Keywords

human performance, response time, parameter estimation, optimization, lognormal

Abstract

Accurate parameter estimation is fundamental to statistical modeling, shaping the validity of inference, prediction, and decision-making. Although Maximum Likelihood Estimation (MLE) and Bayesian methods are well established theoretically, their performance relative to alternative estimators in small-sample, skewed-data contexts remains less clear. This thesis addresses this gap through a systematic evaluation of estimation techniques applied to human response time data from a controlled seek-and-place jigsaw puzzle task, where distributions are characteristically right-skewed.

A performance-modified lognormal model was developed to capture the relationship between task complexity and response times. Four estimation approaches were investigated: MLE, Method of Moments (MoM), Bayesian estimation under different prior assumptions, and Quantile-Matching Estimation (QME). Additionally, several computational strategies for obtaining MLEs were compared, including closed-form solutions, gradient-based optimization, and discrete grid search. All methods were applied to the same dataset, enabling a controlled comparison of statistical accuracy, efficiency, and computational demands.

The analysis demonstrated that MLE and Bayesian methods produced nearly identical parameter estimates, exhibiting greater efficiency and lower predictive error than MoM or QME. MoM and QME showed higher variability and bias, consistent with theoretical expectations under small-sample skewed data. For MLE computation, closed-form expressions were most efficient when available, while grid search outperformed gradient descent in this one-dimensional case.

These findings reinforce the theoretical advantages of likelihood-based methods and highlight the practical importance of selecting computational strategies suited to model structure and data characteristics. By situating the comparison in a realistic experimental setting, this work contributes both theoretical insight and applied guidance. The results are particularly relevant for small-sample, skewed-data problems encountered in cognitive science, reliability analysis, biostatistics, and machine learning, underscoring the central role of estimation methodology in ensuring valid and reliable statistical modeling.

Completion Date

2025

Semester

Fall

Committee Chair

Jongik Chung

Degree

Master of Science (M.S.)

College

College of Sciences

Department

Statistics and Data Science

Format

PDF

Identifier

DP0029748

Document Type

Thesis

Campus Location

Orlando (Main) Campus

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