RISK OF BAYESIAN INFERENCE IN MISSPECIFIED MODELS, AND THE SANDWICH COVARIANCE MATRIX

By Ulrich K. Müller. 2013

165 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Statistics and Probability

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Citations in the corpus

A Simple Baseline for Bayesian Uncertainty in Deep Learning (2019, methodology): “…estimators [see e.g. 47, for a Bayesian analysis in the model mis-speciﬁcation setting], and so A = H ( θ ) − 1 under model well-speciﬁcation [47, 10]. back to We then tie the covariance matrix of the iterates the well known Laplace approximation, which uses H ( θ ) − 1 as its covariance as…”
Monte Carlo Confidence Sets for Identified Sets (2016, unknown): “Following the insight of Müller (2013), we could base our inference on the sandwich log-likelihood function: Ln(θ) = − 1 2 (γ̌ − γ̃(θ))(Σ̂S)(γ̌ − γ̃(θ)) where γ̌ approximately maximizes 1 n ∑n i=1 log qγ(Xi) over Γ̃ and Σ̂S is the sandwich covariance matrix estimator for γ̌.”
Robust generalised Bayesian inference for intractable likelihoods (2021, unknown): “However, we note that the asymptotic precision matrix H ∗ from Theorem 2 differs to the precision matrix H ∗ J − 1 ∗ H ∗ of the minimum KSD estimator from Lemma 4; this is analogous to fact that Bayesian credible sets can have asymptotically incorrect frequentist coverage if the statistical model is”
Inconsistency of Bayesian Inference for Misspecified Linear Models, and a Proposal for Repairing It (2014, methodology): “What exactly are relations between the sandwich posterior (see above) and our approach? It would be good to test SafeBayes on the data sets used by Müller (2013).”
Fast Calibrated Additive Quantile Regression (2017, background): “Müller (2013) proves that, while the posterior of misspecified models is asymptotically Gaussian with mean vector β̂ and covariance matrix V, this posterior is asymptotically worse, in terms of frequentist risk, than a posterior having “sandwich” covariance Ṽ.”
Inference in Linear Regression Models with Many Covariates and Heteroscedasticity (2015, background): “…and White 1985; Wu 1986; Chesher and Jewitt 1987; Shao and Wu 1987; Chesher 1989; Cribari-Neto, Ferrari, and Cordeiro 2000; Kauermann and Carroll 2001; Bera, Suprayitno, and Premaratne 2002; Stock and Watson 2008; Cribari-Neto, da Gloria, and Lima 2011; Müller 2013; Abadie, Imbens, and Zheng 2014).”
On the Evidence for a Common-spectrum Process in the Search for the Nanohertz Gravitational-wave Background with the Parkes Pulsar Timing Array (2021, background): “There is a possibility that neither of these models nor their priors are sufficient descriptions of the data, which is often referred to as model misspecification (e.g. Davidson & MacKinnon 1981; Müller 2013).”
Rare shocks, great recessions (2013, unknown): “A recent paper by Müller (2011) describes some of the dangers associated with departures from Gaussianity when the alternative shock distribution is also misspecified.”
Bayesian inference on structural impulse response functions (2019, background): “Müller (2013) discusses decision theoretic properties of Bayes estimators when the model is mispecified.”
Philosophy and the practice of Bayesian statistics (2010, unknown): “They may not even be the parameter values which give the best predictions (Grünwald and Langford, 2007; Müller, 2011).”
Inference for Misspecified Models With Fixed Regressors (2014, background): “Müller (2013) gave the corresponding confidence intervals a Bayesian interpretation.”