Bayesian inference for nonlinear multivariate diffusion models observed with error
Diffusion processes governed by stochastic differential equations (SDEs) are a well-established tool for modelling continuous time data from a wide range of areas. Consequently, techniques have been developed to estimate diffusion parameters from partial and discrete observations. Likelihood-based i...
Saved in:
| Published in: | Computational statistics & data analysis Vol. 52; no. 3; pp. 1674 - 1693 |
|---|---|
| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Amsterdam
Elsevier B.V
2008
Elsevier Science Elsevier |
| Series: | Computational Statistics & Data Analysis |
| Subjects: | |
| ISSN: | 0167-9473, 1872-7352 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | Diffusion processes governed by stochastic differential equations (SDEs) are a well-established tool for modelling continuous time data from a wide range of areas. Consequently, techniques have been developed to estimate diffusion parameters from partial and discrete observations. Likelihood-based inference can be problematic as closed form transition densities are rarely available. One widely used solution involves the introduction of latent data points between every pair of observations to allow a Euler–Maruyama approximation of the true transition densities to become accurate. In recent literature, Markov chain Monte Carlo (MCMC) methods have been used to sample the posterior distribution of latent data and model parameters; however, naive schemes suffer from a mixing problem that worsens with the degree of augmentation. A global MCMC scheme that can be applied to a large class of diffusions and whose performance is not adversely affected by the number of latent values is therefore explored. The methodology is illustrated by estimating parameters governing an auto-regulatory gene network, using partial and discrete data that are subject to measurement error. |
|---|---|
| AbstractList | Diffusion processes governed by stochastic differential equations (SDEs) are a well-established tool for modelling continuous time data from a wide range of areas. Consequently, techniques have been developed to estimate diffusion parameters from partial and discrete observations. Likelihood-based inference can be problematic as closed form transition densities are rarely available. One widely used solution involves the introduction of latent data points between every pair of observations to allow a Euler-Maruyama approximation of the true transition densities to become accurate. In recent literature, Markov chain Monte Carlo (MCMC) methods have been used to sample the posterior distribution of latent data and model parameters; however, naive schemes suffer from a mixing problem that worsens with the degree of augmentation. A global MCMC scheme that can be applied to a large class of diffusions and whose performance is not adversely affected by the number of latent values is therefore explored. The methodology is illustrated by estimating parameters governing an auto-regulatory gene network, using partial and discrete data that are subject to measurement error. |
| Author | Golightly, A. Wilkinson, D.J. |
| Author_xml | – sequence: 1 givenname: A. surname: Golightly fullname: Golightly, A. email: a.golightly@ncl.ac.uk – sequence: 2 givenname: D.J. surname: Wilkinson fullname: Wilkinson, D.J. email: d.j.wilkinson@ncl.ac.uk |
| BackLink | http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=20017587$$DView record in Pascal Francis http://econpapers.repec.org/article/eeecsdana/v_3a52_3ay_3a2008_3ai_3a3_3ap_3a1674-1693.htm$$DView record in RePEc |
| BookMark | eNp9kUuPFCEUhYkZE3tG_4Cr2uiuangWdOJGJ-Mj6cTE6JpQcMnQqYIW6Db976XSo4tZzOJyN-c7wDnX6CqmCAi9JXggmIy3-8EWZwaKsRywGDDZvkAboiTtJRP0Cm2aSPZbLtkrdF3KHmNMuVQb9OOTOUMJJnYhesgQLXQ-5a75zyGCyd1ynGs4mRxMhc4F748lpNgtycFcujQVyCdw3Z9QHzrIOeXX6KU3c4E3j_sG_fp8__Pua7_7_uXb3cddb7nktedOKUeZEAorLmEySslxslYBOE6AU0_VNGJl_UgMnZjxVNiJqVEKbiei2A16f_E95PT7CKXqJRQL82wipGPRtH2RCcKacHcRZjiA1YccFpPPGgDW0KLRJ82MoO04t2kZqrZCG9bm0KZlxzUZt0w_1KXZvXu81xRrZp9NtKH8t208kULJplMXnc2plAxe21BNbeHVbMKsCdZrd3qv12esnNRY6NZdQ-kT9J_7s9CHC9R6gVOArIsNa6EuZLBVuxSew_8CSDm1EQ |
| CitedBy_id | crossref_primary_10_1016_j_jcp_2019_07_035 crossref_primary_10_1007_s11009_022_09949_y crossref_primary_10_1016_j_neucom_2009_11_026 crossref_primary_10_1111_j_1467_9876_2009_00696_x crossref_primary_10_1016_j_jtbi_2020_110255 crossref_primary_10_1093_biomet_ass034 crossref_primary_10_1007_s11222_011_9310_8 crossref_primary_10_1371_journal_pcbi_1009746 crossref_primary_10_1140_epjb_s10051_021_00149_0 crossref_primary_10_1214_16_AAP1236 crossref_primary_10_1515_snde_2012_0026 crossref_primary_10_1016_j_csda_2019_01_006 crossref_primary_10_1515_sagmb_2014_0071 crossref_primary_10_1111_biom_12152 crossref_primary_10_1214_11_BA608 crossref_primary_10_1007_s11222_007_9043_x crossref_primary_10_1002_env_2353 crossref_primary_10_1016_j_physd_2023_133784 crossref_primary_10_1007_s00180_011_0246_4 crossref_primary_10_1007_s10100_012_0237_8 crossref_primary_10_1093_biomet_asv051 crossref_primary_10_1007_s11222_022_10083_5 crossref_primary_10_1016_j_csda_2008_07_036 crossref_primary_10_1111_j_1467_9868_2009_00736_x crossref_primary_10_1534_genetics_116_187278 crossref_primary_10_1080_10618600_2022_2027243 crossref_primary_10_1007_s11222_011_9255_y crossref_primary_10_1007_s11203_025_09326_9 crossref_primary_10_1080_00949655_2020_1746788 crossref_primary_10_1093_jjfinec_nbp027 crossref_primary_10_1016_j_csda_2010_04_018 crossref_primary_10_1214_20_BA1216 crossref_primary_10_1214_25_AOS2496 crossref_primary_10_1214_16_BA1009 crossref_primary_10_1016_j_jcp_2015_12_043 crossref_primary_10_1080_10618600_2013_783484 crossref_primary_10_1007_s00180_017_0728_0 crossref_primary_10_1137_17M1151900 crossref_primary_10_1111_rssb_12497 crossref_primary_10_1177_00375497211009576 crossref_primary_10_1093_bib_bbp072 crossref_primary_10_1007_s11222_011_9244_1 crossref_primary_10_1016_j_csda_2014_10_011 crossref_primary_10_1007_s11222_015_9625_y crossref_primary_10_1007_s00180_018_0846_3 crossref_primary_10_1016_j_jat_2010_05_002 crossref_primary_10_1016_j_csda_2009_07_025 crossref_primary_10_1080_01621459_2012_714715 crossref_primary_10_1093_biostatistics_kxs052 crossref_primary_10_1111_sjos_12362 crossref_primary_10_1080_03610918_2017_1291960 crossref_primary_10_1007_s11222_013_9441_1 crossref_primary_10_1093_rfs_hhn110 crossref_primary_10_1007_s00180_012_0352_y crossref_primary_10_1111_rssb_12061 crossref_primary_10_1371_journal_pone_0019616 crossref_primary_10_1109_JIOT_2024_3365657 crossref_primary_10_1002_cjs_10096 crossref_primary_10_1002_wics_1585 crossref_primary_10_1007_s11203_019_09199_9 crossref_primary_10_1007_s00249_009_0520_3 crossref_primary_10_1007_s11336_019_09664_7 crossref_primary_10_1038_nrg2509 crossref_primary_10_1007_s00285_017_1099_4 crossref_primary_10_1016_j_spa_2012_12_001 crossref_primary_10_1080_17442508_2017_1381097 crossref_primary_10_1111_j_1467_9469_2012_00812_x crossref_primary_10_1080_02664763_2019_1677573 crossref_primary_10_1007_s11009_023_10056_9 crossref_primary_10_1111_rssb_12118 crossref_primary_10_1175_MWR_D_15_0261_1 crossref_primary_10_1007_s11222_014_9469_x crossref_primary_10_1214_15_BA948 crossref_primary_10_1016_j_jcp_2020_109635 crossref_primary_10_1063_5_0081668 crossref_primary_10_1016_j_mbs_2013_03_008 crossref_primary_10_1017_apr_2024_12 crossref_primary_10_1080_01621459_2012_720899 crossref_primary_10_1111_rssc_12222 crossref_primary_10_1137_16M1079282 crossref_primary_10_1007_s11222_016_9660_3 crossref_primary_10_1098_rsos_200270 crossref_primary_10_1080_01621459_2012_655995 crossref_primary_10_1002_aic_14409 crossref_primary_10_1016_j_neuroimage_2012_12_018 crossref_primary_10_1016_j_compchemeng_2014_01_006 crossref_primary_10_1155_2012_752631 crossref_primary_10_3934_fods_2022008 crossref_primary_10_1214_08_BA332 crossref_primary_10_1088_1751_8113_41_35_355002 crossref_primary_10_1515_sagmb_2017_0046 |
| Cites_doi | 10.1016/j.spa.2006.04.004 10.1016/S0168-9525(98)01659-X 10.2307/2670179 10.1198/106186002835 10.1016/0378-4371(92)90283-V 10.1007/s11222-006-9392-x 10.1093/biomet/88.3.603 10.1109/78.978383 10.1111/j.1467-9868.2006.00552.x 10.1111/1468-0262.00226 10.1093/biomet/84.3.653 10.1089/cmb.2006.13.838 10.1023/A:1008935410038 10.2307/2965410 10.2307/3318679 10.1049/ip-f-2.1993.0015 10.2307/2289457 10.1198/073500101316970403 10.2307/2328983 10.1086/260062 10.1093/genetics/149.4.1633 10.1007/PL00008786 10.2307/1911242 10.1111/j.1541-0420.2005.00345.x 10.1198/073500102288618397 |
| ContentType | Journal Article |
| Copyright | 2007 Elsevier B.V. 2008 INIST-CNRS |
| Copyright_xml | – notice: 2007 Elsevier B.V. – notice: 2008 INIST-CNRS |
| DBID | AAYXX CITATION IQODW DKI X2L 8FD FR3 P64 RC3 |
| DOI | 10.1016/j.csda.2007.05.019 |
| DatabaseName | CrossRef Pascal-Francis RePEc IDEAS RePEc Technology Research Database Engineering Research Database Biotechnology and BioEngineering Abstracts Genetics Abstracts |
| DatabaseTitle | CrossRef Genetics Abstracts Engineering Research Database Technology Research Database Biotechnology and BioEngineering Abstracts |
| DatabaseTitleList | Genetics Abstracts |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics Statistics |
| EISSN | 1872-7352 |
| EndPage | 1693 |
| ExternalDocumentID | eeecsdana_v_3a52_3ay_3a2008_3ai_3a3_3ap_3a1674_1693_htm 20017587 10_1016_j_csda_2007_05_019 S0167947307002198 |
| GroupedDBID | --K --M -~X .~1 0R~ 1B1 1OL 1RT 1~. 1~5 29F 4.4 457 4G. 5GY 5VS 7-5 71M 8P~ 9JN 9JO AAAKF AAAKG AABNK AACTN AAEDT AAEDW AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AARIN AAXUO AAYFN ABAOU ABBOA ABFNM ABMAC ABTAH ABUCO ABXDB ABYKQ ACAZW ACDAQ ACGFS ACNNM ACRLP ACZNC ADBBV ADEZE ADGUI ADJOM ADMUD ADTZH AEBSH AECPX AEKER AENEX AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AHJVU AHZHX AI. AIALX AIEXJ AIGVJ AIKHN AITUG AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ AOUOD APLSM ARUGR ASPBG AVWKF AXJTR AZFZN BJAXD BKOJK BLXMC CS3 DU5 EBS EFJIC EFLBG EJD EO8 EO9 EP2 EP3 F5P FDB FEDTE FGOYB FIRID FNPLU FYGXN G-2 G-Q GBLVA GBOLZ HAMUX HLZ HMJ HVGLF HZ~ H~9 IHE J1W JJJVA KOM LG9 LY1 M26 M41 MHUIS MO0 N9A O-L O9- OAUVE OZT P-8 P-9 P2P PC. Q38 R2- RIG RNS ROL RPZ SBC SDF SDG SDS SES SEW SME SPC SPCBC SSB SSD SST SSV SSW SSZ T5K VH1 VOH WUQ XPP ZMT ZY4 ~02 ~G- 9DU AAHBH AATTM AAXKI AAYWO AAYXX ABJNI ABWVN ACLOT ACRPL ACVFH ADCNI ADNMO ADXHL AEIPS AEUPX AFJKZ AFPUW AGQPQ AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP CITATION EFKBS ~HD AFXIZ AGCQF AGRNS BNPGV IQODW SSH 02 0R 1 8P ABFLS ABPTK ADALY DKI G- HZ IPNFZ K M STF X X2L 8FD FR3 P64 RC3 |
| ID | FETCH-LOGICAL-c474t-4d88d235580847eba8876bcc8eed41e42f28b608cf61a2b3af25cb386754cb183 |
| ISICitedReferencesCount | 135 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000253669700031&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0167-9473 |
| IngestDate | Sat Sep 27 23:15:48 EDT 2025 Wed Aug 18 03:10:08 EDT 2021 Mon Jul 21 09:15:25 EDT 2025 Sat Nov 29 03:40:34 EST 2025 Tue Nov 18 22:17:51 EST 2025 Fri Feb 23 02:20:06 EST 2024 |
| IsDoiOpenAccess | false |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 3 |
| Keywords | MCMC Nonlinear stochastic differential equation Innovation scheme Bayesian inference Reparameterisation Particle filter Density estimation Parameter estimation Mixing Statistical distribution Error estimation Differential equation Continuous time Multivariate analysis Stochastic method Stochastic process Markov chain Distribution function Diffusion process Integral equation Approximation theory Latent value Measurement error Posterior distribution Stochastic equation Bayes estimation Mixed distribution Monte Carlo method Data analysis Approximation Discrete data Statistical estimation Numerical analysis Statistical computation Non linear model |
| Language | English |
| License | https://www.elsevier.com/tdm/userlicense/1.0 CC BY 4.0 |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c474t-4d88d235580847eba8876bcc8eed41e42f28b608cf61a2b3af25cb386754cb183 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
| OpenAccessLink | https://durham-repository.worktribe.com/output/1214220 |
| PQID | 20243513 |
| PQPubID | 23462 |
| PageCount | 20 |
| ParticipantIDs | proquest_miscellaneous_20243513 repec_primary_eeecsdana_v_3a52_3ay_3a2008_3ai_3a3_3ap_3a1674_1693_htm pascalfrancis_primary_20017587 crossref_citationtrail_10_1016_j_csda_2007_05_019 crossref_primary_10_1016_j_csda_2007_05_019 elsevier_sciencedirect_doi_10_1016_j_csda_2007_05_019 |
| PublicationCentury | 2000 |
| PublicationDate | 2008 2008-1-00 20080101 |
| PublicationDateYYYYMMDD | 2008-01-01 |
| PublicationDate_xml | – year: 2008 text: 2008 |
| PublicationDecade | 2000 |
| PublicationPlace | Amsterdam |
| PublicationPlace_xml | – name: Amsterdam |
| PublicationSeriesTitle | Computational Statistics & Data Analysis |
| PublicationTitle | Computational statistics & data analysis |
| PublicationYear | 2008 |
| Publisher | Elsevier B.V Elsevier Science Elsevier |
| Publisher_xml | – name: Elsevier B.V – name: Elsevier Science – name: Elsevier |
| References | Ptashne (bib30) 1992 Berzuini, Best, Gilks, Larizza (bib2) 1997; 92 Del Moral, Jacod, Protter (bib9) 2002; 120 Tanner, Wong (bib36) 1987; 82 Beskos, Papaspiliopoulos, Roberts, Fearnhead (bib3) 2006; 68 Chib, Pitt, Shephard (bib7) 2006 Elerian, Chib, Shephard (bib13) 2001; 69 Latchman (bib23) 2002 Storvik (bib33) 2002; 50 Golightly, Wilkinson (bib18) 2006; 16 Golightly, Wilkinson (bib17) 2005; 61 Eraker (bib14) 2001; 19 Bibby, Sørensen (bib4) 1995; 1 Doucet, Godsill, Andrieu (bib11) 2000; 10 Golightly, Wilkinson (bib19) 2006; 13 Gordon, N.J., Salmond, D.J., Smith, A.F.M., 1993. Novel approach to nonlinear/non-Gaussian Bayesian state estimation. IEE Proc-F 140, 107–113. Pitt, Shephard (bib29) 1999; 446 Stroud, Polson, Muller (bib35) 2004 Øksendal (bib26) 1995 Johannes, Polson, Stroud (bib21) 2006 Arkin, Ross, McAdams (bib1) 1998; 149 Chan, Karolyi, Longstaff, Sanders (bib6) 1992; 47 Black, Scholes (bib5) 1973; 81 Liu, West (bib24) 2001 Stramer, O., Yan, J., 2007. Asymptotics of an efficient Monte Carlo estimation for the transition density of diffusion processes. Methodol. Comput. Appl. doi Kalogeropoulos (bib22) 2006 Shephard, Pitt (bib32) 1997; 84 Gillespie (bib16) 1992; 188 Wilkinson (bib37) 2003 Roberts, Stramer (bib31) 2001; 88 Durham, Gallant (bib12) 2002; 20 McAdams, Arkin (bib25) 1999; 15 Papaspiliopolous, Roberts, Skôld (bib27) 2003 Pedersen (bib28) 1995; 1995 . Cox, Ingersoll, Ross (bib8) 1985; 53 Fearnhead (bib15) 2002; 11 Wilkinson (bib38) 2006 Delyon, Hu (bib10) 2006; 116 Storvik (10.1016/j.csda.2007.05.019_bib33) 2002; 50 Gillespie (10.1016/j.csda.2007.05.019_bib16) 1992; 188 Papaspiliopolous (10.1016/j.csda.2007.05.019_bib27) 2003 10.1016/j.csda.2007.05.019_bib34 Roberts (10.1016/j.csda.2007.05.019_bib31) 2001; 88 Cox (10.1016/j.csda.2007.05.019_bib8) 1985; 53 Latchman (10.1016/j.csda.2007.05.019_bib23) 2002 Arkin (10.1016/j.csda.2007.05.019_bib1) 1998; 149 Wilkinson (10.1016/j.csda.2007.05.019_bib37) 2003 Berzuini (10.1016/j.csda.2007.05.019_bib2) 1997; 92 Beskos (10.1016/j.csda.2007.05.019_bib3) 2006; 68 Golightly (10.1016/j.csda.2007.05.019_bib18) 2006; 16 Shephard (10.1016/j.csda.2007.05.019_bib32) 1997; 84 Pedersen (10.1016/j.csda.2007.05.019_bib28) 1995; 1995 Doucet (10.1016/j.csda.2007.05.019_bib11) 2000; 10 Johannes (10.1016/j.csda.2007.05.019_bib21) 2006 Kalogeropoulos (10.1016/j.csda.2007.05.019_bib22) 2006 Tanner (10.1016/j.csda.2007.05.019_bib36) 1987; 82 Chan (10.1016/j.csda.2007.05.019_bib6) 1992; 47 Fearnhead (10.1016/j.csda.2007.05.019_bib15) 2002; 11 Pitt (10.1016/j.csda.2007.05.019_bib29) 1999; 446 10.1016/j.csda.2007.05.019_bib20 Elerian (10.1016/j.csda.2007.05.019_bib13) 2001; 69 McAdams (10.1016/j.csda.2007.05.019_bib25) 1999; 15 Ptashne (10.1016/j.csda.2007.05.019_bib30) 1992 Stroud (10.1016/j.csda.2007.05.019_bib35) 2004 Bibby (10.1016/j.csda.2007.05.019_bib4) 1995; 1 Durham (10.1016/j.csda.2007.05.019_bib12) 2002; 20 Eraker (10.1016/j.csda.2007.05.019_bib14) 2001; 19 Black (10.1016/j.csda.2007.05.019_bib5) 1973; 81 Chib (10.1016/j.csda.2007.05.019_bib7) 2006 Delyon (10.1016/j.csda.2007.05.019_bib10) 2006; 116 Golightly (10.1016/j.csda.2007.05.019_bib17) 2005; 61 Øksendal (10.1016/j.csda.2007.05.019_bib26) 1995 Del Moral (10.1016/j.csda.2007.05.019_bib9) 2002; 120 Liu (10.1016/j.csda.2007.05.019_bib24) 2001 Golightly (10.1016/j.csda.2007.05.019_bib19) 2006; 13 Wilkinson (10.1016/j.csda.2007.05.019_bib38) 2006 |
| References_xml | – volume: 50 start-page: 281 year: 2002 end-page: 289 ident: bib33 article-title: Particle filters for state-space models with the presence of unknown static parameters publication-title: IEEE. Trans. Signal. Process. – volume: 82 start-page: 528 year: 1987 end-page: 540 ident: bib36 article-title: The calculation of posterior distributions by data augmentation publication-title: J. Amer. Statist. Assoc. – reference: Stramer, O., Yan, J., 2007. Asymptotics of an efficient Monte Carlo estimation for the transition density of diffusion processes. Methodol. Comput. Appl. doi: – year: 2006 ident: bib7 article-title: Likelihood based inference for diffusion driven models – year: 2006 ident: bib38 article-title: Stochastic Modelling for Systems Biology – reference: Gordon, N.J., Salmond, D.J., Smith, A.F.M., 1993. Novel approach to nonlinear/non-Gaussian Bayesian state estimation. IEE Proc-F 140, 107–113. – year: 1995 ident: bib26 article-title: Stochastic Differential Equations: An Introduction with Applications – volume: 149 start-page: 633 year: 1998 end-page: 648 ident: bib1 article-title: Stochastic kinetic analysis of developmental pathway bifurcation in phage lambda-infected publication-title: Genetics – year: 2001 ident: bib24 article-title: Combined parameter and state estimation in simulation-based filtering publication-title: Sequential Monte Carlo Methods in Practice – volume: 446 start-page: 590 year: 1999 end-page: 599 ident: bib29 article-title: Filtering via simulation: auxiliary particle filters publication-title: J. Amer. Statist. Assoc. – volume: 84 start-page: 653 year: 1997 end-page: 667 ident: bib32 article-title: Likelihood analysis of non-Gaussian measurement time series publication-title: Biometrika – start-page: 307 year: 2003 end-page: 326 ident: bib27 article-title: Non-centered parameterisations for hierarchical models and data augmentation publication-title: Bayesian Statistics 7 – volume: 15 start-page: 65 year: 1999 end-page: 69 ident: bib25 article-title: Its a noisy business: genetic regulation at the nanomolar scale publication-title: Trends. Genet. – volume: 120 start-page: 346 year: 2002 end-page: 368 ident: bib9 article-title: The Monte Carlo method for filtering with discrete-time observations publication-title: Probab. Theory Related Fields – volume: 88 start-page: 603 year: 2001 end-page: 621 ident: bib31 article-title: On inference for partially observed nonlinear diffusion models using the Metropolis–Hastings algorithm publication-title: Biometrika – start-page: 323 year: 2003 end-page: 324 ident: bib37 article-title: Discussion to ‘Non centred parameterisations for hierarchical models and data augmentation’ by Papaspiliopoulos, Roberts and Skold publication-title: Bayesian Statistics 7 – volume: 47 start-page: 1209 year: 1992 end-page: 1228 ident: bib6 article-title: An empirical comparison of alternative models of the short-term interest publication-title: J. Finance – volume: 10 start-page: 197 year: 2000 end-page: 208 ident: bib11 article-title: On sequential Monte Carlo sampling methods for Bayesian filtering publication-title: Statistist. Comput. – volume: 188 start-page: 404 year: 1992 end-page: 425 ident: bib16 article-title: A rigorous derivation of the chemical master equation publication-title: Physica A – volume: 61 start-page: 781 year: 2005 end-page: 788 ident: bib17 article-title: Bayesian inference for stochastic kinetic models using a diffusion approximation publication-title: Biometrics – year: 2006 ident: bib22 article-title: Likelihood-based inference for a class of multivariate diffusions with unobserved paths – volume: 69 start-page: 959 year: 2001 end-page: 993 ident: bib13 article-title: Likelihood inference for discretely observed nonlinear diffusions publication-title: Econometrica – volume: 16 start-page: 323 year: 2006 end-page: 338 ident: bib18 article-title: Bayesian sequential inference for nonlinear multivariate diffusions publication-title: Statist. Comput. – start-page: 236 year: 2004 end-page: 247 ident: bib35 article-title: Practical filtering for stochastic volatility models publication-title: State Space and Unobserved Components Models – volume: 19 start-page: 177 year: 2001 end-page: 191 ident: bib14 article-title: MCMC analysis of diffusion models with application to finance publication-title: J. Bus. Econ. Statist. – volume: 1 start-page: 17 year: 1995 end-page: 39 ident: bib4 article-title: Martingale estimating functions for discretely observed diffusion processes publication-title: Bernouilli – volume: 81 start-page: 637 year: 1973 end-page: 659 ident: bib5 article-title: The pricing of options and corporate liabilities publication-title: J. Polit. Econ. – year: 2002 ident: bib23 article-title: Gene Regulation: A Eukaryotic Perspective – volume: 1995 start-page: 55 year: 1995 end-page: 71 ident: bib28 article-title: A new approach to maximum likelihood estimation for stochastic differential equations based on discrete observations publication-title: Scand. J. Statist. – volume: 13 start-page: 838 year: 2006 end-page: 851 ident: bib19 article-title: Bayesian sequential inference for stochastic kinetic biochemical network models publication-title: J. Comput. Biol. – year: 2006 ident: bib21 article-title: Optimal filtering of jump diffusions: extracting latent states from asset prices – volume: 20 start-page: 279 year: 2002 end-page: 316 ident: bib12 article-title: Numerical techniques for maximum likelihood estimation of continuous-time diffusion processes publication-title: J. Bus. Econ. Statist. – volume: 11 start-page: 848 year: 2002 end-page: 862 ident: bib15 article-title: MCMC, sufficient statistics and particle filters publication-title: J. Graphical Statist. – volume: 53 start-page: 385 year: 1985 end-page: 407 ident: bib8 article-title: A theory of the term structure of interest rates publication-title: Econometrica – volume: 92 start-page: 1403 year: 1997 end-page: 1412 ident: bib2 article-title: Dynamic conditional independence models and Markov chain Monte Carlo methods publication-title: J. Amer. Statist. Assoc. – year: 1992 ident: bib30 article-title: A Genetic Switch: Phage – volume: 116 start-page: 1660 year: 2006 end-page: 1675 ident: bib10 article-title: Simulation of conditioned diffusion and application to parameter estimation publication-title: Stochastic Process. Appl. – reference: . – volume: 68 start-page: 1 year: 2006 end-page: 29 ident: bib3 article-title: Exact and computationally efficient likelihood-based estimation for discretely observed diffusion processes publication-title: J. Roy. Statist. Soc. Ser. B. Methodology – volume: 116 start-page: 1660 year: 2006 ident: 10.1016/j.csda.2007.05.019_bib10 article-title: Simulation of conditioned diffusion and application to parameter estimation publication-title: Stochastic Process. Appl. doi: 10.1016/j.spa.2006.04.004 – ident: 10.1016/j.csda.2007.05.019_bib34 – year: 2006 ident: 10.1016/j.csda.2007.05.019_bib21 – start-page: 307 year: 2003 ident: 10.1016/j.csda.2007.05.019_bib27 article-title: Non-centered parameterisations for hierarchical models and data augmentation – volume: 15 start-page: 65 year: 1999 ident: 10.1016/j.csda.2007.05.019_bib25 article-title: Its a noisy business: genetic regulation at the nanomolar scale publication-title: Trends. Genet. doi: 10.1016/S0168-9525(98)01659-X – year: 2002 ident: 10.1016/j.csda.2007.05.019_bib23 – year: 1992 ident: 10.1016/j.csda.2007.05.019_bib30 – volume: 446 start-page: 590 issue: 94 year: 1999 ident: 10.1016/j.csda.2007.05.019_bib29 article-title: Filtering via simulation: auxiliary particle filters publication-title: J. Amer. Statist. Assoc. doi: 10.2307/2670179 – volume: 11 start-page: 848 year: 2002 ident: 10.1016/j.csda.2007.05.019_bib15 article-title: MCMC, sufficient statistics and particle filters publication-title: J. Graphical Statist. doi: 10.1198/106186002835 – volume: 188 start-page: 404 year: 1992 ident: 10.1016/j.csda.2007.05.019_bib16 article-title: A rigorous derivation of the chemical master equation publication-title: Physica A doi: 10.1016/0378-4371(92)90283-V – volume: 16 start-page: 323 issue: 4 year: 2006 ident: 10.1016/j.csda.2007.05.019_bib18 article-title: Bayesian sequential inference for nonlinear multivariate diffusions publication-title: Statist. Comput. doi: 10.1007/s11222-006-9392-x – year: 2006 ident: 10.1016/j.csda.2007.05.019_bib22 – volume: 1995 start-page: 55 issue: 22 year: 1995 ident: 10.1016/j.csda.2007.05.019_bib28 article-title: A new approach to maximum likelihood estimation for stochastic differential equations based on discrete observations publication-title: Scand. J. Statist. – volume: 88 start-page: 603 issue: 4 year: 2001 ident: 10.1016/j.csda.2007.05.019_bib31 article-title: On inference for partially observed nonlinear diffusion models using the Metropolis–Hastings algorithm publication-title: Biometrika doi: 10.1093/biomet/88.3.603 – volume: 50 start-page: 281 issue: 2 year: 2002 ident: 10.1016/j.csda.2007.05.019_bib33 article-title: Particle filters for state-space models with the presence of unknown static parameters publication-title: IEEE. Trans. Signal. Process. doi: 10.1109/78.978383 – volume: 68 start-page: 1 year: 2006 ident: 10.1016/j.csda.2007.05.019_bib3 article-title: Exact and computationally efficient likelihood-based estimation for discretely observed diffusion processes publication-title: J. Roy. Statist. Soc. Ser. B. Methodology doi: 10.1111/j.1467-9868.2006.00552.x – volume: 69 start-page: 959 issue: 4 year: 2001 ident: 10.1016/j.csda.2007.05.019_bib13 article-title: Likelihood inference for discretely observed nonlinear diffusions publication-title: Econometrica doi: 10.1111/1468-0262.00226 – start-page: 323 year: 2003 ident: 10.1016/j.csda.2007.05.019_bib37 article-title: Discussion to ‘Non centred parameterisations for hierarchical models and data augmentation’ by Papaspiliopoulos, Roberts and Skold – volume: 84 start-page: 653 year: 1997 ident: 10.1016/j.csda.2007.05.019_bib32 article-title: Likelihood analysis of non-Gaussian measurement time series publication-title: Biometrika doi: 10.1093/biomet/84.3.653 – volume: 13 start-page: 838 issue: 3 year: 2006 ident: 10.1016/j.csda.2007.05.019_bib19 article-title: Bayesian sequential inference for stochastic kinetic biochemical network models publication-title: J. Comput. Biol. doi: 10.1089/cmb.2006.13.838 – start-page: 236 year: 2004 ident: 10.1016/j.csda.2007.05.019_bib35 article-title: Practical filtering for stochastic volatility models – year: 2006 ident: 10.1016/j.csda.2007.05.019_bib7 – volume: 10 start-page: 197 year: 2000 ident: 10.1016/j.csda.2007.05.019_bib11 article-title: On sequential Monte Carlo sampling methods for Bayesian filtering publication-title: Statistist. Comput. doi: 10.1023/A:1008935410038 – volume: 92 start-page: 1403 issue: 440 year: 1997 ident: 10.1016/j.csda.2007.05.019_bib2 article-title: Dynamic conditional independence models and Markov chain Monte Carlo methods publication-title: J. Amer. Statist. Assoc. doi: 10.2307/2965410 – volume: 1 start-page: 17 year: 1995 ident: 10.1016/j.csda.2007.05.019_bib4 article-title: Martingale estimating functions for discretely observed diffusion processes publication-title: Bernouilli doi: 10.2307/3318679 – ident: 10.1016/j.csda.2007.05.019_bib20 doi: 10.1049/ip-f-2.1993.0015 – year: 1995 ident: 10.1016/j.csda.2007.05.019_bib26 – volume: 82 start-page: 528 issue: 398 year: 1987 ident: 10.1016/j.csda.2007.05.019_bib36 article-title: The calculation of posterior distributions by data augmentation publication-title: J. Amer. Statist. Assoc. doi: 10.2307/2289457 – volume: 19 start-page: 177 year: 2001 ident: 10.1016/j.csda.2007.05.019_bib14 article-title: MCMC analysis of diffusion models with application to finance publication-title: J. Bus. Econ. Statist. doi: 10.1198/073500101316970403 – volume: 47 start-page: 1209 year: 1992 ident: 10.1016/j.csda.2007.05.019_bib6 article-title: An empirical comparison of alternative models of the short-term interest publication-title: J. Finance doi: 10.2307/2328983 – volume: 81 start-page: 637 year: 1973 ident: 10.1016/j.csda.2007.05.019_bib5 article-title: The pricing of options and corporate liabilities publication-title: J. Polit. Econ. doi: 10.1086/260062 – volume: 149 start-page: 633 year: 1998 ident: 10.1016/j.csda.2007.05.019_bib1 article-title: Stochastic kinetic analysis of developmental pathway bifurcation in phage lambda-infected Escherichia coli cells publication-title: Genetics doi: 10.1093/genetics/149.4.1633 – year: 2006 ident: 10.1016/j.csda.2007.05.019_bib38 – volume: 120 start-page: 346 year: 2002 ident: 10.1016/j.csda.2007.05.019_bib9 article-title: The Monte Carlo method for filtering with discrete-time observations publication-title: Probab. Theory Related Fields doi: 10.1007/PL00008786 – volume: 53 start-page: 385 year: 1985 ident: 10.1016/j.csda.2007.05.019_bib8 article-title: A theory of the term structure of interest rates publication-title: Econometrica doi: 10.2307/1911242 – year: 2001 ident: 10.1016/j.csda.2007.05.019_bib24 article-title: Combined parameter and state estimation in simulation-based filtering – volume: 61 start-page: 781 issue: 3 year: 2005 ident: 10.1016/j.csda.2007.05.019_bib17 article-title: Bayesian inference for stochastic kinetic models using a diffusion approximation publication-title: Biometrics doi: 10.1111/j.1541-0420.2005.00345.x – volume: 20 start-page: 279 year: 2002 ident: 10.1016/j.csda.2007.05.019_bib12 article-title: Numerical techniques for maximum likelihood estimation of continuous-time diffusion processes publication-title: J. Bus. Econ. Statist. doi: 10.1198/073500102288618397 |
| SSID | ssj0002478 |
| Score | 2.2983508 |
| Snippet | Diffusion processes governed by stochastic differential equations (SDEs) are a well-established tool for modelling continuous time data from a wide range of... |
| SourceID | proquest repec pascalfrancis crossref elsevier |
| SourceType | Aggregation Database Index Database Enrichment Source Publisher |
| StartPage | 1674 |
| SubjectTerms | Bayesian inference Exact sciences and technology General topics Innovation scheme Mathematics MCMC Multivariate analysis Nonlinear stochastic differential equation Numerical analysis Numerical analysis. Scientific computation Numerical methods in probability and statistics Parametric inference Particle filter Probability and statistics Reparameterisation Sciences and techniques of general use Statistics |
| Title | Bayesian inference for nonlinear multivariate diffusion models observed with error |
| URI | https://dx.doi.org/10.1016/j.csda.2007.05.019 http://econpapers.repec.org/article/eeecsdana/v_3a52_3ay_3a2008_3ai_3a3_3ap_3a1674-1693.htm https://www.proquest.com/docview/20243513 |
| Volume | 52 |
| WOSCitedRecordID | wos000253669700031&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVESC databaseName: Elsevier SD Freedom Collection Journals 2021 customDbUrl: eissn: 1872-7352 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0002478 issn: 0167-9473 databaseCode: AIEXJ dateStart: 19950101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV3Lb9MwGLeg5bAJIRggymP4wK3K1Dp2kxwHFDY0NgRFKifLdhyxiaVR0lbbf8_n-LF0ggEHDo6qKG6i_H7298j3QOgVmBxUg10QAeCTiALoUSZYEcV5DtqCTEaaibbZRHJ8nM7n2ScXVtS07QSSskwvLrLqv0IN5wBskzr7D3CHP4UT8BtAhyPADse_Av61uNRtZuSpz-VrQwlLWxND1DaGcA02MqiZbYOUlfGY2Z44zXAhjZ_WB6Xrul7UXQXWdoHwHkSTjuQqPRsKmXDToXBlTkJkz8nR4fuD2dG3Dc-pcxyctFEGb_fc1ynvfkivvGE-I8ZtQl0nJWy-GbUtSvwuy0iHTXFnyzRpEB3xa4rD_HJrt16Gsz3V5MKVnjQVV7MrQeY_3l-TbyHq0ISPgXmU3EZ9koAh1UP9_cPp_EOQ3IRaye2f3yVZ2XjA6_f9nSJztxINLK_C9kXZMFz6ta606ugvs_vonjM88L4lzAN0S5c7aPtjqNrb7KCtLwHOh-iz5xEOPMLAIxx4hLs8woFH2PIIex5hwyPc8ugR-vpuOntzELkGHJGiCV1GNE_TnJgC_CNQYrQUIJEmUqkUFCs61pQUJJWTUaqKyVgQGYuCMCXjFIxQqiQIi8eoB0-lnyBMJJi-Y5lLUuQ0YUQypqimSZZpU0OSDdDYv02uXHV60yTlB_dhiGfcIGDapiZ8xDggMEDDMKeytVluvJp5kLjTLq3WyIFhN87b3UA03MrTaYBeeog57M3mg5so9WLVwBUErJFxPEDTFvkwVWttblMKvuaxYAQOlzDalrCxOIURw6hgmNXBzZrg35fnT__0KM_Qlo1nMi7C56i3rFf6Bbqj1kCeetfR_SfxQ8cp |
| linkProvider | Elsevier |
| 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=Bayesian+inference+for+nonlinear+multivariate+diffusion+models+observed+with+error&rft.jtitle=Computational+statistics+%26+data+analysis&rft.au=GOLIGHTLY%2C+A&rft.au=WILKINSON%2C+D.+J&rft.date=2008&rft.pub=Elsevier+Science&rft.issn=0167-9473&rft.volume=52&rft.issue=3&rft.spage=1674&rft.epage=1693&rft_id=info:doi/10.1016%2Fj.csda.2007.05.019&rft.externalDBID=n%2Fa&rft.externalDocID=20017587 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0167-9473&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0167-9473&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0167-9473&client=summon |