Revising Beliefs in Nonidentified Models

Poirier, Dale J.

doi:10.1017/s0266466698144043

Cited by 199 publications

(175 citation statements)

References 38 publications

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“…This result is well known in the literature (Barankin (60), Florens and Mouchart (74), Picci (77), Dawid (1979), Poirier (1998), among many others), and it can be interpreted that the data only allows us to revise belief on the su¢ cient parameters , while it does not for the conditional prior of given .…”

Section: Posterior Of In the Presence Of Su¢ Cient Parameterssupporting

confidence: 54%

Inference and decision for set identified parameters using posterior lower and upper probabilities

Kitagawa

2011

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This paper develops inference and statistical decision for set-identi…ed parameters from the robust Bayes perspective. When a model is set-identi…ed, prior knowledge for model parameters is decomposed into two parts: the one that can be updated by data (revisable prior knowledge) and the one that never be updated (unrevisable prior knowledge.) We introduce a class of prior distributions that shares a single prior distribution for the revisable, but allows for arbitrary prior distributions for the unrevisable. A posterior inference procedure proposed in this paper operates on the resulting class of posteriors by focusing on the posterior lower and upper probabilities. We analyze point estimation of the set-identi…ed parameters with applying the gamma-minimax criterion. We propose a robusti…ed posterior credible region for the set-identi…ed parameters by focusing on a contour set of the posterior lower probability. Our framework o¤ers a procedure to eliminate set-identi…ed nuisance parameters, and yields inference for the marginalized identi…ed set. For an interval identi…ed parameter case, we establish asymptotic equivalence of the lower probability inference to frequentist inference for the identi…ed set.Keywords: Partial Identi…cation, Bayesian Robustness, Belief Function, Imprecise Probability, Gamma-minimax, Random Set.JEL Classi…cation: C12, C15, C21.

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Section: Posterior Of In the Presence Of Su¢ Cient Parameterssupporting

confidence: 54%

Inference and decision for set identified parameters using posterior lower and upper probabilities

Kitagawa

2011

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“…This point is uncontroversial and is well recognized in the literature since at least the contributions by Kadane (1974), Drèze (1974), Drèze & Richard (1983) and Poirier (1998).…”

Section: Introductionmentioning

confidence: 86%

Assessing Identifying Restrictions in SVAR Models

Piffer

2015

SSRN Journal

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in

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“…Provided the prior is proper (as is the case for all priors used in this paper), a valid posterior density for 2 exists. This is merely a re ‡ection of the well-known Bayesian result that non-identi…cation does not pose a di¢ culty for Bayesians, but that the posterior for a non-identi…ed region of the parameter space will typically be equal to the prior (see, e.g., Poirier, 1998). 3 In one sense, our Unrestricted Uniform prior can be thought of as a simple trick for avoiding the "pile-up of prior probability at the end-of-sample" problem of the Restricted Uniform prior.…”

Section: Theoretical Considerationsmentioning

confidence: 99%

Prior Elicitation in Multiple Change-Point Models

Potter

Koop

2004

SSRN Journal

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This paper discusses Bayesian inference in change-point models. The main existing approaches either attempt to be noninformative by using a Uniform prior over change-points or use an informative hierarchical prior. Both these approaches assume a known number of change-points. We show how they have some potentially undesirable properties and discuss how these properties relate to the imposition of a …xed number of change-points. We develop a new Uniform prior which allows some of the change-points to occur out-of sample. This prior has desirable properties, can reasonably be interpreted as "noninformative"and handles the case where the number of change-pointsWe would like to thank Edward Leamer for useful conversations and also seminar participants at the Federal Reserve Bank of St. Louis and University of Kansas. The views expressed in this paper are those of the authors and do not necessarily re ‡ect the views of the Federal Reserve Bank of New York or the Federal Reserve System. 1 is unknown. We show how the general ideas of our approach can be extended to informative hierarchical priors. With arti…cial data and two empirical illustrations, we show how these di¤erent priors can have a substantial impact on estimation and prediction even with moderately large data sets.

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Revising Beliefs in Nonidentified Models

Cited by 199 publications

References 38 publications

Inference and decision for set identified parameters using posterior lower and upper probabilities

Inference and decision for set identified parameters using posterior lower and upper probabilities

Assessing Identifying Restrictions in SVAR Models

Prior Elicitation in Multiple Change-Point Models

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