In this paper, we investigate three particular algorithms: A sto- chastic simulation algorithm (SSA), and explicit and implicit tau-leaping al- gorithms. To compare these methods, we used them to analyze two infection models: A Vancomycin-resistant enterococcus (VRE) infection model at the population level, and a Human Immunode ciency Virus (HIV) within host in- fection model. While the rst has a low species count and few transitions, the second is more complex with a comparable number of species involved. The relative effciency of each algorithm is determined based on computational time and degree of precision required. The numerical results suggest that all three algorithms have the similar computational effciency for the simpler VRE model, and the SSA is the best choice due to its simplicity and accuracy. In addition, we have found that with the larger and more complex HIV model, implementation and modication of tau-Leaping methods are preferred.

Joint models for the association of a longitudinal binary and a longitudinal continuous process are proposed for situations in which their association is of direct interest. The models are parameterized such that the dependence between the two processes is characterized by unconstrained regression coefficients. Bayesian variable selection techniques are used to parsimoniously model these coefficients. A Markov chain Monte Carlo (MCMC) sampling algorithm is developed for sampling from the posterior distribution, using data augmentation steps to handle missing data. Several technical issues are addressed to implement the MCMC algorithm efficiently. The models are motivated by, and are used for, the analysis of a smoking cessation clinical trial in which an important question of interest was the effect of the (exercise) treatment on the relationship between smoking cessation and weight gain.

In der Arbeit wird ein neuartiges Lernverfahren für Gauß-Mischverteilungen entwickelt. Es basiert auf der Technik der Markov-Chain Monte-Carlo Verfahren und ist in der Lage, in einem Zuge die Größe der Mischverteilung sowie deren Parameter zu bestimmen. Das Verfahren zeichnet sich sowohl durch eine gute Anpassung an die Trainingsdaten als auch durch eine gute Generalisierungsleistung aus. Ausgehend von einer Beschreibung der stochastischen Grundlagen und einer Analyse der Probleme, die beim Lernen von Gauß-Mischverteilungen auftreten, wird in der Abeit das neue Lernverfahren schrittweise entwickelt und seine Eigenschaften untersucht. Ein experimenteller Vergleich mit bekannten Lernverfahren für Gauß-Mischverteilungen weist die Eignung des neuen Verfahrens auch empirisch nach.

Cette thèse contient deux parties: la simulation des événements rares et le rééchantillonnage non-intrusif stratifié pour la programmation dynamique. La première partie consiste à quantifier des statistiques liées aux événements très improbables mais dont les conséquences sont sévères. Nous proposons des transformations markoviennes sur l'espace des trajectoires et nous les combinons avec les systèmes de particules en interaction et l'ergodicité de chaîne de Markov, pour proposer des méthodes performantes et applicables en grande généralité. La deuxième partie consiste à résoudre numériquement le problème de programmation dynamique dans un contexte où nous avons à disposition seulement des données historiques en faible nombre et nous ne connaissons pas les valeurs des paramètres du modèle. Nous développons et analysons un nouveau schéma composé de stratification et rééchantillonnage / This thesis contains two parts: rare events simulation and non-intrusive stratified resampler for dynamic programming. The first part consists of quantifying statistics related to events which are unlikely to happen but which have serious consequences. We propose Markovian transformation on path spaces and combine them with the theories of interacting particle system and of Markov chain ergodicity to propose methods which apply very generally and have good performance. The second part consists of resolving dynamic programming problem numerically in a context where we only have historical observations of small size and we do not know the values of model parameters. We propose and analyze a new scheme with stratification and resampling techniques.

No description available.

京都大学 / 0048 / 新制・課程博士 / 博士(情報学) / 甲第20517号 / 情博第645号 / 新制||情||111(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 髙橋 豊, 教授 太田 快人, 教授 大塚 敏之, 准教授 増山 博之 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

No description available.

This study attempts to improve forecasts of solar energy production (SEP), so that energy trading companies can propose more accurate bids to Nord Pool. The aim ismake solar energy a more lucrative business, and therefore lead to more investments in this green energy form. The model that is introduced is a hidden Markov model (HMM) that we call a Time-dynamic Markov-chain (TDMC). The TDMC is presented in general, but applied to the energy sector SE4 in south of Sweden. A simple linear regression model is used to compare with the performance of the TDMC model. Regarding the mean absolute error (MAE) and the root-mean-square error (RMSE), the TDMC model outperforms a simple linear regression; both when the training data is relatively fresh and also when the training data has not been updated in over 300 days. A paired t-test also shows a non-significant deviation from the true SEP per day, at the 0.05 significance level, when simulating the first two months of 2023 with the TDMC model. The simple linear regression model, however, shows a significant difference from reality, in comparison.

In many areas of the world, seismic hazards pose a great risk to both human and natural populations. In particular, earthquake-induced tsunamis are especially dangerous to many areas in the Pacific. The study and quantification of these seismic events can both help scientists better understand how these natural hazards occur and help at-risk populations make better preparations for these events. However, many events of interest occurred too long ago to be recorded by modern instruments, so data on these earthquakes are sparse and unreliable. To remedy this, a Bayesian method for reconstructing the source earthquakes for these historical tsunamis based on anecdotal data, called TsunamiBayes, has been developed and used to study historical events that occurred in 1852 and 1820. One drawback of this method is the computational cost to reconstruct posterior distributions on tsunami source parameters. In this work, we improve on the TsunamiBayes method by introducing higher-order MCMC methods, specifically the Hamiltonian Monte Carlo (HMC) method to increase sample acceptance rate and therefore reduce computation time. Unfortunately the exact gradient for this problem is not available, and so we make use of a surrogate gradient via a neural network fitted to the forward model. We examine the effects of this surrogate gradient HMC sampling method on the posterior distribution for an 1852 event in the Banda Sea, compare results to previous results collected usisng random walk, and note the benefits of the surrogate gradient in this context.

Along with being one of the most populated regions of the world, Indonesia has one of the highest natural disaster rates worldwide. One such natural disaster that Indonesia is particularly prone to are tsunamis. Tsunamis are primarily caused by earthquakes, volcanoes, landslides and debris flows. To effectively allocate resources and create emergency plans we need an understanding of the risk factors of the region. Understanding the source events of destructive tsunamis of the past are critical to understanding the these risk factors. We expand upon previous work focusing on earthquake-generated tsunamis to consider landslide-generated tsunamis. Using Bayesian inference and modern scientific computing we construct a posterior distribution of potential landslide sources based on anecdotal data of historically observed tsunamis. After collecting 30,000 samples we find a landslide source event provides a reasonable match to our anecdotal accounts. However, viable landslides may be on the edge of what is physically possible. Future work creating a coupled landslide-earthquake model may account for the weaknesses with having a solely landslide or earthquake source event.