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There are two main schools of thought about statistical inference: frequentist and Bayesian. The frequentist approach relies solely on available data for predictions, while the Bayesian approach incorporates both data and prior knowledge about the event of interest. Bayesian methods were developed hundreds of years ago; however, they were rarely used due to computational challenges and conflicts between the two schools of thought. Recent advances in computational capabilities and a shift toward leveraging prior knowledge for inferences have led to increased use of Bayesian methods.
Methods:
Many biostatisticians with expertise in frequentist approaches lack the skills to apply Bayesian techniques. To address this gap, four faculty experts in Bayesian modeling at the University of Michigan developed a practical, customized workshop series. The training, tailored to accommodate the schedules of full-time staff, focused on immersive, project-based learning rather than traditional lecture-based methods. Surveys were conducted to assess the impact of the program.
Results:
All 20 participants completed the program and when surveyed reported an increased understanding of Bayesian theory and greater confidence in using these techniques. Capstone projects demonstrated participants’ ability to apply Bayesian methodology. The workshop not only enhanced the participants’ skills but also positioned them to readily apply Bayesian techniques in their work.
Conclusions:
Accommodating the schedules of full-time biostatistical staff enabled full participation. The immersive project-based learning approach resulted in building skills and increasing confidence among staff statisticians who were unfamiliar with Bayesian methods and their practical applications.
While the Poisson distribution is a classical statistical model for count data, the distributional model hinges on the constraining property that its mean equal its variance. This text instead introduces the Conway-Maxwell-Poisson distribution and motivates its use in developing flexible statistical methods based on its distributional form. This two-parameter model not only contains the Poisson distribution as a special case but, in its ability to account for data over- or under-dispersion, encompasses both the geometric and Bernoulli distributions. The resulting statistical methods serve in a multitude of ways, from an exploratory data analysis tool, to a flexible modeling impetus for varied statistical methods involving count data. The first comprehensive reference on the subject, this text contains numerous illustrative examples demonstrating R code and output. It is essential reading for academics in statistics and data science, as well as quantitative researchers and data analysts in economics, biostatistics and other applied disciplines.
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