Variance–covariance from a metropolis chain on a curved, singular manifold

A. Ronald Gallant

Journal of Econometrics, 2023, vol. 235, issue 2, 843-861

Abstract: We consider estimation of variance and covariance from a point cloud that are draws from a posterior distribution that lie on a curved, singular manifold. The motivating application is Bayesian inference regarding a likelihood subject to overidentified moment equations using MCMC (Markov Chain Monte Carlo). The MCMC draws lie on a singular manifold that typically is curved. Variance and covariance are Euclidean concepts. A curved, singular manifold is not typically a Euclidean space. We explore some suggestions on how to adapt a Euclidean concept to a non-Euclidean space then build on them to propose and illustrate appropriate methods.

Keywords: Method of moments; Bayesian inference; Simultaneously valid credibility intervals; Point cloud; Curved; Singular manifold (search for similar items in EconPapers)
JEL-codes: C11 C14 C15 C32 C36 C58 (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:235:y:2023:i:2:p:843-861

DOI: 10.1016/j.jeconom.2022.08.002

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