The Integrated Nested Laplace Approximations (INLA) method has become a commonly used tool for researchers and practitioners to perform approximate Bayesian inference for various fields of applications. It has become essential to incorporate more complex models and expand the method’s capabilities with more features. In this dissertation, we contribute to the INLA method in different aspects. First, we present a new framework, INLA$^+$, based on dense matrices to perform approximate Bayesian inference. An application of the new approach is fitting disease-mapping models for count data with complex interactions. When the precision matrix is dense, the new approach scales better than the existing INLA method and utilizes the power of multiprocessors on shared and distributed memory architectures in today’s computational resources. Second, we propose an adaptive technique to improve gradient estimation for the convex gradient-based optimization framework in INLA. We propose a simple limited-memory technique for improving the accuracy of the numerical gradient of the marginal posterior of the hyperparameter by exploiting a coordinate transformation of the gradient and the history of previously taken descent directions. Third, we extend the commonly utilized Bayesian spatial model in disease mapping, known as the Besag model, into a non-stationary spatial model. This new model considers variations in spatial dependency among a predetermined number of sub-regions. The model incorporates multiple precision parameters, which enable different intensities of spatial dependence in each sub-region. To avoid overfitting and enhance generalization, we derive a joint penalized complexity prior for these parameters. These contributions expand the capabilities of the INLA method, improving its scalability, accuracy, and flexibility for a wider range of applications.

The goal in this thesis is to develop a novel statistical approach to identity functional interactions between regions in a brain network. Wavelets are effective for capturing time varying properties of non-stationary signals because they have compact support that can be compressed or stretched according to the dynamic properties of the signal. Wavelets provide a multi-scale decomposition of signals and thus can be few for exploring potential cross-scale interactions between signals. To achieve this, we propose the scale-specific sub-processes of a multivariate locally stationary wavelet stochastic process. Under this proposed framework, a novel cross-scale dependence measurement is developed, which provides a measure for dependence structure of components at different scales of multivariate time series. Extensive simulation experiments are conducted to demonstrate that the theoretical properties hold in practice. The developed cross-scale analysis is performed on the electroencephalogram (EEG) data to study alterations in the functional connectivity structure in children diagnosed with attention deficit hyperactivity disorder (ADHD). Our approach identified novel interesting cross-scale interactions between channels in the brain network. The proposed framework can be extended to other signals, which can also capture the statistical association between the stocks at different time scales.

Dagens sophantering är inte hållbar då exploateringen blir tätare och samhällenabelastas med mer mängd avfall. För en hållbar utveckling så måste sophanteringen blimer miljö- och funktionssmart.Syftet med rapporten är att undersöka olika sopsugsmodeller för olika ändamål.Undersökningen har sin utgångspunkt följande områden: Sopsugsystemetsuppbyggnad för stationär och mobil anläggning, komponenter i systemen, hållbarutveckling, tillvägagångssätt för nyproduktion respektive ROT-arbeten,användningsområden och intervjuer med kommuner om befintliga system.Informationen om sopsugsystemen har tagits dels från Logiwaste AB genomintervjuer, föredrag, dokument och fem intervjuer med kommuner för att få en verkliginblick hur systemen fungerat.För att kunna genomföra en byggnation av en sopsugsanläggning har vi analyseratbyggtekniska metoder för att uppnå ett renare och hållbart samhälle.Dagens sophantering är inte hållbar för framtiden. De modernasopsugsanläggningarna är ett alternativ till en utvecklad och hållbar sophantering.Vid en fortsatt läsning av rapporten kommer läsaren få en fördjupning i områdenasom tagits upp. / Today's waste disposal is not sustainable as exploitation becomes denser and societiesare loaded with more waste. For a more sustainable development, waste managementneeds to be more environmentally and functional.The purpose of the report is to investigate different waste disposal systems fordifferent purposes. The study is based on the following areas: The contexture of wastedisposal system for stationary and mobile installations, components in systems,sustainable development. New production, renovation and extension approaches.Applications and interviews with municipalities about existing systems.The information about the waste disposal systems has been taken from Logiwaste ABthrough interviews, lectures, documents and five interviews with municipalities to geta real insight into how the systems worked.In order to carry out a construction of a disposal systems we have analyzed buildingtechnology methods to achieve a cleaner and sustainable society.Today`s garbage disposal is not sustainable for the future. The modern automaticwaste collection facilities are an alternative to developed and sustainable wastemanagement.At a further reading of the report the reader will get an indentation in the areasmentioned.

This study investigates if momentum effects can be found on the Swedish stock market by testing a cross-sectional momentum strategy on historical data. To explain the results mathematically, a second approach, involving time series regression for predicting future returns is introduced and thereby extends the cross-sectional theory. The result of the study shows that momentum effects through the cross-sectional strategy exist on the Swedish stock market. Although positive return is found, the time series regression do not give any significance for predicting future returns. Hence, there is a contradiction between the two approaches. / Denna studie undersöker om momentumeffekter föreligger på den svenska aktiemarknaden med hjälp av två olika tillvägagångssätt. Först testas momentumstrategin på historisk data och därefter genomförs tidseriesregression för att undersöka om resultaten har statistisk signifikans för att prediktera framtida avkastning. Resultatet visar att momentumeffekter existerar på den svenska aktiemarknaden. Trots att positiv avkastning erhålls ger tidserieregressionen ingen indikation på att prediktering av framtida avkastning är möjlig. Följaktligen finns det en motsägelse mellan de två tillvägagångssätten.

The impact parameter (IP) approximation is a semiclassical model in quantum scattering theory wherein N large masses interact with one small mass. We study this model in one spatial dimension using the tools of time-dependent scattering theory, considering a system of two large-mass particles and one small-mass particle. We demonstrate that the model's predictive power becomes arbitrarily good as the masses of the two heavy particles are made larger by studying the S-matrix for a particular scattering channel. We also show that the IP wave functions can be made arbitrarily close to the full three-body solution, uniformly in time, provided one of the large masses is fixed in place, and that such a result probably will not hold if we allow all the masses to move. / Ph. D.

Ever faster data transmission in wireless communication is desired to satisfy emerging markets for various media services, such as voice, picture and video calls, multimedia messaging, music and video downloads, and even television. With the explosive increase in the use of mobile devices such as cellular phones, PDAs, GPS, and laptop computers, power consumption has become a prime consideration in the design of mobile communication systems. In order to reliably maintain a high rate of transmission and low power consumption, it is imperative that the receiver obtains as much knowledge as possible about the current state of the channel. A more accurate model of wireless communication channels will indisputably help in obtaining more knowledge about the transient channel state, providing a more accurate and efficient reproduction of the transmitted signal, and decreased power consumption by the receiver. With careful choice and consideration of the channel model, systemic optimization based on the selected channel model will improve the system performance of the transmitter and receiver through better encoding and decoding, as well as through better control of transmitted signal's power level. This thesis focuses on understanding the physical and statistical characteristics of wireless channels, and investigates how to represent wireless channels using simple mathematical models. This thesis initially studied a simple time-varying stationary channel, i.e.a multipath fiat fading channel without terminal motion, which is typically used for indoor wireless communication. With an introduction of stochastic differential equations, we derived a first-order AR stochastic process to represent this stationary channel. For a general multipath fiat fading channel with terminal motion, the traditional Clarke's model was then extended by incorporating the effects of fluctuations in the component phases and analyzed statistically. The resulting theoretical power spectrum was shown to fit practical measured spectra, in contrast to the traditional theoretical fiat fading channel spectra (Jakes' spectrum in [19]) . Finally, we developed a state-space model that represents a wireless channel using these modified spectral characteristics. This was achieved by developing a relationship between the state-space model and the theory of a rational transfer function. A novel method for designing a rational transfer function for linear systems was then proposed. In this method, the rational transfer function is represented via the Observable Canonical Form (OCF) to obtain the state-space model, which can be used to represent and simulate a fiat fading wireless channel. The presented state-space approach is simple and provides rapid computation. The present AR and state-space models provide valuable contributions that can be integrated with other algorithms for better system optimization of wireless communication networks. / Thesis / Doctor of Philosophy (PhD)

In this thesis we study multipole moments of axisymmetric spacetimes. Using the recursive definition of the multipole moments of Geroch and Hansen we develop a method for computing all multipole moments of a stationary axisymmetric spacetime without the use of a recursion. This is a generalisation of a method developed by Herberthson for the static case. Using Herberthson’s method we also develop a method for finding a static axisymmetric spacetime with arbitrary prescribed multipole moments, subject to a specified convergence criteria. This method has, in general, a step where one has to find an explicit expression for an implicitly defined function. However, if the number of multipole moments are finite we give an explicit expression in terms of power series. / <p>Note: The two articles are also available in the pdf-file. Report code: LiU-TEK-LIC-2006:4.</p>

The work in this thesis has demonstrated the chiral recognition through the adaptation of chromatographically derived chiral recognition systems by electrospray ionization mass spectrometry (ESI-MS). Mass-labeled, pseudoenantiomeric chiral selectors (where each pseudoenantiomer had the opposite stereochemistry, but was slightly different in mass due to labeling of one enantiomer) were prepared as soluble analogues of Pirkle type chiral stationary phases. When mixed with a chiral analyte, solutions containing these pseudoenantiomeric selectors afforded selector-analyte complexes in the ESI-MS, and the relative peak intensities of the complexes could be related back to the enantiomeric composition of the analyte. In each case of this study, the complex intensity fraction for either of the selector-analyte complexes in the ESI-MS varies linearly with the enantiomeric composition of the analyte. This linear relationship provides a measure of the extent of enantioselectivity and allows quantitative analysis of the enantiomeric composition of analyte.

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