According to official AAMC data, 72.7% of entering U.S. medical students in 2025 took a gap year—one or more years between obtaining an undergraduate degree and matriculating into medical school. This represents a 22% increase compared to matriculating students in 2016, less than 10 years prior. Despite this rapidly increasing trend in medical school admissions, little scholarly research exists on how taking a gap year affects admission to medical school. The long-term goals of this study are to 1) identify factors that determine whether a pre-medical student may benefit from a gap year, 2) evaluate how a gap year may strengthen a medical school application, and 3) determine whether a gap year may improve or predict successful matriculation to medical school, questions that are currently not well understood. This project compiles current scholarly literature and data on pre-medical gap years to assess the existing knowledge on this topic. This study conducted a PRISMA systematic review of pre-medical gap year literature, categorizing works based on whether gap years were viewed favorably, neutrally, or negatively and analyzing them within the framework of the AAMC Premed Competencies. The literature review found that themes consistent with the AAMC Premed competency “commitment to learning and growth” were mentioned most frequently in discussions and opinions of gap years. Development of the competencies “interpersonal skills” and “empathy and compassion” during a gap year was most strongly supported by both qualitative and quantitative data. Notably, the review revealed that most available research examines gap years retrospectively, analyzing qualities of current medical students or residents that were influenced by their gap year. However, little research examines undergraduate students prospectively and their decision-making process regarding whether to take a gap year before applying to medical school. These findings highlight a significant gap in pre-medical gap year research that should be addressed in future studies to better guide pre-medical students and their advisors in decisions about taking a gap year and how it may affect admission outcomes.

The Frogs Aiding Dragons College Initiative works with the TCU organization Frogs Aiding Immigrants and Refugees (FAIR) to support Fort Worth immigrant and refugee communities, especially through partnerships with the International Newcomer Academy (INA). INA is a school specifically for 6th-9th grade refugee students. Many of these students have had no educational background or don’t fluently read or speak English. So, the goal of Frogs Aiding Dragons College Initiative is to encourage students to continue pursuing an education and convey that college is a possible goal for them. We work with a group of 62 9th graders where we bring them to TCU and host a Thanksgiving feast, campus tour, and panel with TCU immigrant students. We then bring the college experience to INA with presentations and hands-on activities from various students representing various TCU departments, including Chemistry, Pre-Health, the Fine Arts, and Engineering. We assess the effectiveness of this initiative using a survey measuring INA students’ attitudes towards desire to attend college, how much they know about college, and if they feel like they have more resources to apply to and attend college.

In quantitative studies comparing a treatment and a control group, treatment effect is often viewed simply as the difference in group means. However, any treatment can have an impact beyond simply shifting the mean outcome. In this work, we consider a linear treatment effect (LTE) model, meaning we simultaneously consider the difference in means and the ratio of standard deviations between two populations to better characterize the effect of the treatment. Estimation is done using an empirical likelihood (EL) formulation. The EL framework provides a nonparametric approach for conducting inference without making strong assumptions about the underlying population model. Generally, the EL statistic has a limiting chi-square distribution. However, in small sample settings, the EL statistic can exhibit strong deviations from this ideal. To address this issue, we investigate the use of the Bartlett correction, which is a multiplicative adjustment to the EL statistic to improve the chi-square approximation. This correction has been shown to substantially improve confidence region coverage accuracy, especially for small and moderate sample sizes. Through simulation, we examine the performance of the EL statistic in the LTE model, with and without a Bartlett correction applied. Our results demonstrate that the Bartlett-corrected EL approach provides improved performance, yielding confidence regions with coverage closer to desired nominal levels.

In this thesis, we introduce a way to implement Stochastic Processes - particularly Markov chain properties - for analyzing Liar’s Poker, a variant of Poker Texas Hold’Em that incorporates hidden information and a card-switching mechanic. Poker, and in particular Liar's Poker, presents a complex environment in which probabilities evolve as information is revealed and players make sequential decisions under uncertainty, so Markov modeling of this game requires a more flexible state-based representation. The study focuses on two main objectives: first, to construct a state space and transition matrix that are sufficiently compact for analysis while still capturing meaningful changes in hand-strength and game dynamic; and second, to investigate how the game’s exclusive card-switching feature can be incorporated into an optimal decision-making strategy. To address these goals, the thesis models gameplay as a sequence of probabilistic state transitions driven by card draws, hidden information, and strategic actions. By extending Stochastic Process methods to a poker setting with imperfect information and dynamic transition, this thesis aims to provide a structured mathematical framework for evaluating strategy in Liar’s Poker.

Incurred But Not Reported (IBNR) reserves refer to insurance claims that have already taken place, but have not yet been reported to the insurance provider. This presentation formulates a Bayesian modeling framework to estimate the IBNR reserves. The Bayesian framework allows us to incorporate prior knowledge, typically available from historical data and expert opinions, along with the observed claim data, to estimate model parameters and predict future claim liabilities. We emphasize prior models that have heavy tails and therefore can accommodate extreme, rare losses that can be underestimated otherwise. Specifically, we consider Pareto (Type I) and log-t models for the expected ultimate claim amounts for each insurance period. The data generating mechanisms considered are Poisson, negative binomial, and gamma. The analysis of real data also considers model sensitivity to the choice of the prior parameters. In doing so, we aim to produce more robust reserve estimates and better reflect the uncertainty inherent in unpaid claim liabilities. Ultimately, modeling IBNR reserves is important because it ensures insurance companies set aside sufficient funds to cover future claim obligations and avoid unexpected losses that could impact profitability.