Inferential Models

Reasoning with Uncertainty

Ryan Martin, Chuanhai Liu

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English

Chapman & Hall/CRC
25 September 2015

Probability & statistics; Mathematical modelling

Series: Chapman & Hall/CRC Monographs on Statistics and Applied Probability

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.

By: Ryan Martin, Chuanhai Liu
Imprint: Chapman & Hall/CRC
Country of Publication: United States
Volume: 145
Dimensions: Height: 234mm, Width: 156mm, Spine: 20mm
Weight: 544g
ISBN: 9781439886489
ISBN 10: 1439886482
Series: Chapman & Hall/CRC Monographs on Statistics and Applied Probability
Pages: 256
Publication Date: 25 September 2015
Audience: General/trade , College/higher education , Professional and scholarly , ELT Advanced , Primary
Format: Hardback
Publisher's Status: Active

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.

Ryan Martin is an associate professor in the Department of Mathematics, Statistics, and Computer Science at the University of Illinois at Chicago. Chuanhai Liu is a professor in the Department of Statistics at Purdue University.

Reviews for Inferential Models: Reasoning with Uncertainty

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 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