UTeach summer masters statistics course : a journey from traditional to Bayesian analysis

This paper will outline some of the key parts of the Statistics course offered through the UTeach Summer Master’s Program as taught by Dr. Martha K. Smith. The paper begins with the introduction of the normal probability density function and is proven with calculus techniques and Euclidean geometry. Probability is discussed at great length in Smith’s course and the importance of understanding probability in statistical analysis is demonstrated through a reference to a study on how medical doctors confuse false positives in breast cancer testing. The frequentist perspective is concluded with a proof that the normal probability density function is zero.

The shift from traditional to Bayesian inference begins with a brief introduction to the terminology involved, as well as an example with patient testing. The pros and cons of Bayesian inference are discussed and a proof is shown using the normal probability density function in finding a Bayes estimate for µ.

It will be argued that a Statistics course moving from traditional to Bayesian analysis, such as that offered by the UTeach Summer Master’s Program and Smith, would supplement the traditional Statistics course offered at most universities. Such a course would be relevant for the mathematics major, mathematics educator, professionals in the medical industry, and individuals seeking to gain insights into how to understand data sets in new ways.