Graduation Year

2019

Document Type

Open Access Senior Thesis

Degree Name

Bachelor of Science

Department

Mathematics

Second Department

Computer Science

Reader 1

Michael Orrison

Reader 2

Neil Rhodes

Rights Information

Madelyn Gaumer

Abstract

Given the rise in the application of neural networks to all sorts of interesting problems, it seems natural to apply them to statistical tests. This senior thesis studies whether neural networks built to classify discrete circular probability distributions can outperform a class of well-known statistical tests for uniformity for discrete circular data that includes the Rayleigh Test1, the Watson Test2, and the Ajne Test3. Each neural network used is relatively small with no more than 3 layers: an input layer taking in discrete data sets on a circle, a hidden layer, and an output layer outputting probability values between 0 and 1, with 0 mapping to uniform and 1 mapping to nonuniform. In evaluating performances, I compare the accuracy, type I error, and type II error of this class of statistical tests and of the neural networks built to compete with them.

1 Jammalamadaka, S. Rao(1-UCSB-PB); SenGupta, A.(6-ISI-ASU)
Topics in circular statistics. (English summary)
With 1 IBM-PC floppy disk (3.5 inch; HD). Series on Multivariate Analysis, 5. World Scientific Publishing Co., Inc., River Edge, NJ, 2001. xii+322 pp. ISBN: 981-02-3778-2

2 Watson, G. S.
Goodness-of-fit tests on a circle. II.
Biometrika 49 1962 57–63.

3 Ajne, B.
A simple test for uniformity of a circular distribution.
Biometrika 55 1968 343–354.

COinS