Physical Sciences and Mathematics Commons^™

Applications Of Bayesian Statistics In Fluvial Bed Load Transport, Mark L. Schmelter

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The science of fluvial sediment transport studies the processes involved in the movement of river sediments. It is commonly understood that when rivers flood they have a great capacity to move sand, gravel, and even larger cobbles and boulders. This process is not only limited to the big floods that usually attract so much attention, but also the more common river flows play a very important role in forming a river. As engineers and scientists, we like to be able to develop equations and relationships that describe some natural phenomenon—in this case, fluvial sediment transport. While we are able to …

Probability Of Discrete Failures, Weibull Distribution, Mary Jo Hansen

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The intent of this research and these is to describe the development of a series of charts and tables that provide the individual and cumulative probabilities of failure applying to the Weibull statistical distribution. The mathematical relationships are developed and the computer programs are described for deterministic and Monte Carlo models that compute and verify the results. Charts and tables reflecting the probabilities of failure for a selected set of parameters of the Weibull distribution functions are provided.

A Comparative Analysis Of The Use Of A Markov Chain Versus A Binomial Probability Model In Estimating The Probability Of Consecutive Rainless Days, Jack Wilfred Homeyer

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The Markov chain process for predicting the occurence of a sequence of rainless days, a standard technique, is critically examined in light of the basic underlying assumptions that must be made each time it is used. This is then compared to a simple binomial model wherein an event is defined to be a series of rainless days of desired length. Computer programs to perform the required calculations are then presented and compared as to complexity and operating characteristics. Finally, an example of applying both programs to real data is presented and further comparisons are drawn between the two techniques.

An Exposition On Bayesian Inference, John Laffoon

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The Bayesian approach to probability and statistics is described, a brief history of Bayesianism is related, differences between Bayesian and Frequentist schools of statistics are defined, protential applications are investigated, and a literature survey is presented in the form of a machine-sort card file.

Bayesian thought is increasing in favor among statisticians because of its ability to attack problems that are unassailable from the Frequentist approach. It should become more popular among practitioners because of the flexibility it allows experimenters and the ease with which prior knowledge can be combined with experimental data.