Semi-exact control functionals from Sard’s method
Summary A novel control variate technique is proposed for the post-processing of Markov chain Monte Carlo output, based on both Stein’s method and an approach to numerical integration due to Sard. The resulting estimators of posterior expected quantities of interest are proven to be polynomially exa...
Saved in:
| Published in | Biometrika Vol. 109; no. 2; pp. 351 - 367 |
|---|---|
| Main Authors | , , , , |
| Format | Journal Article |
| Language | English |
| Published |
Oxford University Press
01.06.2022
|
| Subjects | |
| Online Access | Get full text |
Cover
Loading…
| Abstract | Summary
A novel control variate technique is proposed for the post-processing of Markov chain Monte Carlo output, based on both Stein’s method and an approach to numerical integration due to Sard. The resulting estimators of posterior expected quantities of interest are proven to be polynomially exact in the Gaussian context, while empirical results suggest that the estimators approximate a Gaussian cubature method near the Bernstein–von Mises limit. The main theoretical result establishes a bias-correction property in settings where the Markov chain does not leave the posterior invariant. Empirical results across a selection of Bayesian inference tasks are presented. |
|---|---|
| AbstractList | Summary
A novel control variate technique is proposed for the post-processing of Markov chain Monte Carlo output, based on both Stein’s method and an approach to numerical integration due to Sard. The resulting estimators of posterior expected quantities of interest are proven to be polynomially exact in the Gaussian context, while empirical results suggest that the estimators approximate a Gaussian cubature method near the Bernstein–von Mises limit. The main theoretical result establishes a bias-correction property in settings where the Markov chain does not leave the posterior invariant. Empirical results across a selection of Bayesian inference tasks are presented. |
| Author | Girolami, M South, L F Karvonen, T Oates, C J Nemeth, C |
| Author_xml | – sequence: 1 givenname: L F surname: South fullname: South, L F email: leah.south@hdr.qut.edu.au – sequence: 2 givenname: T surname: Karvonen fullname: Karvonen, T – sequence: 3 givenname: C surname: Nemeth fullname: Nemeth, C – sequence: 4 givenname: M surname: Girolami fullname: Girolami, M – sequence: 5 givenname: C J surname: Oates fullname: Oates, C J |
| BookMark | eNotj81KAzEURoO04LR16zpbF7E3k59JllLUCgUX1fWQSW5wpDMpmSnoztfw9XwSW9rVx-GDA2dGJn3qkZBbDvccrFg2bepwXLrBNSD0FSm41JIJxWFCCgDQTEgpr8lsGD5PqJUuiNhi1zL8cn6kPvVjTjsaD70f29S73UBjTh3duhz-fn4HevR_pLAg03j88Oayc_L-9Pi2WrPN6_PL6mHDvJB8ZNhYDtqp0DTGuApLaSrA0grOg_VVdNKgCl4ba4xSytoYjLclCgUW0JViTu7O3nTY1_vcdi5_1xzqU219rq0vteIfBbBMqg |
| CitedBy_id | crossref_primary_10_1146_annurev_statistics_040220_091727 crossref_primary_10_1214_24_STS923 crossref_primary_10_1007_s11222_022_10183_2 crossref_primary_10_3150_21_BEJ1415 |
| ContentType | Journal Article |
| Copyright | 2021 Biometrika Trust 2021 |
| Copyright_xml | – notice: 2021 Biometrika Trust 2021 |
| DBID | TOX |
| DOI | 10.1093/biomet/asab036 |
| DatabaseName | Open Access: Oxford University Press Open Journals |
| DatabaseTitleList | |
| Database_xml | – sequence: 1 dbid: TOX name: Open Access: Oxford University Press Open Journals url: https://academic.oup.com/journals/ sourceTypes: Publisher |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Statistics Biology |
| EISSN | 1464-3510 |
| EndPage | 367 |
| ExternalDocumentID | 10.1093/biomet/asab036 |
| GroupedDBID | -DZ -E4 -~X ..I .2P .55 .DC .GJ .I3 0R~ 1TH 23N 3R3 4.4 482 48X 53G 5GY 5RE 5VS 5WA 6.Y 6J9 6OB 70D 79B 8U8 AAIJN AAJKP AAJQQ AAMVS AAOGV AAPQZ AAPXW AARHZ AASNB AAUAY AAUQX AAVAP AAWDT ABBHK ABDTM ABEUO ABFAN ABIXL ABJNI ABLJU ABNKS ABPFR ABPPZ ABPTD ABQLI ABQTQ ABSAR ABSMQ ABWST ABXSQ ABXVV ABYAD ABYWD ABZBJ ACBEA ACFRR ACGFO ACGFS ACGOD ACIPB ACIWK ACMRT ACMTB ACNCT ACPQN ACPRK ACTMH ACTWD ACUBG ACUFI ACUTJ ACYTK ACZBC ADACV ADEYI ADEZT ADGZP ADHKW ADHZD ADIPN ADLSF ADMHC ADOCK ADODI ADQBN ADRDM ADRIX ADRTK ADULT ADVEK ADYVW ADZXQ AECKG AEGPL AEGXH AEJOX AEKKA AEKPW AEKSI AELPN AEMDU AENEX AENZO AEPUE AETBJ AEUPB AEWNT AFFZL AFIYH AFOFC AFRAH AFSHK AFVYC AFXEN AFXHP AFYAG AGINJ AGKEF AGKRT AGMDO AGQXC AGSYK AHXPO AIAGR AIJHB AJEEA AJEUX ALMA_UNASSIGNED_HOLDINGS ALTZX ALUQC ANFBD APIBT APJGH APWMN AQDSO ASAOO ASPBG AS~ ATDFG ATGXG ATTQO AVWKF AXUDD AZFZN AZVOD BAYMD BCRHZ BEYMZ BHONS BQUQU BTQHN C45 CAG CDBKE COF CS3 CXTWN CZ4 DAKXR DFGAJ DILTD DQDLB DSRWC DU5 D~K EBS ECEWR EE~ EJD ELUNK ESX F5P F9B FEDTE FLIZI FLUFQ FOEOM FQBLK FVMVE GAUVT GJXCC H13 H5~ HAR HGD HQ6 HVGLF HW0 HZ~ H~9 IOX IPSME J21 JAAYA JAS JBMMH JBZCM JENOY JHFFW JKQEH JLEZI JLXEF JMS JPL JSODD JST JXSIZ KAQDR KBUDW KC5 KOP KSI KSN M-Z M49 MBTAY ML0 MVM N9A NGC NMDNZ NOMLY NTWIH NU- NVLIB O0~ O9- ODMLO OJQWA OJZSN OVD OWPYF O~Y P2P PAFKI PB- PEELM PQQKQ Q1. Q5Y QBD R44 RD5 RIG RNI RNS ROL ROX ROZ RUSNO RW1 RXO RZF RZO SA0 TCN TEORI TJP TN5 TOX UAP WH7 X7H X7M XSW YAYTL YKOAZ YXANX ZCG ZGI ZKX ~02 ~91 |
| ID | FETCH-LOGICAL-c341t-eb9106a5dbb88a7e24870e29311d9c7fa48e5dc6898855599fd8c92e35090ea23 |
| IEDL.DBID | TOX |
| ISSN | 0006-3444 |
| IngestDate | Wed Aug 28 03:17:21 EDT 2024 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 2 |
| Keywords | Control variate Stein operator Variance reduction |
| Language | English |
| License | This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited. |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c341t-eb9106a5dbb88a7e24870e29311d9c7fa48e5dc6898855599fd8c92e35090ea23 |
| OpenAccessLink | https://dx.doi.org/10.1093/biomet/asab036 |
| PageCount | 17 |
| ParticipantIDs | oup_primary_10_1093_biomet_asab036 |
| PublicationCentury | 2000 |
| PublicationDate | 2022-06-01 |
| PublicationDateYYYYMMDD | 2022-06-01 |
| PublicationDate_xml | – month: 06 year: 2022 text: 2022-06-01 day: 01 |
| PublicationDecade | 2020 |
| PublicationTitle | Biometrika |
| PublicationYear | 2022 |
| Publisher | Oxford University Press |
| Publisher_xml | – name: Oxford University Press |
| SSID | ssj0006656 |
| Score | 2.4324517 |
| Snippet | Summary
A novel control variate technique is proposed for the post-processing of Markov chain Monte Carlo output, based on both Stein’s method and an approach... |
| SourceID | oup |
| SourceType | Publisher |
| StartPage | 351 |
| Title | Semi-exact control functionals from Sard’s method |
| Volume | 109 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwjV1LS8QwEA6yIOxFdFV8E8Rr2KR5ND2KuCwe9LC70FuZtFPwYBVbQW_7N_x7_hKTpiwiHrzlkBwyQ-abzOMbQq6slGhUqJ6yAplySc2c0ZJ56Ocucby20Ff53pv5St3lOh_Iots_UviZnPZ96N0UWnDe3Hpr652U8ASXD_nG5hrTz2kNKyaVUht6xt_HYx_bDwiZ7ZKdwfej11FZe2QLmwnZjtMgPyZkHBy_yJu8T-QCnx4ZvkPZ0aGcnAYMiqG7loa2ELrw6v1af7Y0zoE-IKvZ7fJmzoYBB6z04NExdB6sDejKOWshxcT_Hjh6ABaiysq0BmVRV6WxmbU6UIPVlS2zBKVHeY6QyEMyap4bPCJUVEY4BKxqzRWmKQDnkAlXlxpQODgml_7exUuksChi6lkWUTjFIJyT_2w6JeMktAD0kYgzMupe3_DcA3PnLnqdfAPuJYzx |
| link.rule.ids | 315,786,790,1611,27955,27956 |
| linkProvider | Oxford University Press |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Semi-exact+control+functionals+from+Sard%E2%80%99s+method&rft.jtitle=Biometrika&rft.au=South%2C+L+F&rft.au=Karvonen%2C+T&rft.au=Nemeth%2C+C&rft.au=Girolami%2C+M&rft.date=2022-06-01&rft.pub=Oxford+University+Press&rft.issn=0006-3444&rft.eissn=1464-3510&rft.volume=109&rft.issue=2&rft.spage=351&rft.epage=367&rft_id=info:doi/10.1093%2Fbiomet%2Fasab036&rft.externalDocID=10.1093%2Fbiomet%2Fasab036 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0006-3444&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0006-3444&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0006-3444&client=summon |