This project applied statistical inference methods to historical data of mixed martial arts (MMA) matches from the Ultimate Fighting Championship (UFC). The goal of the project was to create a model to predict the outcome of Ultimate Fighting Championship matches with the best possible accuracy. The main methods used in the project were logistic regression and Bayesian regression. The data used for said model was taken from matches between early April 2000 and mid April 2024. The predictions made by these models were compared with the predictions of various betting sites as well as with the true outcomes of the matches. The logistic regression model and the Bayesian model predicted the true outcome of the matches 60% and 70% of the time respectively, with both having comparable predictions to those of the betting sites.

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Binary response data is often modeled using the logistic regression model, a well known nonlinear model. Designing an optimal experiment for this nonlinear situation poses some problems not encountered with a linear model. The application of several optimality design criteria to the logistic regression model is explored, and many resulting optimal designs are given. The implementation of these optimal designs requires the parameters of the model to be known. However, the model parameters are not known. If they were, there would be no need to design an experiment. Consequently the parameters must be estimated prior to implementing a design. Standard one-stage optimal designs are quite sensitive to parameter misspecification and are therefore unsatisfactory in practice. A two-stage Bayesian design procedure is developed which effectively deals with poor parameter knowledge while maintaining high efficiency. The first stage makes use of Bayesian design as well as Bayesian estimation in order to cope with parameter misspecification. Using the parameter estimates from the first stage, the second stage conditionally optimizes a chosen design optimality criterion. Asymptotically, the two-stage design procedure is considerably more efficient than the one-stage design when the parameters are misspecified and only slightly less efficient when the parameters are known. The superiority of the two-stage procedure over the one-stage is even more evident for small samples. / Ph. D.

In Victorian and Edwardian England, the grieving process involved numerous mortuary practices but the final and longest lasting of these is the stone monument placed over the grave or an engraving on an existing monument. However, comparison of burial records to monument records in rural Cambridgeshire, England would indicate that not all individuals received such a monument at their passing. This study explores the root of this variation through one of the most psychologically difficult deaths to navigate: that of a child. In this study, I compare those children who did not receive a stone monument to those that did as a function of the family’s socioeconomic class, the year of death, as well as the child’s age, gender, and place in the birth order at time of death. With a database of 11,578 individuals between the ages of 3 and 25 from 114 parishes in Cambridgeshire, this study is the largest of its kind and thus permits the exploration of interactions between these different factors. Using logistic regression modeling, I illustrate that the decision to erect a stone monument is demonstrably related to the child’s lived experience and the role they played in their household and community. Although rate of commemoration is not commonly explored in historical cemetery studies, this measurement offers valuable insight on the following themes: the emergence of adolescence and the ‘New Woman’, the drop in child fertility and mortality, the rise of the lower class over time, the role of girls within the household, the shift from conceptualizing children as economically useful to economically useless but emotionally priceless over time, the impact of major events like the agricultural depression and the First World War, and the impact that primogeniture had on the likelihood of commemoration. / Thesis / Doctor of Philosophy (PhD) / The death of a child evokes pain and loss that is, in part, reconciled through the grieving process. For Victorian and Edwardian parents in rural Cambridgeshire, England, this process involved burying their child in a local churchyard or cemetery and, in some cases, erecting a stone monument over the grave or having the child’s name carved on an existing monument. But comparison of burial and monument inscription records would indicate that only some children received this relatively expensive and permanent marker at their passing. This study explores differences in commemorative decision-making as a product of the child’s age at death, gender, the socioeconomic class of the family, the year they passed away, and the family structure. While the stone monument is unsurprisingly more common among children of the higher socioeconomic classes, I found that social change, such as shifts in gendered expectations, were also expressed in commemorative practice.

Thesis advisor: Zhushan Mandy Li / Differential item functioning (DIF) occurs when examinees of equal ability from different groups have different probabilities of correctly responding to certain items. DIF analysis aims to identify potentially biased items to ensure the fairness and equity of instruments, and has become a routine procedure in developing and improving assessments. This study proposed a DIF detection method using regularization techniques, which allows for simultaneous investigation of all items on a test for both uniform and nonuniform DIF. In order to evaluate the performance of the proposed DIF detection models and understand the factors that influence the performance, comprehensive simulation studies and empirical data analyses were conducted. Under various conditions including test length, sample size, sample size ratio, percentage of DIF items, DIF type, and DIF magnitude, the operating characteristics of three kinds of regularized logistic regression models: lasso, elastic net, and adaptive lasso, each characterized by their penalty functions, were examined and compared. Selection of optimal tuning parameter was investigated using two well-known information criteria AIC and BIC, and cross-validation. The results revealed that BIC outperformed other model selection criteria, which not only flagged high-impact DIF items precisely, but also prevented over-identification of DIF items with few false alarms. Among the regularization models, the adaptive lasso model achieved superior performance than the other two models in most conditions. The performance of the regularized DIF detection model using adaptive lasso was then compared to two commonly used DIF detection approaches including the logistic regression method and the likelihood ratio test. The proposed model was applied to analyzing empirical datasets to demonstrate the applicability of the method in real settings. / Thesis (PhD) — Boston College, 2019. / Submitted to: Boston College. Lynch School of Education. / Discipline: Educational Research, Measurement and Evaluation.

För alpina skidåkare mäter man prestationer i så kallad FIS-ranking. Vi undersöker några metoder för hur man kan analysera data där responsen består av ranger som dessa. Vid situationer då responsdata utgörs av urval av ranger finns ingen självklar analysmetod. Det vi undersöker är skillnaderna vid användandet av olika regressionsanpassningar så som linjär, logistisk och ordinal logistisk regression för att analysera data av denna typ. Vidare används bootstrap för att bilda konfidensintervall. Det visar sig att för våra datamaterial ger metoderna liknande resultat när det gäller att hitta betydelsefulla förklarande variabler. Man kan därmed utgående från denna undersökning, inte se några skäl till varför man ska använda de mer avancerade modellerna. / Alpine skiers measure their performance in FIS ranking. We will investigate some methods on how to analyze data where response data is based on ranks like this. In situations where response data is based on ranks there is no obvious method of analysis. Here, we examine differences in the use of linear, logistic and ordinal logistic regression to analyze data of this type. Bootstrap is used to make confidence intervals. For our data these methods give similar results when it comes to finding important explanatory variables. Based on this survey we cannot see any reason why one should use the more advanced models.

If customers respond differently to a campaign, it is worthwhile to find those customers who respond most positively and direct the campaign towards them. This can be done by using so called incremental response analysis where respondents from a campaign are compared with respondents from a control group. Customers with the highest increased response from the campaign will be selected and thus may increase the company’s return. Incremental response analysis is applied to the mobile operator Tres historical data. The thesis intends to investigate which method that best explain the incremental response, namely to find those customers who give the highest incremental response of Tres customers, and what characteristics that are important.The analysis is based on various classification methods such as logistic regression, Lassoregression and decision trees. RMSE which is the root mean square error of the deviation between observed and predicted incremental response, is used to measure the incremental response prediction error. The classification methods are evaluated by Hosmer-Lemeshow test and AUC (Area Under the Curve). Bayesian logistic regression is also used to examine the uncertainty in the parameter estimates.The Lasso regression performs best compared to the decision tree, the ordinary logistic regression and the Bayesian logistic regression seen to the predicted incremental response. Variables that significantly affect the incremental response according to Lasso regression are age and how long the customer had their subscription.

Every day most people are using applications and services that are utilising machine learning, in some way, without even knowing it. Some of these applications and services could, for example, be Google’s search engine, Netflix’s recommendations, or Spotify’s music tips. For machine learning to work it needs data, and often a large amount of it. Roughly 2,5 quintillion bytes of data are created every day in the modern information society. This huge amount of data can be utilised to make applications and systems smarter and automated. Time logging systems today are usually not smart since users of these systems still must enter data manually. This bachelor thesis will explore the possibility of applying machine learning to task logging systems, to make it smarter and automated. The machine learning algorithm that is used to predict the user’s task, is called multiclass logistic regression, which is categorical. When a small amount of training data was used in the machine learning process the predictions of a task had a success rate of about 91%.

This thesis investigates the factors that are associated with annual changes in the share price of Johannesburg Stock Exchange (JSE) listed companies. In this study, an increase in value of a share is when the share price of a company goes up by the end of the financial year as compared to the previous year. Secondary data that was sourced from McGregor BFA website was used. The data was from 2004 up to 2011. Deciding which share to buy is the biggest challenge faced by both investment companies and individuals when investing on the stock exchange. This thesis uses binary logistic regression to identify the variables that are associated with share price increase. The dependent variable was annual change in share price (ACSP) and the independent variables were assets per capital employed ratio, debt per assets ratio, debt per equity ratio, dividend yield, earnings per share, earnings yield, operating profit margin, price earnings ratio, return on assets, return on equity and return on capital employed. Different variable selection methods were used and it was established that the backward elimination method produced the best model. It was established that the probability of success of a share is higher if the shareholders are anticipating a higher return on capital employed, and high earnings/ share. It was however, noted that the share price is negatively impacted by dividend yield and earnings yield. Since the odds of an increase in share price is higher if there is a higher return on capital employed and high earning per share, investors and investment companies are encouraged to choose companies with high earnings per share and the best returns on capital employed. The final model had a classification rate of 68.3% and the validation sample produced a classification rate of 65.2% / Mathematical Sciences / M.Sc. (Statistics)

This thesis investigates the factors that are associated with annual changes in the share price of Johannesburg Stock Exchange (JSE) listed companies. In this study, an increase in value of a share is when the share price of a company goes up by the end of the financial year as compared to the previous year. Secondary data that was sourced from McGregor BFA website was used. The data was from 2004 up to 2011. Deciding which share to buy is the biggest challenge faced by both investment companies and individuals when investing on the stock exchange. This thesis uses binary logistic regression to identify the variables that are associated with share price increase. The dependent variable was annual change in share price (ACSP) and the independent variables were assets per capital employed ratio, debt per assets ratio, debt per equity ratio, dividend yield, earnings per share, earnings yield, operating profit margin, price earnings ratio, return on assets, return on equity and return on capital employed. Different variable selection methods were used and it was established that the backward elimination method produced the best model. It was established that the probability of success of a share is higher if the shareholders are anticipating a higher return on capital employed, and high earnings/ share. It was however, noted that the share price is negatively impacted by dividend yield and earnings yield. Since the odds of an increase in share price is higher if there is a higher return on capital employed and high earning per share, investors and investment companies are encouraged to choose companies with high earnings per share and the best returns on capital employed. The final model had a classification rate of 68.3% and the validation sample produced a classification rate of 65.2% / Mathematical Sciences / M.Sc. (Statistics)