A Mathematical Explication of Human Psychology

Our scientific knowledge of human behavior has taken great leaps with the formalization of quantitative psychology. This dissertation is an amalgamation of mathematical models in the field of psychology, specifically as it pertains to higher order cognition. The goal is to provide a variety of useful contributions to psychology in three unique areas of the field. The first focuses on Signal Processing Models in recognition memory. I begin by outlining the two most popular models and describing their mathematical properties. This is done to promote both models usefulness as measurement tools, regardless of their mathematical differences. I continue by developing a novel extension for each model to further elucidate their usefulness in psychology. The second area of research discussed in this dissertation moves away from purely theoretical applications of mathematical models towards real-world applications of a stochastic system. Here, we develop and explore a Hidden Markov Model for memory deficits, with the goal of understanding dementia. Since clinical trials contain a variety of memory tests, a second paper devoted to further understanding memory decay in Alzheimers is provided. Finally, the last two chapters of this dissertation focus on decision making as it applies to information pooling techniques. We utilize the mathematical concepts developed throughout the dissertation in order to identify an area of improvement for models in current use, and offer an innovative new interpretation of existing theory. The final paper explores a natural extension to the theory for continuous-type responses, and outlines further opportunities for additional research in this area