In this series of six lectures, under the name of “Inferential Models”, we will discuss tremendous efforts made ever since to tackle fundamental but still unsolved problems in statistical inference. The focus will be on three basic questions: (1) how to make calibrated probabilistic assessments of uncertainty in converting data to knowledge, (2) how to effectively combine information, and (3) how to marginalize when low dimensional functions of high dimensional parameters is of interest. The fundamental many-normal-means problem that has greatly influenced the statistical research in last half century will be taken as a concrete example.

In addition, we will take this opportunity to explore ideas on the development of iterative algorithms with the focus on how statistical thinking can be helpful. Also, we will discuss current efforts in creating distributed computing platforms in large data analysis that needs more advanced statistical methods such as methods that can deal with missing data. In particular, we will discuss the efforts in developing SupR and its new version to be called SupR 2.0.