Hi All,
I teach an MA stat course in neuroscience and recently began incorporating the history of statistics to trace how the field evolved. I share short excerpts from primary texts so students can get a feel for the original tone and context: Bernoulli’s Ars Conjectandi (the urns), Bayes and Price (the billiard table), Laplace’s Sixth Principle (birth sex ratios), Gauss (the orbit of Ceres), Fisher (the lady tasting tea), and finally contemporary scholars—including several members of this forum (apologies for the many omissions… the course is short!).
One question I have never been able to fully resolve is whether, beneath all these huge historical trends and paradigm shifts, everyone essentially shared the same view of the generative model: a fixed set of true parameters that we are trying to recover. Despite vast differences in philosophy, tone, and method, it feels as though everyone was ultimately chasing the same target. Whether we look at Bernoulli’s moral certainty, Laplace’s inverse probability, Fisher’s exact methods, or modern Bayesian inference, isn’t everyone assuming a single set of underlying parameters that generated the observations? We routinely teach the textbook distinction, that Bayesians treat data as fixed and parameters as random variables, while frequentists do the reverse, but strip away the formalism, and doesn’t everyone still picture a single data-generating process governed by fixed parameters?
This is a conceptual gap I have been struggling to close, and I would really appreciate your thoughts and expertise. As you can see, I am trying to pin down whether this philosophical divide actually changes the underlying generative story we tell our students.
Best,
Nitzan