A New Approach to Sound Statistical Reasoning
Inferential Models: Reasoning with Uncertainty introduces the authors’ recently developed approach to inference: the inferential model (IM) framework. This logical framework for exact probabilistic inference does not require the user to input prior information. The authors show how an IM produces meaningful prior-free probabilistic inference at a high level.
The book covers the foundational motivations for this new IM approach, the basic theory behind its calibration properties, a number of important applications, and new directions for research. It discusses alternative, meaningful probabilistic interpretations of some common inferential summaries, such as p-values. It also constructs posterior probabilistic inferential summaries without a prior and Bayes’ formula and offers insight on the interesting and challenging problems of conditional and marginal inference.
This book delves into statistical inference at a foundational level, addressing what the goals of statistical inference should be. It explores a new way of thinking compared to existing schools of thought on statistical inference and encourages you to think carefully about the correct approach to scientific inference.
Preliminaries. Prior-Free Probabilistic Inference. Two Fundamental Principles. Inferential Models. Predictive Random Sets. Conditional Inferential Models. Marginal Inferential Models. Normal Linear Models. Prediction of Future Observations. Simultaneous Inference on Multiple Assertions. Generalized Inferential Models. Future Research Topics. Bibliography. Index.
"The book . . . delivers on its promise. It should be read by all statisticians with an interest in the foundations and development of the statistical methods for inference."
~Michael J. Lew, University of Melbourne
" . . . the book covers the motivations for the IM framework, the basic theory behind its calibration properties, a number of its applications and gives a new way of thinking compared to existing schools of thought on statistical inference"
~Apostolos Batsidis (Ioannina), Zentralblatt MATH