Denna uppsats bygger på de tre klassiska problemen för en dold Markovmodell. Alla tre problemen kommer att matematiskt beskrivas på ett fullständigt sätt. Bland annat kommer problemet med hur man tränar en modell alltså lösas analytiskt med Lagrange multiplikator samt motivera varför Expectation-Maximization fungerar. En väsentlig del kommer också vara att introducera beräkningseffektiva algoritmer för att göra det möjligt att lösa dessa problem.

In this thesis, we investigate the estimation problem of treatment effect from Bayesian perspective through which one can first obtain the posterior distribution of unobserved potential outcome from observed data, and then obtain the posterior distribution of treatment effect. We mainly consider how to represent a joint distribution of two potential outcomes - one from treated group and another from control group, which can give us an indirect impression of correlation, since the estimation of treatment effect depends on correlation between two potential outcomes. The first part of this thesis illustrates the effectiveness of adapting Gaussian mixture models in solving the treatment effect problem. We apply the mixture models - Gaussian Mixture Regression (GMR) and Gaussian Mixture Linear Regression (GMLR)- as a potentially simple and powerful tool to investigate the joint distribution of two potential outcomes. For GMR, we consider a joint distribution of the covariate and two potential outcomes. For GMLR, we consider a joint distribution of two potential outcomes, which linearly depend on covariate. Through developing an EM algorithm for GMLR, we find that GMR and GMLR are effective in estimating means and variances, but they are not effective in capturing correlation between two potential outcomes. In the second part of this thesis, GMLR is modified to capture unobserved covariance structure (correlation between outcomes) that can be explained by latent variables introduced through making an important model assumption. We propose a much more efficient Pre-Post EM Algorithm to implement our proposed GMLR model with unobserved covariance structure in practice. Simulation studies show that Pre-Post EM Algorithm performs well not only in estimating means and variances, but also in estimating covariance.

To improve meat quality and consistency, cattle feeders have moved towards implementing end-point marketing strategies (EPM) based on visual estimates of physiological characteristics. A commonly used 0.5 inch backfat target was used in this analysis. Recognizing that physiological targets will not necessarily result in profit maximization; this research developed a profit maximization rule (PMR) that accounts for the dynamics of animal growth, output prices and costs. A natural field experiment was conducted in Iowa to evaluate the potential for the PMR. One hundred twenty three fed cattle were randomly assigned into two treatments (PMR and EPM). Realized profit results indicate that EPM outperformed the PMR methodology by $24.35 per head. However, simulations that relax some experimental constraints resulted in the PMR outperforming EPM by $102.06 per head. Interestingly, the PMR did not negatively affect carcass quality. Therefore, relaxing PMR constraints in future experimental studies is expected to improve realized profitability.

Yes / The Riser of a Fluid Catalytic Cracking (FCC) unit cracks gas oil to make fuels such as gasoline and diesel. However, changes in quality, nature of crude oil blends feedstocks, environmental changes and the desire to obtain higher profitability, lead to many alternative operating conditions of the FCC riser. The production objective of the riser is usually the maximization of gasoline and diesel. Here, an optimisation framework is developed in gPROMS to maximise the gasoline in the riser of an industrial FCC unit (reported in the literature) while optimising mass flowrates of catalyst and gas oil. A detailed mathematical model of the process developed is incorporated in the optimisation framework. It was found that, concurrent use of the optimal values of mass flowrates of catalyst (310.8 kg/s) and gas oil (44.8 kg/s) gives the lowest yield of gases, but when these optimum mass flowrates are used one at time, they produced the same and better yield of gasoline (0.554 kg lump/ kg feed). / Petroleum Technology Development Fund, Nigeria, financially sponsored the study.

Yes / The FCC riser cracks gas oil into useful fuels such as gasoline, diesel and some lighter products such as ethylene and propylene, which are major building blocks for the polyethylene and polypropylene production. The production objective of the riser is usually the maximization of gasoline and diesel, but it can also be to maximize propylene. The optimization and parameter estimation of a six-lumped catalytic cracking reaction of gas oil in FCC is carried out to maximize the yield of propylene using an optimisation framework developed in gPROMS software 5.0 by optimizing mass flow rates and temperatures of catalyst and gas oil. The optimal values of 290.8 kg/s mass flow rate of catalyst and 53.4 kg/s mass flow rate of gas oil were obtained as propylene yield is maximized to give 8.95 wt%. When compared with the base case simulation value of 4.59 wt% propylene yield, the maximized propylene yield is increased by 95%.

A non-parametric data clustering technique for achieving efficient data-clustering and improving the number of clusters is presented in this thesis. K-Means and Expectation-Maximization algorithms have been widely deployed in data-clustering applications. Result findings in related works revealed that both these algorithms have been found to be characterized with shortcomings. K-Means was established not to guarantee convergence and the choice of clusters heavily influenced the results. Expectation-Maximization’s premature convergence does not assure the optimality of results and as with K-Means, the choice of clusters influence the results. To overcome the shortcomings, a fast automatic K-EM algorithm is developed that provide optimal number of clusters by employing various internal cluster validity metrics, providing efficient and unbiased results. The algorithm is implemented on a wide array of data sets to ensure the accuracy of the results and efficiency of the algorithm.

Dynamic Causal Modeling (DCM) uses dynamical systems to represent the high-level neural processing strategy for a given cognitive task. The logical network topology of the model is specified by a combination of prior knowledge and statistical analysis of the neuro-imaging signals. Parameters of this a-priori model are then estimated and competing models are compared to determine the most likely model given experimental data. Inter-subject analysis using DCM is complicated by differences in model topology, which can vary across subjects due to errors in the first-level statistical analysis of fMRI data or variations in cognitive processing. This requires considerable judgment on the part of the experimenter to decide on the validity of assumptions used in the modeling and statistical analysis; in particular, the dropping of subjects with insufficient activity in a region of the model and ignoring activation not included in the model. This manual data filtering is required so that the fMRI model's network size is consistent across subjects. This thesis proposes a solution to this problem by treating missing regions in the first-level analysis as missing data, and performing estimation of the time course associated with any missing region using one of four candidate methods: zero-filling, average-filling, noise-filling using a fixed stochastic process, or one estimated using expectation-maximization. The effect of this estimation scheme was analyzed by treating it as a preprocessing step to DCM and observing the resulting effects on model evidence. Simulation studies show that estimation using expectation-maximization yields the highest classification accuracy using a simple loss function and highest model evidence, relative to other methods. This result held for various data set sizes and varying numbers of model choice. In real data, application to Go/No-Go and Simon tasks allowed computation of signals from the missing nodes and the consequent computation of model evidence in all subjects compared to 62 and 48 percent respectively if no preprocessing was performed. These results demonstrate the face validity of the preprocessing scheme and open the possibility of using single-subject DCM as an individual cognitive phenotyping tool. / Ph. D.

The problem of influence maximization has been studied extensively with applications that include viral marketing, recommendations, and feed ranking. The optimization problem, first formulated by Kempe, Kleinberg and Tardos, is known to be NP-hard. Thus, several heuristics have been proposed to solve this problem. This thesis studies the problem of influence maximization under the deterministic linear threshold model and presents a novel heuristic for finding influential nodes in a graph with the goal of maximizing contagion spread that emanates from these influential nodes. Inputs to our algorithm include edge weights and vertex thresholds. The threshold difference greedy algorithm presented in this thesis takes into account both the edge weights as well as vertex thresholds in computing influence of a node. The threshold difference greedy algorithm is evaluated on 14 real-world networks. Results demonstrate that the new algorithm performs consistently better than the seven other heuristics that we evaluated in terms of final spread size. The threshold difference greedy algorithm has tuneable parameters which can make the algorithm run faster. As a part of the approach, the algorithm also computes the infected nodes in the graph. This eliminates the need for running simulations to determine the spread size from the influential nodes. We also study the target set selection problem with our algorithm. In this problem, the final spread size is specified and a seed (or influential) set is computed that will generate the required spread size. / Master of Science

This paper’s aim is to discover the impact of economical, demographic and traditional determinants on clubs’ on-pitch success in UEFA Champions League. Generally it is assumed by people that financially strong clubs tend to win on the pitch most of the time. Is it really true? Is it always the same wealthy teams which win in the end? Football is a type of entertainment and people would like to see games with uncertain outcomes and a balanced competitiveness between two sides. In this way they can enjoy this entertainment. In that case, how uncertain is the outcome and how balanced is the competition in UEFA Champions League? In order to answer all these questions a multiple regression analysis is built including economic, demographic and traditional variables both at club and country level. These mentioned explanatory variables are GDP per capita of the home country, population of the host city, total market value of the team’s players, capacity of the stadium, country’s participation in international tournaments, club’s age, rank of the next best team from the same country and country’s hosting an international tournament. It turned out that financially advantageous clubs which have stadiums with larger capacities and located in more populated cities have more chances of winning than the others. Then again, it is observed that countries’ football tradition and dedication does not have a significant impact on clubs’ on-pitch success in UEFA Champions League.

Le projet s'inscrit dans la dynamique de systématisation statistique qui s'opère aujourd'hui dans le champ de l'écologie comparative. Les différents traits quantitatifs d'un jeu d'espèces échantillonné peuvent être vus comme le résultat d'un processus stochastique courant le long d'un arbre phylogénétique, ce qui permet de prendre en compte des corrélations issues d'histoires évolutives communes. Certains changements environnementaux peuvent produire un déplacement de niches évolutive, qui se traduisent par un saut dans la valeur du processus stochastique décrivant l'évolution au cours du temps du trait des espèces concernées. Parce qu'on ne mesure la valeur du processus dynamique qu'à un seul instant, pour les espèces actuelles, certains scénarii d'évolution ne peuvent être reconstruits, ou présentent des problèmes d'identifiabilité, que l'on étudie avec soin. On construit ici un modèle à données incomplètes d'inférence statistique, que l'on implémente efficacement. La position des sauts est détectée de manière automatique, et leur nombre est choisi grâce à une procédure de sélection de modèle adaptée à la structure du problème, et pour laquelle on dispose de certaines garanties théoriques. Un arbre phylogénétique ne prend pas en compte les phénomènes d'hybridation ou de transferts de gènes horizontaux, qui sont fréquents dans certains groupes d'organismes, comme les plantes ou les bactéries. Pour pallier ce problème, on utilise alors un réseau phylogénétique, pour lequel on propose une adaptation du modèle d'évolution de traits quantitatifs décrit précédemment. Ce modèle permet d'étudier l'hétérosis, qui se manifeste lorsqu'un hybride présente un trait d'une valeur exceptionnelle par rapport à celles de ses deux parents. / This project is aiming at taking a step further in the process of systematic statistical modeling that is occurring in the field of comparative ecology. A way to account for correlations between quantitative traits of a set of sampled species due to common evolutionary histories is to see the current state as the result of a stochastic process running on a phylogenetic tree. Due to environmental changes, some ecological niches can shift in time, inducing a shift in the parameters values of the stochastic process modeling trait evolution. Because we only measure the value of the process at a single time point, for extant species, some evolutionary scenarios cannot be reconstructed, or have some identifiability issues, that we carefully study. We construct an incomplete-data model for statistical inference, along with an efficient implementation. We perform an automatic shift detection, and choose the number of shifts thanks to a model selection procedure, specifically crafted to handle the special structure of the problem. Theoretical guaranties are derived in some special cases. A phylogenetic tree cannot take into account hybridization or horizontal gene transfer events, that are widely spread in some groups of species, such as plants or bacterial organisms. A phylogenetic network can be used to deal with these events. We develop a new model of trait evolution on this kind of structure, that takes non-linear effects such as heterosis into account. Heterosis, or hybrid vigor or depression, is a well studied effect, that happens when a hybrid species has a trait value that is outside of the range of its two parents.