Publication Date

2026

Document Type

Dissertation/Thesis

First Advisor

Polansky, Alan M.

Degree Name

M.S. (Master of Science)

Legacy Department

Department of Statistics and Actuarial Science

Abstract

A Galton board is a physical device in which a ball passes through a triangular array of pegs and is deflected left or right before landing in one of several bins. Under an idealized model, deflections are independent with probability 0.5 of moving right, implying a binomial distribution for the terminal bin location. Physical boards may deviate from this ideal due to asymmetries and other sources of bias. This thesis develops a Bayesian model for a 12-level Galton board in which each peg has its own right-move probability. Independent Beta priors are assigned to peg probabilities, and terminal bin counts from repeated drops are modeled with a multinomial likelihood whose terminal bin probabilities are determined by the peg-level parameters. The induced landing probabilities are computed by enumerating all 4096 possible paths and summing their probabilities into terminal bins. Posterior inference is performed using Markov chain Monte Carlo methods in JAGS, and model adequacy is evaluated with posterior predictive checks. The results quantify uncertainty in terminal bin probabilities and assess whether the board behaves approximately fairly.

Extent

276 pages

Language

en

Publisher

Northern Illinois University

Rights Statement

In Copyright

Rights Statement 2

NIU theses are protected by copyright. They may be viewed from Huskie Commons for any purpose, but reproduction or distribution in any format is prohibited without the written permission of the authors.

Media Type

Text

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