Standard Markov chain Monte Carlo (MCMC) sampling methods can experience problem sampling from multi-modal distributions. A variety of sampling methods have been introduced to overcome this problem. The mode jumping method of Tjelmeland & Hegstad (2001) tries to find a mode and propose a value from that mode in each mode jumping attempt. This approach is inefficient in that the work needed to find each mode and model the distribution in a neighbourhood of the mode is carried out repeatedly during the sampling process. We shall propose a new mode jumping approach which retains features of the Tjelmeland & Hegstad (2001) method but differs in that it finds the modes in an initial search, then uses this information to jump between modes effectively in the sampling run. Although this approach does not allow a second chance to find modes in the sampling run, we can show that the overall probability of missing a mode in our approach is still low. We apply our methods to sample from distributions which have continuous variables, discrete variables, a mixture of discrete and continuous variables and variable dimension. We show that our methods work well in each case and in general, are better than the MCMC sampling methods commonly used in these cases and also, are better than the Tjelmeland & Hegstad (2001) method in particular.

The ordering processes of ferroelectric and multiferroic materials were investigated via neutron total scattering and the reverse Monte Carlo method. The results presented in this thesis are from three materials where ferroelectric behaviour is a result of ordering of molecular groups rather than individual atoms. Two of the materials are metal-organic frameworks, three dimensional cage-like structures with guest ions inside the pores; the third material, is a room temperature ferroelectric. In the high-temperature phase of dimethylammonium manganese formate, the framework distorts around the disordered cation, and the cations form shorter hydrogen bonds with the formate framework than the average structure suggests. Framework deformations became increasingly unfavourable as the material cooled. The cations continue to order as the material was cooled below Tc. Analysis of the high-temperature phase atomistic configurations showed that in addition to the three known orientations about the threefold axis, a significant minority of the cations lie mid-way between these positions, a feature which could not have been observed via standard crystallographic techniques. The mechanisms for thermal expansion of potassium imidazolium hexacyanoferrate change between the intermediate-temperature phase and the high-temperature phase. In the hightemperature phase the framework distorts around the disordered guest, but in the intermediatetemperature phase the framework stiffens. I propose that the temperature of the dielectric transition is dependent of the volume inside the framework, but that the temperature range of the intermediate-temperature phase is dependent on the rate of contraction of the framework around the guest cation. For triglycine sulfate no correlation was observed between the orientation of the polar molecules and the motion of the intermediate deuterium. Furthermore, in the high temperature phase the atomistic configurations produced models with macroscopic polarisation. I propose that this material forms domains of aligned polar molecules above Tc and that these domains are larger than the atomistic configurations.

Orientador: Miriam Harumi Tsunemi / Resumo: Em inúmeras situações práticas a relação entre uma variável resposta e uma ou mais covariáveis é curvada. Dentre as diversas formas de representar esta curvatura, Royston e Altman (1994) propuseram uma extensa famı́lia de funções denominada de Polinômios Fracionários (Fractional Polynomials - FP ). Bové e Held (2011) im- plementaram o paradigma bayesiano para FP sob a suposição de normalidade dos erros. Sua metodologia é fundamentada em uma distribuição a priori hiper − g (Liang et al., 2008), que, além de muitas propriedades assintóticas interessantes, garante uma predição bayesiana de modelos consistente. Nesta tese, compara-se as abordagens clássica e Bayesiana para PF a partir de dados reais disponı́veis na litera- tura, bem como por simulações. Além disso, propõem-se uma abordagem Bayesiana para modelos FPs em que a potência, diferentemente dos métodos usuais, pode as- sumir qualquer valor num determinado intervalo real e é estimada via métodos de simulação HMC (Monte Carlo Hamiltoniano) e MCMC (Métodos de Monte Carlo via Cadeias de Markov). Neste modelo, para o caso de um FP de segunda ordem, ao contrário dos modelos atualmente disponı́veis, apenas uma potência é estimada. Avalia-se este modelo a partir de dados simulados e em dados reais, sendo um deles com transformação de Box-Cox. / Abstract: In many practical situations the relationship between the response variable and one or more covariates is curved. Among the various ways of representing this curvature, Royston and Altman (1994) proposed an extended family of functions called Fractional Polynomials (FP). Bov´e and Held (2011) implemented the Bayesian paradigm for FP on the assumption of error normality. Their methodology is based on a hyperg prior distribution, which, in addition to many interesting asymptotic properties, guarantees a consistent Bayesian model average (BMA). In addition, a Bayesian approach is proposed for FPs models in which power, unlike the usual methods, can obtain any numerical real interval value and is estimated via HMC (Monte Carlo Hamiltonian) and MCMC (Markov chain Monte Carlo). In this model, in the case of a second-order FP, unlike the currently available models, only one power is estimated. This model is evaluated from simulated data and real data, one of them with Box-Cox transformation. / Doutor

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Proton therapy is an established radiotherapy technique for the treatment of complex cancers. However, problems exist in the planning of treatments where the use of inaccurate dose modelling may lead to treatments being delivered which are not optimal. Most of the problems with dose modelling tools used in proton therapy treatment planning lie in their treatment of processes such as multiple Coulomb scattering, therefore a technique that accurately models such effects is preferable. Monte Carlo simulation alleviates many of the problems in current dose models but, at present, well-validated full-physics Monte Carlo simulations require more time than is practical in clinical use. Using the well-known and well-validated Monte Carlo toolkit Geant4, an application-called PTMC-has been developed for the simulation of proton therapy treatment plans. Using PTMC, several techniques to improve throughput were developed and evaluated, including changes to the tracking algorithm in Geant4 and application of large scale parallelism using novel computing architectures such as the Intel Xeon Phi co-processor. In order to quantify any differences in the dose-distributions simulated when applying these changes, a new dose comparison tool was also developed which is more suited than current techniques for use with Monte Carlo simulated dose distributions. Using an implementation of the Woodcock algorithm developed in this work, it is possible to track protons through a water phantom up to eight times faster than using the PRESTA algorithm present in Geant4, with negligible loss of accuracy. When applied to a patient simulation, the Woodcock algorithm increases throughput by up to thirty percent, though step limitation was necessary to preserve simulation accuracy. Parallelism was implemented on an Intel Xeon Phi co-processor card, where PTMC was tested with up to 244 concurrent threads. Difficulties imposed by the limited RAM available were overcome through the modification of the Geant4 toolkit and through the use of a novel dose collation technique. Using a single Xeon Phi co-processor, it is possible to validate a proton therapy treatment plan in two hours; with two co-processors that simulation time is halved. For the treatment plan tested, two Xeon Phi co-processors were roughly equivalent to a single 48-core AMD Opteron machine. The relative costs of Xeon Phi co-processors and traditional machines have also been investigated; at present the Intel Xeon Phi co-processor is not cost competitive with standard hardware, costing around twice as much as an AMD machine with comparable performance. Distributed parallelism was also implemented through the use of the Google Compute Engine (GCE). A tool has been developed-called PYPE-which allows users to launch large clusters in the GCE to perform arbitrary compute-intensive work. PYPE was used with PTMC to perform rapid treatment plan validation in the GCE. Using a large cluster, it is possible to validate a proton therapy treatment plan in ten minutes at a cost of roughly $10; the same plan computed locally on a 24-thread Intel Xeon machine required five hours. As an example calculation using PYPE and PTMC, a robustness study is undertaken for a proton therapy treatment plan; this robustness study shows the usefulness of Monte Carlo when computing dose distributions for robustness studies, and the utility of the PYPE tool to make numerous full physics Monte Carlo simulations quickly. Using the tools developed in this work, a complete treatment plan robustness study can be performed in around 26 hours for a cost of less than $500, while using full-physics Monte Carlo for dose distribution calculations.

Dissertação (mestrado)—Universidade de Brasília, Instituto de Física, Programa de Pós-Graduação em Física, 2016. / Sistemas com interações de longe alcance podem apresentar propriedades termodinâmicas peculiares como não-aditividade, calor específico negativo e inequivalência de ensembles. Neste caso o ensemble mais conveniente para calcular as grandezas termodinâmicas é o ensemble microcanônico. Entretanto, calcular a função de partição microcanônica é, por muitas vezes, uma tarefa difícil, devido à integração sobre as posições. Por isso, métodos computacionais são importantes para resolver esse problema. Neste trabalho é feita uma comparação entre dois métodos de Monte Carlo para estudar a termodinâmica de sistemas com interação de longe alcance, com o intuito de analisar qual algoritmo é superior ao outro em diferentes situações. / Systems with long-range interactions may present strange thermodynamics properties as non-additivity, negative specific heat and inequivalence of ensembles. In this case the most convenient ensemble to calculate the thermodynamic quantities is the microcanonical ensemble. However, calculate the microcanonical partition function is often a hard task, due the integration over the configuration space. Thus, computational methods are important to solve these problems. In this report a comparison is made between two Monte Carlo methods to study the thermodynamics of systems with long-range interactions, in order to analyze what algorithm is superior to the other in different situations.

As for the Monte Carlo Method, we first introduce a brief history of the method and pricing options by using the method. Secondly, the basic idea of using the method in computing option price is described. Thirdly, pricing vanilla options is introduced. Fourthly, we discuss some techniques of improving computing accuracy. They include antithetic variables, control variate methods and importance sampling. / Fifth, we study in detail pricing option problems by using the Monte Carlo method. Then we present a new method on pricing American option, by which, the required memory in computation can be significantly reduced. For most methods of pricing American options, bias exists. However, by using the memory reduction method, minimizing biases is possible. We also discuss the problem for valuation of multiasset options by using our method. In fact, this is an important application of the Monte Carlo method in practical financial problems. / Finally, comparisons of the performances of these numerical results are presented. / Some basic concepts on options are first introduced. Then general methods for pricing options are described. These methods include: analytical formula, finite difference methods and binomial and multinomial methods. These prepare us for the in-depth study on the Monte Carlo method in subsequent chapters. / The Monte Carlo approach has proved to be a valuable and flexible computational tool in modern finance. The Monte Carlo method is the main topic of the thesis. / by Chen Yong. / "August 2002." / Adviser: Raymond Chan. / Source: Dissertation Abstracts International, Volume: 63-10, Section: B, page: 4710. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (p. 77-79). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest dissertations and theses, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

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Téma analýzy rizika je relativně novou oblastí, která poslední dobou nabývá na významu nejen ve světě, ale i v České republice. Tomu však zdaleka neodpovídá zdejší zázemí. V českém jazyce dosud nebyly vydány žádné tituly zabývající se komplexně touto problematikou, a pokud se již podaří nějakou literaturu najít, pak není určena čtenáři, který s analýzou rizika dosud není příliš obeznámen. Proto si tato diplomová práce klade za cíl rozšířit povědomí o této problematice. Informace v tomto dokumentu jsou založeny na renomovaných anglicky psaných publikacích z této oblasti a dále vycházejí z praktických zkušeností, které jsem načerpal při vývoji vlastního nástroje pro analýzu rizika. Záměrem tak není jen plnit roli akademického textu, ale zároveň praktického návodu, který pomůže každému s tvorbou jeho prvních modelů. Diplomová práce se skládá z teoretické a praktické části. Kapitoly teorie jsou děleny na jednotlivé sekce, které představují dílčí kroky celého procesu analýzy rizika. V praktické části pak je krátce popsána aplikace nástroje Profeta na reálném projektu. Celý dokument je koncipován pro využití širokým spektrem čtenářů se zájmem o úvod do analýzy rizika. Zájemce je postupně seznámen se základy tvorby modelů, identifikování klíčových faktorů úspěchu, definování předpokladů, nalezení předpovědí a interpretování výsledků simulace. Dále pak text zprostředkovává kvalitativní i kvantitativní rozbor rizika a poskytuje instrukce k aplikaci jednotlivých metod k identifikaci, kvantifikaci, předpovídání, ohodnocování, zajištění, diversifikování a managementu rizika. Jednotlivé metody jsou představeny z pohledu jejich reálné aplikace prostřednictvím vybraných z nástrojů pro analýzu rizika a jejich významu pro celý rozhodovací proces.

Každý projekt je ze své povahy spojen s jistou dávkou rizika a nejistoty, kterou je nutné zohlednit při volbě adekvátních metod pro jeho řízení. Cílem práce je tyto metody klasifikovat, porovnat a aplikovat na případové studii z podnikové praxe. Podrobněji jsou přitom rozebrány právě ty metody, které byly vhodné pro zkoumaný projekt z případové studie: jedná se o metodu CPM/PERT, simulaci Monte Carlo a analýzu projektu prostřednictvím bayesovských sítí.