SDS 581: Bayesian, Frequentist, and Fiducial Statistics in Data Science — with Xiao-Li Meng

Frequentist vs. Bayesian

The comparison between Frequentist and Bayesian approaches highlights their distinct philosophies in statistical inference. Xiao-Li Meng explains that Frequentists focus on data replication, imagining hypothetical scenarios to predict outcomes. They emphasize the importance of thinking about data that isn't available, which can be limiting when data is fixed 1. In contrast, Bayesians consider all possible scenarios that could have generated the observed data, prioritizing the data at hand to make probabilistic inferences 2. This approach requires considering prior knowledge, which can be controversial. Meng notes, "The Bayes will think about all the different scenarios that could have generated the data I have seen."

   

Fiducial Statistics

Fiducial statistics, a lesser-known approach, offers a unique perspective on statistical inference. Xiao-Li Meng describes it as a controversial method developed by Ari Fischer, aiming to provide answers without assuming prior knowledge 3. This approach attempts to infer distributions by focusing on the noise in data, rather than relying on prior distributions 4. Meng explains, "Fiduciary statistics makes use of the data that you have. It doesn't worry about some unknown distribution that you don't have." Despite its complexity, fiducial statistics is gaining interest in machine learning contexts, where practitioners may unknowingly apply its principles.