New PDF release: Inferential models : reasoning with uncertainty

By Ryan Martin, Chuanhai Liu

ISBN-10: 1439886512

ISBN-13: 9781439886519

A New method of Sound Statistical Reasoning

Inferential types: Reasoning with Uncertainty introduces the authors’ lately constructed method of inference: the inferential version (IM) framework. This logical framework for designated probabilistic inference doesn't require the consumer to enter previous info. The authors express how an IM produces significant prior-free probabilistic inference at a excessive level.

The ebook covers the foundational motivations for this new IM method, the fundamental thought at the back of its calibration houses, a couple of vital functions, and new instructions for examine. It discusses substitute, significant probabilistic interpretations of a few universal inferential summaries, similar to p-values. It additionally constructs posterior probabilistic inferential summaries with out a past and Bayes’ formulation and provides perception at the fascinating and difficult difficulties of conditional and marginal inference.

This publication delves into statistical inference at a foundational point, addressing what the objectives of statistical inference can be. It explores a brand new state of mind in comparison to present faculties of idea on statistical inference and encourages you to consider carefully in regards to the right method of clinical inference.

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Extra resources for Inferential models : reasoning with uncertainty

Sample text

Therefore, we do not completely abandon this kind of frequentist calibration; see Chapter 3 and the various validity results that appear throughout the book. In summary, our opinion is that procedures with good properties should be a consequence of quality inferential output. So, we choose to carry out our work at the higher level of providing meaningful and efficient probabilistic inference, and then easily-derived procedures will automatically inherit the desirable validity and efficiency properties.

That the Jeffreys prior led to a posterior with properly calibrated credible intervals is not a coincidence. In fact, perhaps the strongest theoretical justification for the use of the Jeffreys prior is its “probability matching” property. As first shown in [258], the Jeffreys prior for a scalar parameter is such that one-sided 100(1 − α)% credible intervals Cα (X) = (−∞, θα (X)], constructed to satisfy ΠJX {θ ∈ Cα (X)} = 1 − α, also satisfy PX |θ {Cα (X) θ } = 1 − α + O(n−3/2 ), n → ∞, where X = (X1 , .

Consider a slice HX (c) = {θ : πX (θ ) ≥ c}, and, for a given α ∈ (0, 1), the 100(1 − α)% highest posterior density credible region is obtained by choosing c = cα such that HX (c) πX (θ ) dθ = 1 − α. (a) Describe computation of the highest posterior density region. (b) Explain how the highest posterior density region might not be connected or, in the one-dimensional case, might not be an interval. 16 if and only if the posterior is symmetric. (d) Show that the highest posterior density region is not invariant to transformation.

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Inferential models : reasoning with uncertainty by Ryan Martin, Chuanhai Liu

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