The article featured today is from the Canadian Journal of Statistics with the full Open Access article now available to read here.
Egidi, L., Pauli, F. and Torelli, N. (2022), Avoiding prior–data conflict in regression models via mixture priors. Can J Statistics. https://doi.org/10.1002/cjs.11637
Setting up statistical models is a compromise between mathematics and art, combining subjective and objective sources of information. Of course, especially now in the ‘big-data era’, data convey much information and the call for rich and complex models to accommodate these wide data sets is made urgent. However, when dealing with new data sets for a specific application, the experimenters and analysts may have their own prior information, possibly based on past observations/experiments in the same field of study: from a statistical and scientific perspective, they may want to embed this further source of information in their analysis.
At this stage, a natural question is: how to merge current data information and subjective/personal beliefs in such a way to avoid a conflict, which would be likely to yield wrong and misleading statistical and scientific conclusions? In this work the authors focus on this philosophical aspect and develop an algorithmic procedure within the Bayesian framework to make statistical tool as robust as possible. The take-home message is that the “marriage between data and experts’ beliefs” is not merely of theoretical appeal; rather, it has a broader relevance also in medical applications, as outlined in this paper. For instance, it is of practical importance to assess how to balance the information (e.g. in terms of the sex, the age, the level of plasma proteins, etc.) from a new sample of patients who suffer from diabetes and statistical conclusions about previous samples of patients.
When past information meets new data in real-life applications this paper could then wisely drive the experimenters’ decisions.