Download e-book for iPad: Bayesian Inference for Partially Identified Models: by Paul Gustafson

By Paul Gustafson

ISBN-10: 1439869391

ISBN-13: 9781439869390

Many observational reports in epidemiology and different disciplines face inherent obstacles in learn layout and information caliber, comparable to choice bias, unobserved variables, and poorly measured variables. available to statisticians and researchers from quite a few disciplines, this publication provides an outline of Bayesian inference in in part pointed out types. It comprises many examples to demonstrate the tools and gives R code for his or her implementation at the book’s site. the writer additionally addresses a couple of open inquiries to stimulate extra learn during this area.

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Extra info for Bayesian Inference for Partially Identified Models: Exploring the Limits of Limited Data

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Particularly, say the support of π(λ |φ ) is an interval with endpoints depending on φ , say (a(φ ), b(φ )). Upon taking λ˜ = {λ − a(φ )}/{b(φ ) − a(φ )}, (φ , λ˜ ) would constitute a loose transparent parameterization of the same problem. A more definitive characterization arises from consideration of the prior dependence between φ and the target of inference. With respect to a given choice of prior π(θ ) and an arbitrary transparent parameterization (φ , λ ), say ψ = g(φ , λ ) is the scalar target of inference.

Conversely, if the data speak loudly, then multiple values of φ can give rise to the same identification region but different limiting posterior distributions. We will tend to keep an eye out for situations where the data speak loudly, as they do in Example A. They provide an interesting challenge conceptually. 6 Comparing inference from limited data and ideal data in Example A. The ideal data consist of n = 400 bivariate observations of (X,Y ). The limited data consist of the same n = 400 observations of X independent from n = 400 observations of Y .

This downweights very small and large cell probabilities, and can be interpreted as a prior with an “effective sample size” of eight data observations. Marginally it implies pxy ∼ Beta(2, 6) a priori, for x, y = 0, 1. 1 portrays the resulting LPD for the target parameter s = p11 , for four different values of the true marginal probabilities (q† , r† ). 75), give rise to the same identification region but different limiting posterior densities over this region. More generally, this can happen when q† + r† ≤ 1, since in this case the identification region is the interval from zero to min(q† , r† ), but the shape of the density depends on both min(q† , r† ) and max(q† , r† ).

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Bayesian Inference for Partially Identified Models: Exploring the Limits of Limited Data by Paul Gustafson


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