Brian McGill, an ecologist at the University of Maine and fellow blogger at Dynamic Ecology, recently wrote (last June) a helpful overview and nuanced critique of Bayesian probability titled “Why saying you are a Bayesian is a low information statement“. We not only carefully read his well-reasoned post; like the good Bayesians we are, we also updated our epistemological priors accordingly …
Here, we wish to focus on a very, very good question that McGill poses midway through his June 2013 post. In brief, he asks why would anyone ever “favor serial updating of the probability distribution using repeated applications of Bayes theorem for each new data collection rather than performing a comprehensive meta-analysis on all data collected”? In other words, what’s so great about Bayesian updating?
That’s a great question. Does anyone have any answers?
For our part, this is our tentative take on McGill’s thought-provoking question. Broadly speaking, Bayesian probability is a way of updating one’s priors whenever one receives a new piece of evidence or new information. But, as McGill asks, why not wait until all one’s data is collected before one evaluates such data, just as juries must wait until the end of a case before they are allowed to evaluate the evidence presented by the parties? This question, however, neglects the flexibility and versatility of the Bayesian approach. Yes, there are some situations in which frequentist or traditional statistical methods can take the place of Bayesian methods (as McGill himself notes in his post), but the reverse is not true (something McGill fails to mention). Moreover, Bayesian reasoning is especially applicable not only to single-probability events (like political elections or competitive sports), but to any event with an uncertain outcome that occurs in real time, or when evidence and information are presented in a sequential manner. Jurors, for example, don’t really wait until the end of a case to evaluate the evidence. In reality, jurors are assessing the evidence and engaged in Bayesian reasoning from the start of trial.