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.
Original language | English (US) |
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Pages (from-to) | 843-861 |
Number of pages | 19 |
Journal | Journal of Econometrics |
Volume | 235 |
Issue number | 2 |
DOIs | |
State | Published - Aug 2023 |
All Science Journal Classification (ASJC) codes
- Economics and Econometrics
- Applied Mathematics