Markov Chain Confidence Intervals and Biases
- Yu Hang Jiang
- Tong Liu
- Zhiya Lou
- Jeffrey S. Rosenthal
- Shanshan Shangguan
- Fei Wang
- Zixuan Wu
Abstract
We derive explicit asymptotic confidence intervals for any Markov chain Monte Carlo (MCMC) algorithm with finite asymptotic variance, started at any initial state, without requiring a Central Limit Theorem nor reversibility nor geometric ergodicity nor any bias bound. We also derive explicit non-asymptotic confidence intervals assuming bounds on the bias or first moment, or alternatively that the chain starts in stationarity. We relate those non-asymptotic bounds to properties of MCMC bias, and show that polynomially ergodicity implies certain bias bounds. We also apply our results to several numerical examples. It is our hope that these results will provide simple and useful tools for estimating errors of MCMC algorithms when CLTs are not available.
- Full Text: PDF
- DOI:10.5539/ijsp.v11n1p29
Journal Metrics
- h-index (December 2021): 20
- i10-index (December 2021): 51
- h5-index (December 2021): N/A
- h5-median(December 2021): N/A
( The data was calculated based on Google Scholar Citations. Click Here to Learn More. )
Index
- ACNP
- Aerospace Database
- BASE (Bielefeld Academic Search Engine)
- CNKI Scholar
- COPAC
- DTU Library
- Elektronische Zeitschriftenbibliothek (EZB)
- EuroPub Database
- Excellence in Research for Australia (ERA)
- Google Scholar
- Harvard Library
- Infotrieve
- JournalTOCs
- LOCKSS
- MIAR
- Mir@bel
- PKP Open Archives Harvester
- Publons
- ResearchGate
- SHERPA/RoMEO
- Standard Periodical Directory
- Technische Informationsbibliothek (TIB)
- UCR Library
- WorldCat
Contact
- Wendy SmithEditorial Assistant
- ijsp@ccsenet.org