Aerospace design requirements mandate acceptable levels of structural failure risk. Probabilistic fatigue models enable estimation of the likelihood of fatigue failure. A key step in the development of these models is the accurate inference of the probability distributions for dominant parameters. Since data sets for these inferences are of limited size, the fatigue model parameter distributions are themselves uncertain. A hierarchical Bayesian approach is adopted to account for the uncertainties in both the parameters and their distribution. Variables specifying the distribution of the fatigue model parameters are cast as hyperparameters whose uncertainty is modeled with a hyperprior distribution. Bayes' rule is used to determine the posterior hyperparameter distribution, given available data, thus specifying the probabilistic model. The Bayesian formulation provides an additional advantage by allowing the posterior distribution to be updated as new data becomes available through inspections. By updating the probabilistic model, uncertainty in the hyperparameters can be reduced, and the appropriate level of conservatism can be achieved. In this work, techniques for Bayesian inference and updating of probabilistic fatigue models for metallic components are developed. Both safe-life and damage-tolerant methods are considered. Uncertainty in damage rates, crack growth behavior, damage, and initial flaws are quantified. Efficient computational techniques are developed to perform the inference and updating analyses. The developed capabilities are demonstrated through a series of case studies.

Thesis (M.S.)--University of North Carolina Wilmington, 2009. / Title from PDF title page (February 16, 2010) Includes bibliographical references (p. 30)

Thesis (M.S.)--University of North Carolina Wilmington, 2009. / Title from PDF title page (February 16, 2010) Includes bibliographical references (p. 34-35)

Not available / text

Global spread of infectious disease threatens the well-being of human, domestic, and wildlife health. A proper understanding of global distribution of these diseases is an important part of disease management and policy making. However, data are subject to complexities by heterogeneity across host classes and space-time epidemic processes [Waller et al., 1997, Hosseini et al., 2006]. The use of frequentist methods in Biostatistics and epidemiology are common and are therefore extensively utilized in answering varied research questions. In this thesis, we proposed the Hierarchical Bayesian approach to study the spatial and the spatio-temporal pattern of tuberculosis in Kenya [Knorr-Held et al., 1998, Knorr-Held, 1999, L opez-Qu lez and Munoz, 2009, Waller et al., 1997, Julian Besag, 1991]. Space and time interaction of risk (ψ[ij]) is an important factor considered in this thesis. The Markov Chain Monte Carlo (MCMC) method via WinBUGS and R packages were used for simulations [Ntzoufras, 2011, Congdon, 2010, David et al., 1995, Gimenez et al., 2009, Brian, 2003], and the Deviance Information Criterion (DIC), proposed by [Spiegelhalter et al., 2002], used for models comparison and selection. Variation in TB risk is observed among Kenya counties and clustering among counties with high TB relative risk (RR). HIV prevalence is identified as the dominant determinant of TB. We found clustering and heterogeneity of risk among high rate counties and the overall TB risk is slightly decreasing from 2002-2009. Interaction of TB relative risk in space and time is found to be increasing among rural counties that share boundaries with urban counties with high TB risk. This is as a result of the ability of models to borrow strength from neighbouring counties, such that near by counties have similar risk. Although the approaches are less than ideal, we hope that our formulations provide a useful stepping stone in the development of spatial and spatio-temporal methodology for the statistical analysis of risk from TB in Kenya. / Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2013.

Mit der Liberalisierung des Strommarkts, den unsicheren Aussichten in der Klimapolitik und stark schwankenden Preisen bei Brennstoffen, Emissionsrechten und Kraftwerkskomponenten hat bei Kraftwerksinvestitionen das Risikomanagement an Bedeutung gewonnen. Dies äußert sich im vermehrten Einsatz probabilistischer Verfahren. Insbesondere bei regulativen Risiken liefert der klassische, häufigkeitsbasierte Wahrscheinlichkeitsbegriff aber keine Handhabe zur Risikoquantifizierung. In dieser Arbeit werden Kraftwerksinvestitionen und -portfolien in Deutschland mit Methoden des Bayes'schen Risikomanagements bewertet. Die Bayes'sche Denkschule begreift Wahrscheinlichkeit als persönliches Maß für Unsicherheit. Wahrscheinlichkeiten können auch ohne statistische Datenanalyse allein mit Expertenbefragungen gewonnen werden. Das Zusammenwirken unsicherer Werttreiber wurde mit einem probabilistischen DCF-Modell (Discounted Cash Flow-Modell) spezifiziert und in ein Einflussdiagramm mit etwa 1200 Objekten umgesetzt. Da der Überwälzungsgrad von Brennstoff- und CO2-Kosten und damit die Höhe der von den Kraftwerken erwirtschafteten Deckungsbeiträge im Wettbewerb bestimmt werden, reicht eine einzelwirtschaftliche Betrachtung der Kraftwerke nicht aus. Strompreise und Auslastungen werden mit Heuristiken anhand der individuellen Position der Kraftwerke in der Merit Order bestimmt, d.h. anhand der nach kurzfristigen Grenzkosten gestaffelten Einsatzreihenfolge. Dazu wurden 113 thermische Großkraftwerke aus Deutschland in einer Merit Order vereinigt. Das Modell liefert Wahrscheinlichkeitsverteilungen für zentrale Größen wie Kapitalwerte von Bestandsportfolien sowie Stromgestehungskosten und Kapitalwerte von Einzelinvestitionen (Steinkohle- und Braunkohlekraftwerke mit und ohne CO2-Abscheidung sowie GuD-Kraftwerke). Der Wert der Bestandsportfolien von RWE, E.ON, EnBW und Vattenfall wird primär durch die Beiträge der Braunkohle- und Atomkraftwerke bestimmt. Erstaunlicherweise schlägt sich der Emissionshandel nicht in Verlusten nieder. Dies liegt einerseits an den Zusatzgewinnen der Atomkraftwerke, andererseits an den bis 2012 gratis zugeteilten Emissionsrechten, welche hohe Windfall-Profite generieren. Dadurch erweist sich der Emissionshandel in seiner konkreten Ausgestaltung insgesamt als gewinnbringendes Geschäft. Über die Restlaufzeit der Bestandskraftwerke resultiert ab 2008 aus der Einführung des Emissionshandels ein Barwertvorteil von insgesamt 8,6 Mrd. €. In ähnlicher Dimension liegen die Barwertvorteile aus der 2009 von der Bundesregierung in Aussicht gestellten Laufzeitverlängerung für Atomkraftwerke. Bei einer achtjährigen Laufzeitverlängerung ergäben sich je nach CO2-Preisniveau Barwertvorteile von 8 bis 15 Mrd. €. Mit höheren CO2-Preisen und Laufzeitverlängerungen von bis zu 28 Jahren würden 25 Mrd. € oder mehr zusätzlich anfallen. Langfristig erscheint fraglich, ob unter dem gegenwärtigen Marktdesign noch Anreize für Investitionen in fossile Kraftwerke gegeben sind. Zu Beginn der NAP 2-Periode noch rentable Investitionen in Braunkohle- und GuD-Kraftwerke werden mit der auslaufenden Gratiszuteilung von Emissionsrechten zunehmend unrentabler. Die Rentabilität wird durch Strommarkteffekte der erneuerbaren Energien und ausscheidender alter Gas- und Ölkraftwerke stetig weiter untergraben. Steinkohlekraftwerke erweisen sich selbst mit anfänglicher Gratiszuteilung als riskante Investition. Die festgestellten Anreizprobleme für Neuinvestitionen sollten jedoch nicht dem Emissionshandel zugeschrieben werden, sondern resultieren aus den an Grenzkosten orientierten Strompreisen. Das Anreizproblem ist allerdings bei moderaten CO2-Preisen am größten. Es gilt auch für Kraftwerke mit CO2-Abscheidung: Obwohl die erwarteten Vermeidungskosten für CCS-Kraftwerke gegenüber konventionellen Kohlekraftwerken im Jahr 2025 auf 25 €/t CO2 (Braunkohle) bzw. 38,5 €/t CO2 (Steinkohle) geschätzt werden, wird ihr Bau erst ab CO2-Preisen von 50 bzw. 77 €/t CO2 rentabel. Ob und welche Kraftwerksinvestitionen sich langfristig rechnen, wird letztlich aber politisch entschieden und ist selbst unter stark idealisierten Bedingungen kaum vorhersagbar. / Power plant investors face large uncertainties due to ongoing liberalization, climate policy, and long investment horizons. This study provides a probabilistic appraisal of power plant investments within the framework of Bayesian decision theory. A Bayesian influence diagram is used for setting up a discounted cash flow model and analysing the profitability of power plants. As the study explicitly models merit order pricing, the pass-through of random fuel and carbon costs may be analysed. The study derives probabilistic statements about net present values of single investments and company portfolios and explores the sensitivity of profits to variations of select input variables. In the majority of cases, an increase in the price of emission allowances also increases the net present value of existing power plant portfolios. A substantially increased carbon prices also is the prerequisite to diversify power plant portfolios by gas and CCS plants. For the currently prevailing German electricity market, we argue that investors may lack incentives for new investments in fossil generation, a finding that holds true also with implementation of CCS. Our estimates are conservative, as profitability will further deteriorate with the build-up of renewables.

No description available.

South Africa is at the southern fringe of sub-Saharan African countries which persist in experiencing malaria transmission. The purpose of the study is to analyse the geographical and temporal patterns of malaria transmission from 2000 to 2011 using Bayesian geostatistical modelling in Limpopo Province, South Africa. Hereafter, develop malaria case data-driven spatio-temporal models to assess malaria transmission in Limpopo Province. Malaria case data was acquired from the South African Medical Research Council (MRC). Population data was acquired from AfriPopo; and Normalised Difference Vegetation Index (NDVI), Land Surface Temperature (LST) and Land Cover data were acquired from MODerate-resolution Imaging Spectro-radiometer (MODIS). Rainfall, Altitude and distance to water bodies’ data were acquired from African Data Dissemination Service (ADDS), United States Geological Survey (USGS) and Environmental Systems Research Institute (ESRI), respectively. Bayesian spatio-temporal incidence models were formulated for Gibbs variable selection and models were fitted using the best set of environmental factors. Modelbased predictions were obtained over a regular grid of 1 x 1km. spatial resolution covering the entire province and expressed as rates of per 1 000 inhabitants for the year 2010. To assess the performance of the predicted malaria incidence risk maps, the predictions and field observations were compared. The best set of environmental factors selected by variable selection was Altitude and the night temperature of two months before the case was reported. The environmental factors were then used for model fitting and all of the covariates were important on malaria risk. Predictions were done using all the environmental factors. The predictions showed that Vhembe and Mopani district municipalities have high malaria transmission as compared to other district municipalities in Limpopo Province. Assessment of predictive performance showed scatter plots with the coefficient of determination ( R² ). The values representing the statistical correlation represented by the coefficient of determination ( R² ) were 0.9798 (January), 0.8736 (February), 0.8152 (March), 0.8861 (April), 0.9949 (May), 0.3838 (June), 0.7794 (July), 0.9235 (September), 0.8966 (October), 0.9834 (November) and 0.8958 (December). August had two values reported and predicted which resulted in R² of 1. The numbers of the The produced malaria incidence maps can possibly be considered as one of the baselines for future malaria control programmes. The results highlighted the risk factors of malaria in Limpopo Province which are the most important characteristics of malaria transmission. / M.Sc. University of KwaZulu-Natal, Durban, 2013.

Bayesian principle is conceptually simple and intuitively plausible to carry out but its numerical implementation is not always straightforward. Most of the times we have posterior distributions in terms of complicated analytical funs ions and be known only up to a multiplicative constant. Hence it becomes computationally difficult to attain the marginal densities and the moments of the posterior distributions in closed form. In the present study the leading methods, both analytical and numerical, for implementing Bayesian inference has been explored. In particular, the non-iterative Monte Carlo method known as Importance Sampling has been applied to approximate the posterior expectations of the Lognormal and Cauchy distributions, belonging to the Exponential family and the non-Exponential family of distributions respectively. Sample values from these distributions have been simulated through computer programming. Calculations are done mostly by C++ programming language and Mathematica. / Department of Mathematical Sciences

Zugl.: Fribourg, Univ., Diss., 2008 u.d.T.: Ardia, David: Bayesian estimation of single regime and regime switching GARCH models