Adaptive Psychophysical Procedures and Ulam’s Game

The problem of finding the threshold of a psychometric function is of major interest to researchers in the field of psychophysics, and has applications in many areas of medical diagnosis, particularly those dealing with perception, such as optometry and hearing tests. This problem is closely related to other problems in computer science, such as search with errors, however most existing literature does not make this link. This thesis provides a review of existing algorithms for finding the threshold, with an emphasis on identifying the types of problems for which each algorithm is useful. We also address a number of issues which are not adequately covered in the literature. These include choosing an appropriate loss function to evaluate the performance of an algorithm for a given problem, as well as relating the problem of finding the threshold to binary search with errors problems in computer science. Finally, this research presents a new algorithm for finding the threshold of a psychometric function, EntFirst, which results in improved performance compared to many existing algorithms.