A Validity Condition and the Foundations of Statistical Inference

Statistical methodology has made extraordinary advances in recent years, but the foundations of statistics still are not yet fully developed. In fact, basic questions such as "what is statistical inference?" lack a widely agreed-upon answer. In this talk, the speaker will present a definition of statistical inference and a key validity criterion, highlighting the new perspective on the foundations of statistics these provide, and draw a connection to what has been called the "most important unsolved problem in statistics". After giving some background to put the problem in perspective, he will introduce the new inferential model (IM) framework and argue that it solves that most important unsolved problem. Some examples will be presented to demonstrate the potential of IMs, and he will conclude with some important open problems, interesting to both statisticians and mathematicians.