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.
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