On stochastic error and computational efficiency of the Markov Chain Monte Carlo method
In Markov Chain Monte Carlo (MCMC) simulations, thermal equilibria quantities are estimated by ensemble average over a sample set containing a large number of correlated samples. These samples are selected in accordance with the probability distribution function, known from the partition function of...
| Main Authors: | , , , |
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| Format: | Journal Article |
| Published: |
2014
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| Online Access: | http://hdl.handle.net/20.500.11937/51324 |
| _version_ | 1848758668844072960 |
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| author | Li, J. Vignal, P. Sun, S. Calo, Victor |
| author_facet | Li, J. Vignal, P. Sun, S. Calo, Victor |
| author_sort | Li, J. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | In Markov Chain Monte Carlo (MCMC) simulations, thermal equilibria quantities are estimated by ensemble average over a sample set containing a large number of correlated samples. These samples are selected in accordance with the probability distribution function, known from the partition function of equilibrium state. As the stochastic error of the simulation results is significant, it is desirable to understand the variance of the estimation by ensemble average, which depends on the sample size (i.e., the total number of samples in the set) and the sampling interval (i.e., cycle number between two consecutive samples). Although large sample sizes reduce the variance, they increase the computational cost of the simulation. For a given CPU time, the sample size can be reduced greatly by increasing the sampling interval, while having the corresponding increase in variance be negligible if the original sampling interval is very small. In this work, we report a few general rules that relate the variance with the sample size and the sampling interval. These results are observed and confirmed numerically. These variance rules are derived for theMCMCmethod but are also valid for the correlated samples obtained using other Monte Carlo methods. The main contribution of this work includes the theoretical proof of these numerical observations and the set of assumptions that lead to them. © 2014 Global-Science Press. |
| first_indexed | 2025-11-14T09:47:39Z |
| format | Journal Article |
| id | curtin-20.500.11937-51324 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:47:39Z |
| publishDate | 2014 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-513242018-03-29T09:08:25Z On stochastic error and computational efficiency of the Markov Chain Monte Carlo method Li, J. Vignal, P. Sun, S. Calo, Victor In Markov Chain Monte Carlo (MCMC) simulations, thermal equilibria quantities are estimated by ensemble average over a sample set containing a large number of correlated samples. These samples are selected in accordance with the probability distribution function, known from the partition function of equilibrium state. As the stochastic error of the simulation results is significant, it is desirable to understand the variance of the estimation by ensemble average, which depends on the sample size (i.e., the total number of samples in the set) and the sampling interval (i.e., cycle number between two consecutive samples). Although large sample sizes reduce the variance, they increase the computational cost of the simulation. For a given CPU time, the sample size can be reduced greatly by increasing the sampling interval, while having the corresponding increase in variance be negligible if the original sampling interval is very small. In this work, we report a few general rules that relate the variance with the sample size and the sampling interval. These results are observed and confirmed numerically. These variance rules are derived for theMCMCmethod but are also valid for the correlated samples obtained using other Monte Carlo methods. The main contribution of this work includes the theoretical proof of these numerical observations and the set of assumptions that lead to them. © 2014 Global-Science Press. 2014 Journal Article http://hdl.handle.net/20.500.11937/51324 10.4208/cicp.110613.280214a restricted |
| spellingShingle | Li, J. Vignal, P. Sun, S. Calo, Victor On stochastic error and computational efficiency of the Markov Chain Monte Carlo method |
| title | On stochastic error and computational efficiency of the Markov Chain Monte Carlo method |
| title_full | On stochastic error and computational efficiency of the Markov Chain Monte Carlo method |
| title_fullStr | On stochastic error and computational efficiency of the Markov Chain Monte Carlo method |
| title_full_unstemmed | On stochastic error and computational efficiency of the Markov Chain Monte Carlo method |
| title_short | On stochastic error and computational efficiency of the Markov Chain Monte Carlo method |
| title_sort | on stochastic error and computational efficiency of the markov chain monte carlo method |
| url | http://hdl.handle.net/20.500.11937/51324 |