezum optimalen Entwurf bezüglich einer gewählten Fehlernorm und optionaler Entwurfsbedingungenund -restriktionen. Im Gegensatz zu bisherigen Ansätzen werden solcheoptimalen Entwurfsmethoden auch für mehrstufige ASRC-Strukturen, welche ganzzahligeÜberabtastung mit zeitkontinuierlichen Resampling-Funktionen verbinden, vorgestellt.Für diese Klasse von Strukturen wird eine Reihe angepasster Resampling-Funktionen vorgeschlagen,welche in Verbindung mit den entwickelten optimalen Entwurfsmethoden signifikanteQualitätssteigerungen ermöglichen.Die Vielzahl von ASRC-Strukturen sowie deren Design-Parameter bildet eine Hauptschwierigkeitbei der Auswahl eines für eine gegebene Anwendung geeigneten Verfahrens.Evaluation und Performance-Vergleiche bilden daher einen dritten Schwerpunkt. Dazu wirdzum Einen der Einfluss verschiedener Entwurfsparameter auf die erzielbare Qualität vonASRC-Algorithmen untersucht. Zum Anderen wird der benötigte Aufwand bezüglich verschiedenerPerformance-Metriken in Abhängigkeit von Design-Qualität dargestellt.Auf diese Weise sind die Ergebnisse dieser Arbeit nicht auf WFS beschränkt, sondernsind in einer Vielzahl von Anwendungen unbeschränkter Abtastratenwandlung nutzbar

Celebrated Econometricians: Katarina Juselius and Søren Johansen

This Special Issue collects contributions related to advances in the theory and practice of Econometrics induced by the research of Katarina Juselius and Søren Johansen, whom this Special Issue aims to celebrate. The papers in this Special Issue provide advances on several topics, and they are grouped in the following areas, with three to four papers per group). The first group provides a historical perspective on Katarina’s and Søren’s contributions to Econometrics. The second group of papers concentrates on representation theory, while the third focuses on estimation and inference. The fourth group explores extensions of CVARs for modelling and forecasting, and the fifth and final group is centered on empirical applications

Wavelets and Subband Coding

First published in 1995, Wavelets and Subband Coding offered a unified view of the exciting field of wavelets and their discrete-time cousins, filter banks, or subband coding. The book developed the theory in both continuous and discrete time, and presented important applications. During the past decade, it filled a useful need in explaining a new view of signal processing based on flexible time-frequency analysis and its applications. Since 2007, the authors now retain the copyright and allow open access to the book

The effects of U.S. shrimp imports on the Gulf of Mexico dockside price : a source differentiated mixed demand model

The ever increasing demand for the shrimp products in the 1980s and 1990s caused the volume of shrimp imports to increase. The import of shrimp has had an upward trend, from 847 million pounds in 1997 to 1,636 million pounds in 2010.The imports price has declined since 1997. Along with the decrease in imports price, the U.S. domestic shrimp price has also declined. However, the annual production of shrimp from the Gulf of Mexico has, in the long-run, remained relatively stable. These facts indicate that there is not the same quantity-price relation between the U.S. domestic shrimp market and shrimp imports market. Therefore, an ordinary demand or an inverse demand can only demonstrate one aspect of demand behavior either the quantities consumed are a function of prices or the prices are a function of quantities demanded, and are not able to respond in a more complicated system of demand. The basic objective of this dissertation is to determine a closer approximation of the effects of events in the real U.S. shrimp demand market. To accomplish this objective, a mixed demand system was adopted. A mixed set of demand functions contains both coefficients of a regular demand system and of an inverse demand system (Barton, 1989). This study adopts the Brown and Lee parameterization (2006), known as the mixed Rotterdam demand system. The shrimp products were divided into two subgroups: 1) shrimp imports (group a); and 2) Gulf of Mexico shrimp landings (group b). Countries considered in the analysis include China, Ecuador, India, Indonesia, Mexico, Thailand, Vietnam, and a final category includes all other exporting countries ans named as “Other Countries.” Demand for Gulf shrimp is specified by size of shrimp with three sizes: Large, Medium, and Small. The U.S. imports from these countries were modeled in a quantity dependent framework, while demands for domestic shrimp products were modeled in a price dependent framework. The summary statistics and estimated results for the model parameters indicate that Thailand has the largest share and largest marginal share among all exporting countries and Gulf shrimp landings. As theoretically expected, all own-price elastisities of regular demand are negative, implying an inverse relation between the quantity of imports from a selected country and its price of imports. Among all countries, China, India, Mexico, and Vietnam have the largest and almost the same own-price elasticities (-0.40). Thailand’s own-price elasticity is smaller than these countries, although it has the largest share in U.S. total expenditure on shrimp products. This means that there are fewer substitutes for Thailand’s shrimp than these countries’ shrimp in the U.S. shrimp market. Cross-price elastisities of regular demand were positive, indicating that the price of a selected country’s shrimp has a direct effect on the quantity of other countries’ shrimp exports. The positive cross-price elastisities also indicate that the U.S. shrimp imports from different countries are substitutes for each other, as expected. Thailand’s export prices have the largest cross-price elastisities. This means that other countries’ quantities of exports are more sensitive to a change in Thailand’s export prices than the other countries’ prices and their own prices. The price elasticity/flexibility of inverse demand illustrates that no country’s export prices have a substantial effect on any size of Gulf landings. The most effect is associated with about 0.02% on the price of small size Gulf landings for a 1% change in the price of Thailand’s exports to the United States. Vietnam, India, Mexico, China, and Thailand’s income elasticities are greater than one. Therefore, one can conclude that a change in U.S. expenditure on shrimp products not only increases the consumption of these countries’ shrimp products but that the proportion (share) of these products also goes up in U.S. total expenditure on shrimp. Income elasticities for inverse demand represent the Gulf dockside price sensitivities relative to a change in U.S. expenditure on shrimp. Results illustrate that if U.S. expenditure on shrimp products increases 100%, the Gulf large, medium, and small size shrimp prices will increase 12%, 15%, and 19%, respectively. All of these elasticity estimates are statistically significant at 1% and 5% levels

Trend Dominance in Macroeconomic Fluctuations

This paper investigates multivariate Beveridge-Nelson decomposition of key macro aggregate data. We find (a) inflation seems to be dominated by its trend component, and, perhaps as a result of this, the short-term interest rate is also trend dominated; and (b) consumption also seems to be dominated by its trend component perhaps as the permanent income hypothesis suggests. What is new here is that, although the difficulty of rejecting a unit root for these variables has been long recognized, we show that these unit root processes account for a large share of the variable fluctuations. This result raises a concern about the convention that the non-stationary data is detrended in standard DSGE-type structural estimation, in the sense that a significant portion of data variation actually may come from the trend components

Untangling hotel industry’s inefficiency: An SFA approach applied to a renowned Portuguese hotel chain

The present paper explores the technical efficiency of four hotels from Teixeira Duarte Group - a renowned Portuguese hotel chain. An efficiency ranking is established from these four hotel units located in Portugal using Stochastic Frontier Analysis. This methodology allows to discriminate between measurement error and systematic inefficiencies in the estimation process enabling to investigate the main inefficiency causes. Several suggestions concerning efficiency improvement are undertaken for each hotel studied.info:eu-repo/semantics/publishedVersio