Rozprawy doktorskie: „Mathematical statistics”

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Carlqvist, Håkan. "Multiscale analysis of multi-channel signals". Doctoral thesis, KTH, Matematik (Avd.), 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-230.

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I: Amplitude and phase relationship between alpha and beta oscillations in the human EEG We have studied the relation between two oscillatory patterns within EEG signals (oscillations with main frequency 10 Hz and 20 Hz), with wavelet-based methods. For better comparison, a variant of the continuous wavelet transform, was derived. As a conclusion, the two patterns were closely related and 70-90 % of the activity in the 20 Hz pattern could be seen as a resonance phenomenon of the 10 Hz activity. II: A local discriminant basis algorithm using wavelet packets for discrimination between classes of multidimensional signals We have improved and extended the local discriminant basis algorithm for application on multidimensional signals appearing from multichannels. The improvements includes principal-component analysis and crossvalidation- leave-one out. The method is furthermore applied on two classes of EEG signals, one group of control subjects and one group of subjects with type I diabetes. There was a clear discrimination between the two groups. The discrimination follows known differences in the EEG between the two groups of subjects. III: Improved classification of multidimensional signals using orthogonality properties of a time-frequency library We further improve and refine the method in paper2 and apply it on 4 classes of EEG signals from subjects differing in age and/or sex, which are known factors of EEG alterations. As a method for deciding the best basis we derive an orthogonalbasis- pursuit-like algorithm which works statistically better (Tukey's test for simultaneous confidence intervals) than the basis selection method in the original local discriminant basis algorithm. Other methods included were Fisher's class separability, partial-least-squares and cross-validation-leave-one-subject out. The two groups of younger subjects were almost fully discriminated between each other and to the other groups, while the older subjects were harder to discriminate.
QC 20101001

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2

Tovo, Anna. "Mathematical modelling and statistics of biodiversity". Doctoral thesis, Università degli studi di Padova, 2018. http://hdl.handle.net/11577/3421944.

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Life on Earth is characterised by an amazing variety of living forms which are in continuous evolution to better adapt to the surrounding environment and highly connected one to the other. A deep investigation of different living systems has recently been favoured by the huge quantity of data nowadays available. The present thesis is the final result of a journey through complex patterns in theoretical ecology. We study both models and issues in data analysis as well as the connections between them within a mathematical framework. In particular, we explore the different aspects of the biodiversity of an ecosystem, referring with this term to the variety of its species. Our interest is to investigate how these species interact with each other and with the surrounding environment and how these connections can structure recurrent macro-ecological patterns. Indeed, despite their diversity and complexity, it is straightforward that ecological systems share similar behaviours. This fact suggests that such systems are driven by a common mechanism, which is insensitive to the details of the systems on which it acts. A theoretical understanding is therefore possible through the development of mathematical models rich enough to reproduce the investigated patterns, but containing only the essential ingredients able to originate them. In the first part of the present thesis, we explore the fundamentals of spatial point process theory, a powerful mathematical tool to model data in the form of sets of spatial locations of points. In particular, since our datasets usually consist of information on trees belonging to different species, we focus on the so-called superposed process and its first and second-order statistics. We then study an algorithm to infer the intensity function of a point process which is capable to reduce sampling fluctuations and to capture relevant spatial characteristics of a spatial pattern, as space anisotropy and clustering. Finally, we explore in details the notions of ecological diversity and similarity and some of the most popular indexes used to measure them. In particular, we study how to insert them in the context of point processes’ theory. Our aim is at finding an analytical relation for the decay of similarity between two regions of a landscape as a function of the distance between them, by extending the classic notion of Sørensen’s index to incorporate spatial information. In the second part of the thesis, we tackle the problem of inferring the total bio- diversity of an ecosystem when only scattered samples are observed. In particular, we propose a novel upscaling method which, by exploiting the scaling invariance property of the negative binomial distribution, generates accurate and robust pre- dictions. We test it on both computer-generated and real forests and we show that it outperforms other methods previously proposed in literature.
La vita sulla Terra è caratterizzata da una straordinaria varietà di forme viventi in continua evoluzione per meglio adattarsi all’ambiente circostante e strettamente connesse le une alle altre. Oggigiorno, grazie all’enorme quantità di dati a disposizione, è possibile investigare a fondo su diversi sistemi viventi. La presente tesi è il risultato di un percorso attraverso i complessi pattern della teoria ecologica. In essa trattiamo sia modelli teorici sia problematiche legate all’analisi dei dati, come anche le connessioni tra loro, tutto all’interno di un contesto matematico. Centro d’interesse sono i diversi aspetti della biodiversità di un ecosistema, termine con il quale indichiamo la varietà delle sue specie. In particolare, vogliamo investigare il modo in cui le diverse specie interagiscono le une con le altre e come, da queste connessioni, possano originarsi dei pattern macro-ecologici ricorrenti. Infatti, nonostante la loro apparente diversità e complessità, è oggi evidente che i sistemi ecologici mostrano comportamenti simili. Questo fatto suggerisce che tali sistemi evolvono secondo un meccanismo comune, insensibile ai dettagli del sistema su cui agisce. Di conseguenza, si apre la strada allo sviluppo di modelli teorici che siano abbastanza complessi da riuscire a spiegare tali fenomeni, ma che al contempo non contengano più dettagli di quelli necessari a riprodurli. La prima parte della tesi è dedicata all’esplorazione dei fondamenti della teoria dei processi di punto, uno strumento matematico molto utile quando si va ad investigare dataset contenenti posizioni di punti nello spazio. In particolare, essendo i nostri database relativi a coordinate di alberi appartenenti a specie diverse, ci concentreremo sul cosiddetto processo sovrapposto e sulle sue statistiche di primo e secondo ordine. Poi studieremo un algoritmo che permette di ottenere informazioni sull’intensità di un processo di punto, capace al contempo di ridurre le fluttuazioni di campionamento e di rivelare caratteristiche importanti di un pattern spaziale, come l’anisotropia ed il clustering. Infine, esploreremo in dettaglio le nozioni di diversità e similarità e i vari indici proposti in letteratura per misurarle. In particolare, studieremo come inserire queste nozioni nel contesto dei processi di punto. L’obiettivo è quello di trovare una relazione analitica per il decadimento di similarità tra due regioni in funzione della distanza tra esse estendendo la nozione classica dell’indice di Sørensen in modo da incorporare informazioni spaziali. Nella seconda parte della tesi, affronteremo il problema di inferire la biodiversità totale di un ecosistema avendo a disposizione solo alcuni suoi campioni. In particolare, proporremo un nuovo metodo che, sfruttando la proprietà di invarianza di scala della distribuzione binomiale negativa, permette di avere stime accurate e robuste. Testandolo sia su foreste artificiali che reali, mostreremo che il metodo è più affidabile rispetto ad altri proposti in letteratura.

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3

Parks, Sarah Louise. "Mathematical models and statistics for evolutionary inference". Thesis, University of Cambridge, 2015. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.708749.

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Hua, Hairui. "Survival modelling in mathematical and medical statistics". Thesis, University of Birmingham, 2015. http://etheses.bham.ac.uk//id/eprint/5808/.

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An essential aspect of survival analysis is the estimation and prediction of survival probabilities for individuals. For this purpose, mathematical modelling of the hazard rate function is a fundamental issue. This thesis focuses on the novel estimation and application of hazard rate functions in mathematical and medical research. In mathematical research we focus on the development of a semiparametric kernel-based estimate of hazard rate function and a L\(_1\) error optimal kernel hazard rate estimate. In medical research we concentrate on the development and validation of survival models using individual participant data from multiple studies. We also consider how to fit survival models that predict individual response to treatment effectiveness, given IPD from multiple trials.

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5

Thulin, Måns. "On two classic problems in statistics". Licentiate thesis, Uppsala universitet, Matematisk statistik, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-171962.

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6

Groth, Randall E. Langrall Cynthia Willey Mooney Edward S. "Development of a high school statistical thinking framework". Normal, Ill. Illinois State University, 2003. http://wwwlib.umi.com/cr/ilstu/fullcit?p3087867.

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Thesis (Ph. D.)--Illinois State University, 2003.
Title from title page screen, viewed November 10, 2005. Dissertation Committee: Cynthia W. Langrall, Edward S. Mooney (co-chair), Beverly J. Hartter, Sharon S. McCrone. Includes bibliographical references (leaves 199-212) and abstract. Also available in print.

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7

Zhang, You You. "Brownian excursions in mathematical finance". Thesis, London School of Economics and Political Science (University of London), 2014. http://etheses.lse.ac.uk/3058/.

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The Brownian excursion is defined as a standard Brownian motion conditioned on starting and ending at zero and staying positive in between. The first part of the thesis deals with functionals of the Brownian excursion, including first hitting time, last passage time, maximum and the time it is achieved. Our original contribution to knowledge is the derivation of the joint probability of the maximum and the time it is achieved. We include a financial application of our probabilistic results on Parisian default risk of zero-coupon bonds. In the second part of the thesis the Parisian, occupation and local time of a drifted Brownian motion is considered, using a two-state semi-Markov process. New versions of Parisian options are introduced based on the probabilistic results and explicit formulae for their prices are presented in form of Laplace transforms. The main focus in the last part of the thesis is on the joint probability of Parisian and hitting time of Brownian motion. The difficulty here lies in distinguishing between different scenarios of the sample path. Results are achieved by the use of infinitesimal generators on perturbed Brownian motion and applied to innovative equity exotics as generalizations of the Barrier and Parisian option with the advantage of being highly adaptable to investors’ beliefs in the market.

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8

Rezaei, Sadegh. "The mathematical analysis of crossover designs". Title page, contents and summary only, 1997. http://web4.library.adelaide.edu.au/theses/09PH/09phr4668.pdf.

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Paine, Andrew Steven. "The mathematical modelling of rock blasting". Thesis, University of Southampton, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.315504.

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Fletcher, Matthew. "Mathematical topics in coding and cryptology". Thesis, University of Bath, 1992. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.317570.

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Hofbauer, Pamela S. Mooney Edward S. "Characterizing high school students' understanding of the purpose of graphical representations". Normal, Ill. : Illinois State University, 2007. http://proquest.umi.com/pqdweb?index=0&did=1414114601&SrchMode=1&sid=6&Fmt=2&VInst=PROD&VType=PQD&RQT=309&VName=PQD&TS=1207664408&clientId=43838.

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Thesis (Ph. D.)--Illinois State University, 2007.
Title from title page screen, viewed on April 8, 2008. Dissertation Committee: Edward S. Mooney (chair), Cynthia W. Langrall, Sherry L. Meier, Norma C. Presmeg. Includes bibliographical references (leaves 112-121) and abstract. Also available in print.

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12

Wilson, Boyd L. Plantholt Michael. "The development and evaluation of an instructional program in statistical literacy for use in post-secondary education". Normal, Ill. Illinois State University, 1994. http://wwwlib.umi.com/cr/ilstu/fullcit?p9521347.

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Thesis (D.A.)--Illinois State University, 1994.
Title from title page screen, viewed April 18, 2006. Dissertation Committee: Michael J. Plantholt (chair), Kenneth N. Berk, John A. Dossey, Graham A. Jones, Patricia H. Klass. Includes bibliographical references (leaves 85-96) and abstract. Also available in print.

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13

Taylor, Joan. "Mathematical models for planning social services resources". Thesis, Durham University, 1986. http://etheses.dur.ac.uk/6832/.

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This research discusses a number of computer-based mathematical models which are designed to assist planners to make strategic decisions concerning the allocations of social services resources. A new model is postulated which uses current patterns of care to derive a set of alternative modes or packages of care, chooses a suitable set of allocations of clients to packages of care within given resource constraints and can be used to explore the effect on resource requirements of demographic changes, and to explore alternative ways of caring for clients if populations expand and/or resources are reduced. Comparisons are made with the DHSS Balance of Care model and with other models. An exploration is included of the weighting values used in the postulated model’s objective function.

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14

Lee, Yun-Soo. "On some aspects of distribution theory and statistical inference involving order statistics". Virtual Press, 1991. http://liblink.bsu.edu/uhtbin/catkey/834141.

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Statistical methods based on nonparametric and distribution-free procedures require the use of order statistics. Order statistics are also used in many parametric estimation and testing problems. With the introduction of modern high speed computers, order statistics have gained more importance in recent years in statistical inference - the main reason being that ranking a large number of observations manually was difficult and time consuming in the past, which is no longer the case at present because of the availability of high speed computers. Also, applications of order statistics require in many cases the use of numerical tables and computer is needed to construct these tables.In this thesis, some basic concepts and results involving order statistics are provided. Typically, application of the Theory of Permanents in the distribution of order statistics are discussed. Further, the correlation coefficient between the smallest observation (Y1) and the largest observation (Y,,) of a random sample of size n from two gamma populations, where (n-1) observations of the sample are from one population and the remaining observation is from the other population, is presented.
Department of Mathematical Sciences

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15

Nordvall, Lagerås Andreas. "Markov Chains, Renewal, Branching and Coalescent Processes : Four Topics in Probability Theory". Doctoral thesis, Stockholm University, Department of Mathematics, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-6637.

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This thesis consists of four papers.

In paper 1, we prove central limit theorems for Markov chains under (local) contraction conditions. As a corollary we obtain a central limit theorem for Markov chains associated with iterated function systems with contractive maps and place-dependent Dini-continuous probabilities.

In paper 2, properties of inverse subordinators are investigated, in particular similarities with renewal processes. The main tool is a theorem on processes that are both renewal and Cox processes.

In paper 3, distributional properties of supercritical and especially immortal branching processes are derived. The marginal distributions of immortal branching processes are found to be compound geometric.

In paper 4, a description of a dynamic population model is presented, such that samples from the population have genealogies as given by a Lambda-coalescent with mutations. Depending on whether the sample is grouped according to litters or families, the sampling distribution is either regenerative or non-regenerative.

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Norén, G. Niklas. "Statistical methods for knowledge discovery in adverse drug reaction surveillance". Doctoral thesis, Stockholm University, Department of Mathematics, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-6764.

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Collections of individual case safety reports are the main resource for early discovery of unknown adverse reactions to drugs once they have been introduced to the general public. The data sets involved are complex and based on voluntary submission of reports, but contain pieces of very important information. The aim of this thesis is to propose computationally feasible statistical methods for large-scale knowledge discovery in these data sets. The main contributions are a duplicate detection method that can reliably identify pairs of unexpectedly similar reports and a new measure for highlighting suspected drug-drug interaction.

Specifically, we extend the hit-miss model for database record matching with a hit-miss mixture model for scoring numerical record fields and a new method to compensate for strong record field correlations. The extended hit-miss model is implemented for the WHO database and demonstrated to be useful in real world duplicate detection, despite the noisy and incomplete information on individual case safety reports. The Information Component measure of disproportionality has been in routine use since 1998 to screen the WHO database for excessive adverse drug reaction reporting rates. Here, it is further refined. We introduce improved credibility intervals for rare events, post-stratification adjustment for suspected confounders and an extension to higher order associations that allows for simple but robust screening for potential risk factors. A new approach to identifying reporting patterns indicative of drug-drug interaction is also proposed. Finally, we describe how imprecision estimates specific to each prediction of a Bayes classifier may be obtained with the Bayesian bootstrap. Such case-based imprecision estimates allow for better prediction when different types of errors have different associated loss, with a possible application in combining quantitative and clinical filters to highlight drug-ADR pairs for clinical review.

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Smedh, Hanna. "Utvärdering av ett optimeringsprogram för produktionsplanering". Thesis, Umeå University, Mathematics and Mathematical Statistics, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-31703.

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Målet med detta examensarbete är att utvärdera det program, baserat på dynamisk programmering, som tidigare skrivits för att efterlikna TSS:s produktionsplanering. Till att börja med återfinns i arbetet ett kapitel om programmets uppbyggnad, en kortare beskrivning av vart och ett av delprogrammen samt en förteckning över in- och utdata i respektive program. DP-programmet består av 6 sammankopplade exekverbara m-filer som tillsammans räknar ut den optimerade produktionsplaneringen för var och en av planeringsgrupperna. Programmet läser in och formaterar om data och optimerar sedan produktionen för var och en av artiklarna i en planeringsgrupp. Till sist sätter programmet ihop planeringsgruppens alla artikelplaneringar och får då ut ett produktionsalternativ. När genomgången av programmet var klar återstod körningar på nya data. För att få tillgång till dessa nya data gjordes ett besök hos TSS och efter detta utfördes körningar på den kommande periodens planerade tillverkning. Resultatet från dessa körningar visar, likt tidigare resultat, på att man skulle kunna minska sina kostnader ganska rejält genom att dra ner på lagerhållningen. Överlag skulle man enligt programmet kunna minska sina kostnader med drygt 50 %, vilket ändå måste anses som en rejäl vinst.

The aim of this thesis is benchmarking of the program, based on dynamic programming, that earlier was written to imitate the production planning at TSS. This thesis starts with a chapter about the construction of the DP-program, a shorter description of one and each of the program parts and also a list over the in- and output data in each program part. The DP-program consists of six linked MATLAB-files that together produce an optimized production plan for the different planning groups at TSS. The program reads in and reformat the given data and optimize the production of the articles in one group. Finally it compounds all article production plans and give us a production alternative. After running the program with new data the result shows, resembling with previous results, that TSS could be able to make some distinct cost-savings. According to the program, a 50 % decrease of TSS production costs is possible.

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Hjelmér, Minna. "Skattning av antal träd baserat på data från flygburen laserskanning". Thesis, Umeå University, Mathematics and Mathematical Statistics, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-31711.

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För att skatta skogsegenskaper utifrån data baserade på flygburen laserskanning används framförallt två olika metoder. Den första (areametoden) bygger uteslutande på höjden där laserpulserna reflekterats och en uppskattning av vilka pulser som reflekterats på marken och vilka som reflekterats i vegetationen. Den andra metoden (segmentmetoden) använder en segmentering av punkterna där laserpulserna reflekterats till enskilda träd. Detta är dock svårt att praktiskt genomföra, därför innehåller varje segment mellan 0 och cirka 10 träd. För att kunna utveckla och utvärdera resultaten insamlas även exakt information från ett antal provytor genom fältstudier. I denna rapport föreslås en icke-parametrisk modell för att skatta antalet träd i ett segment med segmentens area och art som förklarande variabler. Modellen skattas med hjälp av alla segment som finns inom en provyta, även de som inte helt ligger inom provytan. Modellen valideras på tre olika sätt och det visar sig att antalet träd i princip skattas väntevärdesriktigt. Dessutom förbättras inte resultatet nämnvärt med trädart som förklarande variabel.

To estimate forest characteristics based on airborne laser scanning data, two methods are used. The first one is on a raster cell level and uses solely the height of where the laser pulse is reflected and whether it is reflected on the ground or not. The second one is on an individual tree level and uses segmentation of the reflection points into individual trees. However, since it is difficult to segment into individual trees, every segment contains between 0 and about 10 trees. To be able to develop and validate the results, exact information about the trees in different field plots is gathered. In this report a nonparametric model is suggested to predict the number of trees in a segment, with area and species of the segments as predictors. In the estimation of the model, all segments within the field plots are used, even those only partly within. The model is validated in three different ways and estimates the number of trees with very small bias. Also the predictor, species of the segments, does not improve the results much.

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19

Lövdahl, Susanna, i Gustav Alfelt. "Undersökning av metoder för att analysera och modellera efter stora datamaterial, hantering av programmet SPSS samt en studie i Kronoberg läns gymnasieelevers psykiska ohälsa". Thesis, Växjö University, School of Mathematics and Systems Engineering, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:vxu:diva-2597.

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Andersson, Daniel. "Contributions to the Stochastic Maximum Principle". Doctoral thesis, KTH, Matematik (Avd.), 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-11301.

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This thesis consists of four papers treating the maximum principle for stochastic control problems. In the first paper we study the optimal control of a class of stochastic differential equations (SDEs) of mean-field type, where the coefficients are allowed to depend on the law of the process. Moreover, the cost functional of the control problem may also depend on the law of the process. Necessary and sufficient conditions for optimality are derived in the form of a maximum principle, which is also applied to solve the mean-variance portfolio problem. In the second paper, we study the problem of controlling a linear SDE where the coefficients are random and not necessarily bounded. We consider relaxed control processes, i.e. the control is defined as a process taking values in the space of probability measures on the control set. The main motivation is a bond portfolio optimization problem. The relaxed control processes are then interpreted as the portfolio weights corresponding to different maturity times of the bonds. We establish existence of an optimal control and necessary conditons for optimality in the form of a maximum principle, extended to include the family of relaxed controls. The third paper generalizes the second one by adding a singular control process to the SDE. That is, the control is singular with respect to the Lebesgue measure and its influence on the state is thus not continuous in time. In terms of the portfolio problem, this allows us to consider two investment possibilities - bonds (with a continuum of maturities) and stocks - and incur transaction costs between the two accounts. In the fourth paper we consider a general singular control problem. The absolutely continuous part of the control is relaxed in the classical way, i.e. the generator of the corresponding martingale problem is integrated with respect to a probability measure, guaranteeing the existence of an optimal control. This is shown to correspond to an SDE driven by a continuous orthogonal martingale measure. A maximum principle which describes necessary conditions for optimal relaxed singular control is derived.
QC 20100618

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21

Svensson, Jens. "On Importance Sampling and Dependence Modeling". Doctoral thesis, KTH, Matematik (Inst.), 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-11272.

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This thesis consists of four papers. In the first paper, Monte Carlo simulation for tail probabilities of heavy-tailed random walks is considered. Importance sampling algorithms are constructed by using mixtures of the original distribution with some other state-dependent distributions. Sufficient conditions under which the relative error of such algorithms is bounded are found, and the bound is calculated. A new mixture algorithm based on scaling of the original distribution is presented and compared to existing algorithms. In the second paper, Monte Carlo simulation of quantiles is treated. It is shown that by using importance sampling algorithms developed for tail probability estimation, efficient quantile estimators can be obtained. A functional limit of the quantile process under the importance sampling measure is found, and the variance of the limit process is calculated for regularly varying distributions. The procedure is also applied to the calculation of expected shortfall. The algorithms are illustrated numerically for a heavy-tailed random walk. In the third paper, large deviation probabilities for a sum of dependent random variables are derived. The dependence stems from a few underlying random variables, so-called factors. Each summand is composed of two parts: an idiosyncratic part and a part given by the factors. Conditions under which both factors and idiosyncratic components contribute to the large deviation behavior are found, and the resulting approximation is evaluated in a simple example. In the fourth paper, the asymptotic eigenvalue distribution of the exponentially weighted moving average covariance estimator is studied. Equations for the asymptotic spectral density and the boundaries of its support are found using the Marchenko-Pastur theorem.
QC 20100811

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22

Jonsson, Fredrik. "Existence and convergence of moments of Student’s t-statistic". Licentiate thesis, Uppsala universitet, Matematisk statistik, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-142146.

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Baranzano, Rosa. "Non-parametric kernel density estimation-based permutation test: Implementation and comparisons". Thesis, Uppsala universitet, Matematisk statistik, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-147052.

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Ndoumbe, Ebongue Steve Armand. "The risk model for insurance portfolio has been adopted to portfolio of derivatives. Describe the models and compare with a focus on the differences". Thesis, Linnéuniversitetet, Institutionen för datavetenskap, fysik och matematik, DFM, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-11293.

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Krouthen, Johannes. "Apartment values in Uppsala: Significant factors that differentiate the selling prices". Thesis, Uppsala universitet, Matematisk statistik, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-155333.

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Hansen, Peder. "Approximating the Binomial Distribution by the Normal Distribution – Error and Accuracy". Thesis, Uppsala universitet, Matematisk statistik, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-155336.

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Wennlund, Mikael. "Methods for checking coupling from the past". Thesis, Uppsala universitet, Matematisk statistik, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-159030.

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Gustin, Sara. "Investigation of some tests for homogeneity of intensity with applications to insurance data". Thesis, Uppsala universitet, Matematisk statistik, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-164588.

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Ahmady, Phoulady Hady. "Brownian Motions and Scaling Limits of Random Trees". Thesis, Uppsala universitet, Matematisk statistik, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-164700.

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Ding, Ding. "Modeling and simulation of highway traffic using a cellular automaton approach". Thesis, Uppsala universitet, Matematisk statistik, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-167359.

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Räisänen, Janne. "Random graphs as model of Peer-to-Peer social networks". Thesis, Uppsala universitet, Matematisk statistik, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-176609.

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Backåker, Fredrik. "The Google Markov Chain: convergence speed and eigenvalues". Thesis, Uppsala universitet, Matematisk statistik, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-176610.

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Almesjö, Fredrik. "Regression modeling of cyclotron spare parts consumption". Thesis, Uppsala universitet, Matematisk statistik, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-179484.

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Gong, Sheng. "Estimation of hot and cold spells with extreme value theory". Thesis, Uppsala universitet, Matematisk statistik, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-180372.

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Berglund, David. "Analysis of Swedish pollutants". Thesis, KTH, Matematik (Inst.), 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-99175.

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Abstract Today’s environmental reports contain flaws in the acquired data. This master thesis has the mission to alleviate the estimations of those flaws. The data in question, originates from Swedish industrial facilities. The thesis involves data-treatment by statistical analysis, which is done through fitting a model by the means of analysis of variance and multilevel modeling. The thesis also involves gathering and work with data from databases, as well as systematic treatment, sorting, categorization and evaluation of the data material. Calculations are made through the SAS statistical analysis program, which rendered estimates of fixed, linear and random effects. The results are presented through graphs and numerical estimates in the later part of the report. Calculations for estimations of the grand pollutant totals are conducted. These are compared to the observed data for relevance. Alternative ways on working on the problem at hand is discussed, as well as problems that have appeared during the work on the master thesis. The relevant code and calculations are attached towards the end.
Sammanfattning Dagens miljörapportering har brister i den rapporterade datan. Examensarbetet har som avsikt att underlätta skattningen av den saknade datan i rapporteringen, vars data härstammar från svenska företagsutsläpp. Arbetet innebär en databehandling via statistisk analys, vilken utförs genom modellanpassning via variansanalys och flernivåmodellering. Arbetet omfattar även hämtning och bearbetning av datamaterial ifrån databaser, så väl som systematisk behandling, sortering, indelning och tolkning av dataobservationer. Beräkningar är utförda i SAS statistiska analysprogram, vilket renderat skattningar och representationer av termer till fasta, linjära och slumpartade effekter. Dessa presenteras med siffror och grafer i senare delen av rapporten. Skattning av totaler beräknas och jämförs med observerad data. Problem och alternativa angreppssätt diskuteras, samt kod och beräkningar bifogas.

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Andersson, Daniel. "Necessary Optimality Conditions for Two Stochastic Control Problems". Licentiate thesis, Stockholm : Matematik, Kungliga Tekniska högskolan, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-4643.

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Molander, Rikard. "Stability conditions for scheduled waiting time in railway traffic". Thesis, Uppsala universitet, Matematisk statistik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-198812.

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Folkvaljon, Yasin. "Predicting Gleason score upgrading and downgrading between biopsy Gleason score and prostatectomy Gleason score – A population-based cohort study". Thesis, Uppsala universitet, Matematisk statistik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-197511.

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Abrahamsson, Linda. "Statistical models of breast cancer tumour growth for mammography screening data". Thesis, Uppsala universitet, Matematisk statistik, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-171980.

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Lindholm, Mathias. "Stochastic Epidemic Models : Different Aspects of Heterogeneity". Doctoral thesis, Stockholm : Department of Mathematics, Stockholm university, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-8335.

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Lindell, Andreas. "Theoretical and Practical Applications of Probability : Excursions in Brownian Motion, Risk Capital Stress Testing, and Hedging of Power Derivatives". Doctoral thesis, Stockholm : Department of Mathematics, Stockholm university, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-8570.

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Hall, Fenella T. H. "Mathematical models for class-D amplifiers". Thesis, University of Nottingham, 2011. http://eprints.nottingham.ac.uk/11891/.

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We here analyse a number of class-D amplifier topologies. Class-D amplifiers operate by converting an audio input signal into a high-frequency square wave output, whose lower-frequency components can accurately reproduce the input. Their high power efficiency and potential for low distortion makes them suitable for use in a wide variety of electronic devices. By calculating the outputs from a classical class-D design implementing different sampling schemes we demonstrate that a more recent method, called the Fourier transform/Poisson resummation method, has many advantages over the double Fourier series method, which is the traditional technique employed for this analysis. We thereby show that when natural sampling is used the input signal is reproduced exactly in the low-frequency part of the output, with no distortion. Although this is a known result, our calculations present the method and notation that we later develop. The classical class-D design is prone to noise, and therefore negative feedback is often included in the circuit. Subsequently we incorporate the Fourier transform/Poisson resummation method into a formalised and succinct analysis of a first-order negative feedback amplifier. Using perturbation expansions we derive the audio-frequency part of the output, demonstrating that negative feedback introduces undesirable distortion. Here we reveal the next order terms in the output compared with previous work, giving further insight into the nonlinear distortion. We then further extend the analysis to examine two more complex negative feedback topologies, namely a second-order and a derivative negative feedback design. Modelling each of these amplifiers presents an increased challenge due to the differences in their respective circuit designs, and in addition, for the derivative negative feedback amplifier we must consider scaling regimes based on the relative magnitudes of the frequencies involved. For both designs we establish novel expressions for the output, including the most significant distortion terms.

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43

Kappelin, Frida, i Jimmie Rudvall. "Fraud Detection within Mobile Money : A mathematical statistics approach". Thesis, Blekinge Tekniska Högskola, Institutionen för datalogi och datorsystemteknik, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:bth-10898.

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Context: Today it is easy to do banking transaction digitally, both on a computer or by using a mobile phone. As the banking-services increases and gets implemented to multi-platforms it makes it easier for a fraudster to commit financial fraud. This thesis will focus on investigating log-files from a Mobile Money system that makes it possible to do banking transactions with a mobile phone. Objectives: The objectives in this thesis is to evaluate if it is possible to combine two statistical methods, Benford's law together with statistical quantiles, to find a statistical way to find fraudsters within a Mobile Money system. Methods: Rules was extracted from a case study with focus on a Mobile Money system and limits was calculated by using quantiles. A fraud detector was implemented that use these rules together with limits and Benford's law in order to detect fraud.The fraud detector used the methods both independently and combined.The performance was then evaluated. Results: The results show that it is possible to use the Benford's law and statistical quantiles within the studied Mobile Money system. It is also shown that there is only a very small difference when the two methods are combined or not both in detection rate and accuracy precision. Conclusions: We conclude that by combining the chosen methods it is possible to get a medium-high true positive rates and very low false positive rates. The most effective method to find fraudsters is by only using quantiles. However, combining Benford's law with quantiles gives the second best result.

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Horta, Eduardo de Oliveira. "Essays in nonparametric econometrics and infinite dimensional mathematical statistics". reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2015. http://hdl.handle.net/10183/133007.

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A presente Tese de Doutorado é composta de quatro artigos científicos em duas áreas distintas. Em Horta, Guerre e Fernandes (2015), o qual constitui o Capítulo 2 desta Tese, é proposto um estimador suavizado no contexto de modelos de regressão quantílica linear (Koenker e Basset, 1978). Uma representação de Bahadur-Kiefer uniforme é obtida, a qual apresenta uma ordem assintótica que domina aquela correspondente ao estimador clássico. Em seguida, prova-se que o viés associado à suavização é negligenciável, no sentido de que o termo de viés é equivalente, em primeira ordem, ao verdadeiro parâmetro. A taxa precisa de convergência é dada, a qual pode ser controlada uniformemente pela escolha do parâmetro de suavização. Em seguida, são estudadas propriedades de segunda ordem do estimador proposto, em termos do seu erro quadrático médio assintótico, e mostra-se que o estimador suavizado apresenta uma melhoria em relação ao usual. Como corolário, tem-se que o estimador é assintoticamente normal e consistente à ordem p n. Em seguida, é proposto um estimador consistente para a matriz de covariância assintótica, o qual não depende de estimação de parâmetros auxiliares e a partir do qual pode-se obter diretamente intervalos de confiança assintóticos. A qualidade do método proposto é por fim ilustrada em um estudo de simulação. Os artigos Horta e Ziegelmann (2015a, 2015b, 2015c) se originam de um ímpeto inicial destinado a generalizar os resultados de Bathia et al. (2010). Em Horta e Ziegelmann (2015a), Capítulo 3 da presente Tese, é investigada a questão de existência de certos processos estocásticos, ditos processos conjugados, os quais são conduzidos por um segundo processo cujo espaço de estados tem como elementos medidas de probabilidade. Através dos conceitos de coerência e compatibilidade, obtémse uma resposta afirmativa à questão anterior. Baseado nas noções de medida aleatória (Kallenberg, 1973) e desintegração (Chang e Pollard, 1997; Pollard, 2002), é proposto um método geral para construção de processos conjugados. A teoria permite um rico conjunto de exemplos, e inclui uma classe de modelos de mudança de regime. Em Horta e Ziegelmann (2015b), Capítulo 4 desta Tese, é proposto – em relação com a construção obtida em Horta e Ziegelmann (2015a) – o conceito de processo fracamente conjugado: um processo estocástico real a tempo contínuo, conduzido por uma sequência de funções de distribuição aleatórias, ambos conectados por uma condição de compatibilidade a qual impõe que aspectos da distribuição do primeiro processo são divisíveis em uma quantidade enumerável de ciclos, dentro dos quais este tem como marginais, precisamente, o segundo processo. Em seguida, mostra-se que a metodologia de Bathia et al. (2010) pode ser aplicada para se estudar a estrutura de dependência de processos fracamente conjugados, e com isso obtém-se resultados de consistência à ordem p n para os estimadores que surgem naturalmente na teoria. Adicionalmente, a metodologia é ilustrada através de uma implementação a dados financeiros. Especificamente, o método proposto permite que características da dinâmica das distribuições de processos de retornos sejam traduzidas em termos de um processo escalar latente, a partir do qual podem ser obtidas previsões de quantidades associadas a essas distribuições. Em Horta e Ziegelmann (2015c), Capítulo 5 da presente Tese, são obtidos resultados de consistência à ordem p n em relação à estimação de representações espectrais de operadores de autocovariância de séries de tempo Hilbertianas estacionárias, em um contexto de medições imperfeitas. Os resultados são uma generalização do método desenvolvido em Bathia et al. (2010), e baseiam-se no importante fato de que elementos aleatórios em um espaço de Hilbert separável são quase certamente ortogonais ao núcleo de seu respectivo operador de covariância. É dada uma prova direta deste fato.
The present Thesis is composed of 4 research papers in two distinct areas. In Horta, Guerre, and Fernandes (2015), which constitutes Chapter 2 of this Thesis, we propose a smoothed estimator in the framework of the linear quantile regression model of Koenker and Bassett (1978). A uniform Bahadur-Kiefer representation is provided, with an asymptotic rate which dominates the standard quantile regression estimator. Next, we prove that the bias introduced by smoothing is negligible in the sense that the bias term is firstorder equivalent to the true parameter. A precise rate of convergence, which is controlled uniformly by choice of bandwidth, is provided. We then study second-order properties of the smoothed estimator, in terms of its asymptotic mean squared error, and show that it improves on the usual estimator when an optimal bandwidth is used. As corollaries to the above, one obtains that the proposed estimator is p n-consistent and asymptotically normal. Next, we provide a consistent estimator of the asymptotic covariance matrix which does not depend on ancillary estimation of nuisance parameters, and from which asymptotic confidence intervals are straightforwardly computable. The quality of the method is then illustrated through a simulation study. The research papers Horta and Ziegelmann (2015a;b;c) are all related in the sense that they stem from an initial impetus of generalizing the results in Bathia et al. (2010). In Horta and Ziegelmann (2015a), Chapter 3 of this Thesis, we address the question of existence of certain stochastic processes, which we call conjugate processes, driven by a second, measure-valued stochastic process. We investigate primitive conditions ensuring existence and, through the concepts of coherence and compatibility, obtain an affirmative answer to the former question. Relying on the notions of random measure (Kallenberg (1973)) and disintegration (Chang and Pollard (1997), Pollard (2002)), we provide a general approach for construction of conjugate processes. The theory allows for a rich set of examples, and includes a class of Regime Switching models. In Horta and Ziegelmann (2015b), Chapter 4 of the present Thesis, we introduce, in relation with the construction in Horta and Ziegelmann (2015a), the concept of a weakly conjugate process: a continuous time, real valued stochastic process driven by a sequence of random distribution functions, the connection between the two being given by a compatibility condition which says that distributional aspects of the former process are divisible into countably many cycles during which it has precisely the latter as marginal distributions. We then show that the methodology of Bathia et al. (2010) can be applied to study the dependence structure of weakly conjugate processes, and therewith provide p n-consistency results for the natural estimators appearing in the theory. Additionally, we illustrate the methodology through an implementation to financial data. Specifically, our method permits us to translate the dynamic character of the distribution of an asset returns process into the dynamics of a latent scalar process, which in turn allows us to generate forecasts of quantities associated to distributional aspects of the returns process. In Horta and Ziegelmann (2015c), Chapter 5 of this Thesis, we obtain p n-consistency results regarding estimation of the spectral representation of the zero-lag autocovariance operator of stationary Hilbertian time series, in a setting with imperfect measurements. This is a generalization of the method developed in Bathia et al. (2010). The generalization relies on the important property that centered random elements of strong second order in a separable Hilbert space lie almost surely in the closed linear span of the associated covariance operator. We provide a straightforward proof to this fact.

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Qi, Qi. "Mathematical modelling of telomere dynamics". Thesis, University of Nottingham, 2011. http://eprints.nottingham.ac.uk/12258/.

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Telomeres are repetitive elements of DNA which are located at the ends of chromosomes. During cell division, telomeres on daughter chromomeres shorten until the telomere length falls below a critical level. This shortening restricts the number of cell divisions. In this thesis, we use mathematical modelling to study dynamics of telomere length in a cell in order to understand normal ageing (telomere shortening),Werner’s syndrome (a disease of accelerated ageing) and the immortality of cells caused by telomerase (telomere constant length maintenance). In the mathematical models we compared four possible mechanisms for telomere shortening. The simplest model assumes that a fixed amount of telomere is lost on each replication; the second supposes that telomere loss depends on telomere length; for the third case the amount of telomeres loss per division is fixed but the probability of dividing depends on telomere length; the fourth cases has both telomere loss and the probability of division dependent on telomere length. We start by developing Monte Carlo simulations of normal ageing using these four cases. Then we generalize the Monte Carlo simulations to consider Werner’s syndrome, where the extra telomeres are lost during replication accelerate the ageing process. In order to investigate how the distribution of telomere length varies with time, we derive, from the discrete model, continuum models for the four different cases. Results from the Monte Carlo simulations and the deterministic models are shown to be in good agreement. In addition to telomere loss, we also consider increases in telomere length caused by the enzyme telomerase, by appropriately extending the earlier Monte Carlo simulations and continuum models. Results from the Monte Carlo simulations and the deterministic models are shown to be in good agreement. We also show that the concentration of telomerase in cells can control their proliferative potential.

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46

Fok, Hou Kei. "Generalizations of some Hermite-Hadamard-type inequalities". Thesis, University of Macau, 2012. http://umaclib3.umac.mo/record=b2592934.

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Rosa, Joao Miguel Feu. "Mathematical programming applied to diet problems in a Brazilian region". Thesis, Lancaster University, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.332375.

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Wang, Baoyong. "Fractionation Statistics". Thèse, Université d'Ottawa / University of Ottawa, 2014. http://hdl.handle.net/10393/31001.

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Paralog reduction, the loss of duplicate genes after whole genome duplication (WGD) is a pervasive process. Whether this loss proceeds gene by gene or through deletion of multi-gene DNA segments is controversial, as is the question of fractionation bias, namely whether one homeologous chromosome is more vulnerable to gene deletion than the other. As a null hypothesis, we first assume deletion events, on one homeolog only, excise a geometrically distributed number of genes with unknown mean mu, and these events combine to produce deleted runs of length l, distributed approximately as a negative binomial with unknown parameter r; itself a random variable with distribution pi(.). A biologically more realistic model requires deletion events on both homeologs distributed as a truncated geometric. We simulate the distribution of run lengths l in both models, as well as the underlying pi(r), as a function of mu, and show how sampling l allows us to estimate mu. We apply this to data on a total of 15 genomes descended from 6 distinct WGD events and show how to correct the bias towards shorter runs caused by genome rearrangements. Because of the difficulty in deriving pi(.) analytically, we develop a deterministic recurrence to calculate each pi(r) as a function of mu and the proportion of unreduced paralog pairs. This is based on a computing formula containing nested sums. The parameter mu can be estimated based on run lengths of single-copy regions. We then reduce the computing formulae, at least in the one-sided case, to closed form. This virtually eliminates computing time due to highly nested summations. We formulate a continuous version of the fractionation process, deleting line segments of exponentially distributed lengths in analogy to geometric distributed numbers of genes. We derive nested integrals and discover that the number of previously deleted regions to be skipped by a new deletion event is exactly geometrically distributed. We undertook a large simulation experiment to show how to discriminate between the gene-by-gene duplicate deletion model and the deletion of a geometrically distributed number of genes. This revealed the importance of the effects of genome size N, the mean of the geometric distribution, the progress towards completion of the fractionation process, and whether the data are based on runs of deleted genes or undeleted genes.

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Ikoro, Gibson Okechukwu. "Mathematical modelling of the statistics of communication in social networks". Thesis, Queen Mary, University of London, 2017. http://qmro.qmul.ac.uk/xmlui/handle/123456789/30710.

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Chat rooms are of enormous interest to social network researchers as they are one of the most interactive internet areas. To understand the behaviour of users in a chat room, there have been studies on the analysis of the Response Waiting Time (RWT) based on traditional approaches of aggregating the network contacts. However, real social networks are dynamic and properties such as RWT change over time. Unfortunately, the traditional approach focuses only on static network and neglecting the temporal variation in RWT which may have lead to misrepresentation of the true nature of RWT. In order to determine the true nature of RWT, we analyse and compare the RWT of three online chat room logs (Walford, IRC and T-REX) putting into consideration the dynamic nature of RWT. Our research shows that the distribution of the RWT exhibits multi-scaling behaviour, which signi cantly a ects the current views on the nature of RWT. This is a shift from simple power-law distribution to a more complex pattern. The previous study on users RWT between pairs of people claims that the RWT has a power-law distribution with an exponent of 1. However, our research shows that multi-scaling behaviour and the exponent has a wider range of values which depend on the environment and time of day. The di erent exponents observed on di erent time scales suggest that the time context or environment has a signi cant in uence on users RWT. Furthermore, using the chat characterise, we predicted the factors which could minimize response waiting time and improving the friendship connection during online chat sessions. We apply our ndings to design an algorithm for chat thread detection. Here, we proposed two variations of cluster algorithm. The rst algorithm involves the traditional approach while in the second one, the temporal variations in RWT was taken into consideration to capture the dynamic nature of a text stream. An advantage of our proposed method over the previous models is that previous models have involved highly computationally intensive methods and often lead to deterioration in the accuracy of the result whereas our proposed approach uses a simple and effective sequential thread detection method, which is less computationally intensive.

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Haque, Mainul. "Mathematical modelling of eukaryotic stress-response gene networks". Thesis, University of Nottingham, 2012. http://eprints.nottingham.ac.uk/12509/.

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Mathematical modelling of gene regulatory networks is a relatively new area which is playing an important role in theoretical and experimental investigations that seek to open the door to understanding the real mechanisms that take place in living systems. The current thesis concentrates on studying the animal stress-response gene regulatory network by seeking to predict the consequence of environmental hazards caused by chemical mixtures (typical of industrial pollution). Organisms exposed to pollutants display multiple defensive stress responses, which together constitute an interlinked gene network (the Stress-Response Network; SRN). Multiple SRN reporter-gene outputs have been monitored during single and combined chemical exposures in transgenic strains of two invertebrates, Caenorhabditis elegans and Drosophila melanogaster. Reporter expression data from both species have been integrated into mathematical models describing the dynamic behaviour of the SRN and incorporating its known regulatory gene circuits. We describe some mathematical models of several types of different stress response networks, incorporating various methods of activation and inhibition, including formation of complexes and gene regulation (through several known transcription factors). Although the full details of the protein interactions forming these types of circuits are not yet well-known, we seek to include the relevant proteins acting in different cellular compartments. We propose and analyse a number of different models that describe four different stress response gene networks and through a combination of analytical (including stability, bifurcation and asymptotic) and numerical methods, we study these models to gain insight on the effect of several stresses on gene networks. A detailed time-dependent asymptotic analysis is performed for relevant models in order to clarify the roles of the distinct biochemical reactions that make up several important proteins production processes. In two models we were able to verify the theoretical predictions with the corresponding laboratory experimental observations that carried out by my coworkers in Britain and India.

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