Multi-Party Inference and Uncongeniality

The Multi-Party Inference Reality

Much of the statistical inference literature uses the familiar framework of “God’s model versus my model.” That is, an unknown model, “God’s model,” generates our data, and our job is to infer this model or at least some of its characteristics (e.g., moments, distributional shape) or implications (e.g., prediction). We first postulate one or several models, and then use an array of estimation, testing, selection, and refinement methods to settle on a model that we judge to be acceptable – according to some sensible criterion, hopefully pre-determined – for the inference goals at hand, even though we almost never can be sure that our chosen model resembles God’s model in critical ways. Indeed, philosophically even the existence of God’s model is not a universally accepted concept, just as theologically the existence of God is not an unchallenged notion.

Whether one does or does...