Theoretical properties of quasi-stationary Monte Carlo methods
This paper gives foundational results for the application of quasi-stationarity to Monte Carlo inference problems. We prove natural sufficient conditions for the quasi-limiting distribution of a killed diffusion to coincide with a target density of interest. We also quantify the rate of convergence...
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| Format: | Journal article |
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Institute of Mathematical Statistics
2018
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| _version_ | 1797092447407308800 |
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| author | Wang, A Kolb, M Roberts, G Steinsaltz, D |
| author_facet | Wang, A Kolb, M Roberts, G Steinsaltz, D |
| author_sort | Wang, A |
| collection | OXFORD |
| description | This paper gives foundational results for the application of quasi-stationarity to Monte Carlo inference problems. We prove natural sufficient conditions for the quasi-limiting distribution of a killed diffusion to coincide with a target density of interest. We also quantify the rate of convergence to quasi-stationarity by relating the killed diffusion to an appropriate Langevin diffusion. As an example, we consider in detail a killed Ornstein–Uhlenbeck process with Gaussian quasi-stationary distribution. |
| first_indexed | 2024-03-07T03:46:01Z |
| format | Journal article |
| id | oxford-uuid:bf7fa782-025a-4649-b527-ce7603b5d315 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T03:46:01Z |
| publishDate | 2018 |
| publisher | Institute of Mathematical Statistics |
| record_format | dspace |
| spelling | oxford-uuid:bf7fa782-025a-4649-b527-ce7603b5d3152022-03-27T05:47:52ZTheoretical properties of quasi-stationary Monte Carlo methodsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:bf7fa782-025a-4649-b527-ce7603b5d315Symplectic Elements at OxfordInstitute of Mathematical Statistics2018Wang, AKolb, MRoberts, GSteinsaltz, DThis paper gives foundational results for the application of quasi-stationarity to Monte Carlo inference problems. We prove natural sufficient conditions for the quasi-limiting distribution of a killed diffusion to coincide with a target density of interest. We also quantify the rate of convergence to quasi-stationarity by relating the killed diffusion to an appropriate Langevin diffusion. As an example, we consider in detail a killed Ornstein–Uhlenbeck process with Gaussian quasi-stationary distribution. |
| spellingShingle | Wang, A Kolb, M Roberts, G Steinsaltz, D Theoretical properties of quasi-stationary Monte Carlo methods |
| title | Theoretical properties of quasi-stationary Monte Carlo methods |
| title_full | Theoretical properties of quasi-stationary Monte Carlo methods |
| title_fullStr | Theoretical properties of quasi-stationary Monte Carlo methods |
| title_full_unstemmed | Theoretical properties of quasi-stationary Monte Carlo methods |
| title_short | Theoretical properties of quasi-stationary Monte Carlo methods |
| title_sort | theoretical properties of quasi stationary monte carlo methods |
| work_keys_str_mv | AT wanga theoreticalpropertiesofquasistationarymontecarlomethods AT kolbm theoreticalpropertiesofquasistationarymontecarlomethods AT robertsg theoreticalpropertiesofquasistationarymontecarlomethods AT steinsaltzd theoreticalpropertiesofquasistationarymontecarlomethods |