In many environmental and climate applications, extreme data are spatial by nature, and hence statistics of spatial extremes is currently an important and active area of research dedicated to developing innovative and flexible statistical models that determine the location, intensity, and magnitude of extreme events. In particular, the development of flexible sub-asymptotic models is in trend due to their flexibility in modeling spatial high threshold exceedances in larger spatial dimensions and with little or no effects on the choice of threshold, which is complicated with classical extreme value processes, such as Pareto processes. In this thesis, we develop new flexible sub-asymptotic extreme value models for modeling spatial and spatio-temporal extremes that are combined with carefully designed gradient-based Markov chain Monte Carlo (MCMC) sampling schemes and that can be exploited to address important scientific questions related to risk assessment in a wide range of environmental applications. The methodological developments are centered around two distinct themes, namely (i) sub-asymptotic Bayesian models for extremes; and (ii) flexible marked point process models with sub-asymptotic marks. In the first part, we develop several types of new flexible models for light-tailed and heavy-tailed data, which extend a hierarchical representation of the classical generalized Pareto (GP) limit for threshold exceedances. Spatial dependence is modeled through latent processes. We study the theoretical properties of our new methodology and demonstrate it by simulation and applications to precipitation extremes in both Germany and Spain. In the second part, we construct new marked point process models, where interest mostly lies in the extremes of the mark distribution. Our proposed joint models exploit intrinsic CAR priors to capture the spatial effects in landslide counts and sizes, while the mark distribution is assumed to take various parametric forms. We demonstrate that having a sub-asymptotic distribution for landslide sizes provides extra flexibility to accurately capture small to large and especially extreme, devastating landslides.

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Clinical drug trials are costly and time-consuming. Bayesian methods alleviate the inefficiencies in the testing process while providing user-friendly probabilistic inference and predictions from the sampled posterior distributions, saving resources, time, and money. We propose a dynamic linear model to estimate the mean response at each dose level, borrowing strength across dose levels. Our model permits nonmonotonicity of the dose-response relationship, facilitating precise modeling of a wider array of dose-response relationships (including the possibility of toxicity). In addition, we incorporate an adaptive approach to the design of the clinical trial, which allows for interim decisions and assignment to doses based on dose-response uncertainty and dose efficacy. The interim decisions we consider are stopping early for success and stopping early for futility, allowing for patient and time savings in the drug development process. These methods complement current clinical trial design research.

京都大学 / 新制・課程博士 / 博士(情報学) / 甲第24980号 / 情博第853号 / 新制||情||143(附属図書館) / 京都大学大学院情報学研究科システム科学専攻 / (主査)教授 田中 利幸, 教授 下平 英寿, 准教授 本多 淳也 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

The statistical analysis of cointegration is crucial for inferring shared stochastic trends between variables and is an important area of Econometrics for analyzing long-term equilibriums in the economy. Bayesian inference of cointegration involves the identification of cointegrating vectors that are determined up to arbitrary linear combinations, for which the Gibbs sampler is often used to simulate draws from the posterior distribution. However, economic theory may not suggest linear relations and regime-switching models can be used to account for non-linearity. Modeling cointegration and regime-switching as well as the combination of them are associated with highly parameterized models that can prove to be difficult for Markov Chain Monte Carlo techniques such as the Gibbs sampler. Hamiltonian Monte Carlo, which aims at efficiently exploring the posterior distribution, may thus facilitate these difficulties. Furthermore, posterior distributions with highly varying curvature in their geometries can be adequately monitored by Hamiltonian Monte Carlo. The aim of the thesis is to analyze how Hamiltonian Monte Carlo performs in simulating draws from the posterior distributions of models accounting for cointegration and regime-switching. The results suggest that while it is not necessarily the case that regime-switching will be identified, Hamiltonian Monte Carlo performs well in exploring the posterior distribution. However, high rates of divergences from the true Hamiltonian trajectory reduce the algorithm to a Random Walk to some extent, limiting the efficiency of the sampling.

Accurate forecasting of stock price movements is crucial for optimizing trade execution and mitigating risk in automated trading environments, especially when leveraging Limit Order Book (LOB) data. However, developing predictive models from LOB data presents substantial challenges due to its inherent complexities and high-frequency nature. In this thesis, the application of the General Compound Hawkes Process (GCHP) is explored to predict price volatility. Within this framework, a Hawkes process is employed to estimate the times of price changes, and a Markovian model is utilized to determine their amplitudes. The price volatility is obtained through both numerical and analytical methodologies. The performance of the GCHP is assessed on a publicly available dataset, including five distinct stocks. To enhance accuracy, the number of states in the Markov chain is gradually increased, and the advantages of incorporating a higher-order Markov chain for refined volatility estimation are demonstrated.

Secondary structure dynamics of biopolymers play a vital role in many of the complex processes within a cell. However, due to the substantial number of atoms in the involved biopolymers along with the multitude of interactions that occur between the molecules, understanding these processes in detail is challenging and often involves computationally demanding simulations. In this thesis, the secondary structure dynamics of three different biopolymer systems were modeled using a single approach, which is based on intuitive principles that facilitate the interpretation. To this end, the kinetic behavior of each system was experimentally determined, and described by simplified reaction schemes, which were then connected to Markov chain models encompassing all principal secondary structural conformations. Firstly, we investigated the toehold-mediated strand displacement reaction, which is widely applied in nanotechnology to create DNA-based nano-devices and biochemical reaction networks. Our model correctly described the impact of base pair mismatches on the kinetics of these reactions, as measured by bulk fluorescence experiments. Additionally, it revealed that incumbent dissociation, base pair fraying, and internal loop formation are important processes during strand displacement. Furthermore, we established two dissipative elements to enhance temporal control over toehold-mediated strand displacement reactions. The first element allowed a reversible and repeatable incumbent strand release, whereas the second element provided the possibility to start the displacement reaction after a programmable temporal delay. Secondly, we studied the target recognition by the CRISPR-Cas effector complex Cascade, a highly promising protein for applications in genome engineering. Our model successfully reproduced all aspects of the torque- and mismatch-dependent R-loop formation time by Cascade obtained by single-molecule torque and bulk fluorescence measurements. Furthermore, we demonstrated that the seed effect observed for Cascade results from DNA supercoiling, rather than a structural property of the protein complex. Lastly, we explored the folding/unfolding of α-helices, which plays a critical role in the folding and function of proteins. Our model accurately described α-helix unfolding kinetics obtained by fast triplet-triplet energy transfer. Moreover, we showed that the complex α-helix unfolding does not follow a simple Einstein-type diffusion but is a combination of the sub-diffusive boundary diffusion and the rather peptide-length-independent coil nucleation. The presented models enabled access to the diverse timescales of the characterized processes, which are generally difficult to access experimentally, despite utilizing just a single approach. In particular, we obtained: tens of microseconds for the branch migration step time of the toehold-mediated strand displacement, hundreds of microseconds for the R-loop formation steps by Cascade, and tens of nanoseconds for folding or unfolding of an α-helix by a single residue. Given the simplicity and accessibility of the established models, we are confident that they will become useful tools for researchers to analyze the dynamics of biomolecules, and anticipate that similar modeling approaches can be applied to other biopolymer systems, being well-described by probabilistic models. / Die Sekundärstrukturdynamik von Biopolymeren spielt eine entscheidende Rolle bei vielen komplexen Prozessen innerhalb einer Zelle. Aufgrund der beträchtlichen Anzahl von Atomen in den beteiligten Biopolymeren und der Vielzahl an Wechselwirkungen zwischen den Molekülen ist es jedoch eine Herausforderung diese Prozesse im Detail zu verstehen, und erfordert oft rechenintensive Simulationen. In dieser Arbeit wurde die Sekundärstrukturdynamik von drei verschiedenen Biopolymersystemen mit einem einzigen Ansatz modelliert, welcher auf intuitiven Prinzipien beruht und somit eine erleichterte Interpretation der Ergebnisse ermöglicht. Hierzu wurde das kinetische Verhalten jedes Systems experimentell bestimmt und durch vereinfachte Reaktionsschemata beschrieben. Diese wurden anschließend mit Markov-Kettenmodellen verknüpft, welche alle wichtigen Konformationen der Sekundärstruktur abbilden. Als erstes System untersuchten wir die DNA Strangaustauschreaktion, welche in der Nanotechnologie häufig zur Herstellung von DNA-basierten Nanomaschinen und biochemischen Reaktionsnetzwerken eingesetzt wird. Unser Modell beschrieb die durch Ensemble-Fluoreszenz-Experimente gemessenen Auswirkungen von Basenfehlpaarungen auf die Kinetik dieser Reaktionen korrekt. Des Weiteren zeigte sich, dass die vorzeitige Strangablösung, das Ausfransen von Basenpaaren und die Bildung interner Schleifen wichtige Prozesse während des Strangaustausches sind. Darüber hinaus konnten wir zwei dissipative Elemente etablieren, um die zeitliche Kontrolle über die Strangaustauschreaktionen zu verbessern. Das erste Element ermöglicht eine reversible und wiederholbare Strangablösung, während das zweite Element die Möglichkeit bietet die Strangaustauschreaktionen nach einer programmierbaren zeitlichen Verzögerung zu starten. Zweitens untersuchten wir den Zielerkennungsprozess durch den CRISPR-Cas Komplex Cascade, ein vielversprechendes Protein für Anwendungen in der Genomtechnologie. Unser Modell reproduzierte erfolgreich alle Aspekte der torsions- und fehlpaarungs-abhängigen R-Schleifenbildung durch Cascade, welche durch Einzelmolekül-Torsions- und Ensemble-Fluoreszenz-Messungen ermittelt wurden. Zusätzlich konnten wir nachweisen, dass der für Cascade beobachtete „seed“-Effekt auf DNA-Verdrehung und nicht auf eine strukturelle Eigenschaft des Proteinkomplexes zurückzuführen ist. Schließlich untersuchten wir die Faltung/Entfaltung von α-Helices, welche eine entscheidende Rolle bei der Faltung und Funktion von Proteinen spielen. Unser Modell beschrieb die durch schnelle Triplett-Triplett-Energietransfer Experimente ermittelte α-Helix-Entfaltungskinetik exakt. Darüber hinaus konnten wir zeigen, dass die komplexe α-Helix-Entfaltung nicht einer einfachen Diffusion vom Einstein-Typ folgt, sondern eine Kombination aus subdiffusiver Grenzdiffusion und der eher peptidlängenunabhängigen Coil-Nukleation ist. Obwohl nur ein einziger Ansatz verwendet wurde, ermöglichten die vorgestellten Modelle den Zugang zu den vielschichtigen Zeitskalen der charakterisierten Prozesse, welche im Allgemeinen experimentell schwer zugänglich sind. Insbesondere konnten die folgenden zeitlichen Bereiche bestimmt werden: Dutzende von Mikrosekunden für die Schrittzeit der Strangaustauschreaktion, Hunderte von Mikrosekunden für die Schritte der R-Schleifenbildung durch Cascade, und Dutzende von Nanosekunden für die Faltung oder Entfaltung einer α-Helix um ein einzelnes Segment. Angesichts der Simplizität und Zugänglichkeit der etablierten Modelle sind wir zuversichtlich, dass sie zu nützlichen Werkzeugen für Forscher werden, um die Dynamik von Biomolekülen zu analysieren. Zusätzlich gehen wir davon aus, dass ähnliche Modellierungsansätze auf andere Biopolymersysteme angewendet werden können, sofern sie gut durch probabilistische Modelle beschrieben werden.

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