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Full-Text Articles in Probability
Using The History Of Statistics To Teach Introductory Statistics, Melissa Hansen
Using The History Of Statistics To Teach Introductory Statistics, Melissa Hansen
All Graduate Reports and Creative Projects, Fall 2023 to Present
While often taught in high school and required as part of a college degree, statistics classes are sometimes viewed by students as an obstacle rather than a support for their overall goals. One way to increase student engagement in a statistics course is to use the history of statistics. Within the literature review, the advantages to using the history of statistics are discussed as well as the more extensive research on using the history of mathematics in mathematics courses. Included are instructional strategies for using the context around the development of mathematical ideas in math classrooms which can be extended …
Predictive Distributions Via Filtered Historical Simulation For Financial Risk Management, Tyson Clark
Predictive Distributions Via Filtered Historical Simulation For Financial Risk Management, Tyson Clark
All Graduate Plan B and other Reports, Spring 1920 to Spring 2023
Filtered historical simulation with an underlying GARCH process can be used as a valuable tool in VaR analysis, as it derives risk estimates that are sensitive to the distributional properties of the historical data of the produced predictive density. I examine the applications to risk analysis that filtered historical simulation can provide, as well as an interpretation of the predictive density as a poor man’s Bayesian posterior distribution. The predictive density allows us to make associated probabilistic statements regarding the results for VaR analysis, giving greater measurement of risk and the ability to maintain the optimal level of risk per …