Roberts, Gareth O.; Rosenthal, Jeffrey S. Polynomial convergence rates of piecewise deterministic Markov processes. (English) Zbl 1519.60068 Methodol. Comput. Appl. Probab. 25, No. 1, Paper No. 6, 18 p. (2023). Reviewer: Ze-Chun Hu (Chengdu) MSC: 60J25 60J22 PDFBibTeX XMLCite \textit{G. O. Roberts} and \textit{J. S. Rosenthal}, Methodol. Comput. Appl. Probab. 25, No. 1, Paper No. 6, 18 p. (2023; Zbl 1519.60068) Full Text: DOI
Zhou, Quan; Yang, Jun; Vats, Dootika; Roberts, Gareth O.; Rosenthal, Jeffrey S. Dimension-free mixing for high-dimensional Bayesian variable selection. (English) Zbl 07686598 J. R. Stat. Soc., Ser. B, Stat. Methodol. 84, No. 5, 1751-1784 (2022). MSC: 62-XX PDFBibTeX XMLCite \textit{Q. Zhou} et al., J. R. Stat. Soc., Ser. B, Stat. Methodol. 84, No. 5, 1751--1784 (2022; Zbl 07686598) Full Text: DOI arXiv
Roberts, Gareth O.; Rosenthal, Jeffrey S.; Tawn, Nicholas G. Skew Brownian motion and complexity of the ALPS algorithm. (English) Zbl 1497.60101 J. Appl. Probab. 59, No. 3, 777-796 (2022). MSC: 60J25 60J05 60J22 60J65 PDFBibTeX XMLCite \textit{G. O. Roberts} et al., J. Appl. Probab. 59, No. 3, 777--796 (2022; Zbl 1497.60101) Full Text: DOI arXiv
Yang, Jun; Roberts, Gareth O.; Rosenthal, Jeffrey S. Optimal scaling of random-walk Metropolis algorithms on general target distributions. (English) Zbl 1455.60100 Stochastic Processes Appl. 130, No. 10, 6094-6132 (2020). MSC: 60J22 65C05 PDFBibTeX XMLCite \textit{J. Yang} et al., Stochastic Processes Appl. 130, No. 10, 6094--6132 (2020; Zbl 1455.60100) Full Text: DOI arXiv
Tawn, Nicholas G.; Roberts, Gareth O.; Rosenthal, Jeffrey S. Weight-preserving simulated tempering. (English) Zbl 1431.60082 Stat. Comput. 30, No. 1, 27-41 (2020). MSC: 60J22 62M05 65C05 PDFBibTeX XMLCite \textit{N. G. Tawn} et al., Stat. Comput. 30, No. 1, 27--41 (2020; Zbl 1431.60082) Full Text: DOI arXiv
Roberts, Gareth O.; Rosenthal, Jeffrey S. Hitting time and convergence rate bounds for symmetric Langevin diffusions. (English) Zbl 1428.60123 Methodol. Comput. Appl. Probab. 21, No. 3, 921-929 (2019). MSC: 60J70 60J60 60J25 PDFBibTeX XMLCite \textit{G. O. Roberts} and \textit{J. S. Rosenthal}, Methodol. Comput. Appl. Probab. 21, No. 3, 921--929 (2019; Zbl 1428.60123) Full Text: DOI arXiv
Ernst, Philip A.; Kendall, Wilfrid S.; Roberts, Gareth O.; Rosenthal, Jeffrey S. MEXIT: maximal un-coupling times for stochastic processes. (English) Zbl 1403.60062 Stochastic Processes Appl. 129, No. 2, 355-380 (2019). MSC: 60J10 60K35 PDFBibTeX XMLCite \textit{P. A. Ernst} et al., Stochastic Processes Appl. 129, No. 2, 355--380 (2019; Zbl 1403.60062) Full Text: DOI arXiv
Roberts, Gareth O.; Rosenthal, Jeffrey S. Complexity bounds for Markov chain Monte Carlo algorithms via diffusion limits. (English) Zbl 1345.60082 J. Appl. Probab. 53, No. 2, 410-420 (2016). MSC: 60J22 60J10 60J05 60J60 60F05 60G50 60J25 65C05 65C40 62F10 62F15 PDFBibTeX XMLCite \textit{G. O. Roberts} and \textit{J. S. Rosenthal}, J. Appl. Probab. 53, No. 2, 410--420 (2016; Zbl 1345.60082) Full Text: DOI arXiv Euclid Link
Craiu, Radu V.; Gray, Lawrence; Łatuszyński, Krzysztof; Madras, Neal; Roberts, Gareth O.; Rosenthal, Jeffrey S. Stability of adversarial Markov chains, with an application to adaptive MCMC algorithms. (English) Zbl 1328.60169 Ann. Appl. Probab. 25, No. 6, 3592-3623 (2015). MSC: 60J05 60J22 62F10 62F15 65C40 65C05 PDFBibTeX XMLCite \textit{R. V. Craiu} et al., Ann. Appl. Probab. 25, No. 6, 3592--3623 (2015; Zbl 1328.60169) Full Text: DOI arXiv Euclid
Sherlock, Chris; Thiery, Alexandre H.; Roberts, Gareth O.; Rosenthal, Jeffrey S. On the efficiency of pseudo-marginal random walk Metropolis algorithms. (English) Zbl 1326.65015 Ann. Stat. 43, No. 1, 238-275 (2015). Reviewer: Vassil Grozdanov (Blagoevgrad) MSC: 65C05 65C40 60F05 60J05 60J10 60J22 60G50 PDFBibTeX XMLCite \textit{C. Sherlock} et al., Ann. Stat. 43, No. 1, 238--275 (2015; Zbl 1326.65015) Full Text: DOI arXiv Euclid
Jones, Galin L.; Roberts, Gareth O.; Rosenthal, Jeffrey S. Convergence of conditional Metropolis-Hastings samplers. (English) Zbl 1379.60082 Adv. Appl. Probab. 46, No. 2, 422-445 (2014). MSC: 60J22 60J05 65C05 62F15 PDFBibTeX XMLCite \textit{G. L. Jones} et al., Adv. Appl. Probab. 46, No. 2, 422--445 (2014; Zbl 1379.60082) Full Text: DOI Euclid
Roberts, Gareth O.; Rosenthal, Jeffrey S. Minimising MCMC variance via diffusion limits, with an application to simulated tempering. (English) Zbl 1298.60078 Ann. Appl. Probab. 24, No. 1, 131-149 (2014). Reviewer: Alex V. Kolnogorov (Novgorod) MSC: 60J22 65C40 62M05 62F10 PDFBibTeX XMLCite \textit{G. O. Roberts} and \textit{J. S. Rosenthal}, Ann. Appl. Probab. 24, No. 1, 131--149 (2014; Zbl 1298.60078) Full Text: DOI arXiv Euclid
Roberts, Gareth O.; Rosenthal, Jeffrey S. A note on formal constructions of sequential conditional couplings. (English) Zbl 1285.60077 Stat. Probab. Lett. 83, No. 9, 2073-2076 (2013). MSC: 60J22 PDFBibTeX XMLCite \textit{G. O. Roberts} and \textit{J. S. Rosenthal}, Stat. Probab. Lett. 83, No. 9, 2073--2076 (2013; Zbl 1285.60077) Full Text: DOI
Łatuszyński, Krzysztof; Roberts, Gareth O.; Rosenthal, Jeffrey S. Adaptive Gibbs samplers and related MCMC methods. (English) Zbl 1263.60067 Ann. Appl. Probab. 23, No. 1, 66-98 (2013). MSC: 60J22 60J05 65C05 62F15 PDFBibTeX XMLCite \textit{K. Łatuszyński} et al., Ann. Appl. Probab. 23, No. 1, 66--98 (2013; Zbl 1263.60067) Full Text: DOI arXiv Euclid
Atchadé, Yves F.; Roberts, Gareth O.; Rosenthal, Jeffrey S. Towards optimal scaling of Metropolis-coupled Markov chain Monte Carlo. (English) Zbl 1223.65001 Stat. Comput. 21, No. 4, 555-568 (2011). MSC: 65C05 65C40 60J22 60G50 PDFBibTeX XMLCite \textit{Y. F. Atchadé} et al., Stat. Comput. 21, No. 4, 555--568 (2011; Zbl 1223.65001) Full Text: DOI
Bai, Yan; Roberts, Gareth O.; Rosenthal, Jeffrey S. On the containment condition for adaptive Markov chain Monte Carlo algorithms. (English) Zbl 1225.60130 Adv. Appl. Stat. 21, No. 1, 1-54 (2011). Reviewer: Martin Riedler (Linz) MSC: 60J22 60J05 65C40 65C05 PDFBibTeX XMLCite \textit{Y. Bai} et al., Adv. Appl. Stat. 21, No. 1, 1--54 (2011; Zbl 1225.60130) Full Text: Link
Roberts, Gareth O.; Rosenthal, Jeffrey S. Quantitative non-geometric convergence bounds for independence samplers. (English) Zbl 1222.60054 Methodol. Comput. Appl. Probab. 13, No. 2, 391-403 (2011). Reviewer: Martin Riedler (Linz) MSC: 60J22 60J05 65C40 68W20 PDFBibTeX XMLCite \textit{G. O. Roberts} and \textit{J. S. Rosenthal}, Methodol. Comput. Appl. Probab. 13, No. 2, 391--403 (2011; Zbl 1222.60054) Full Text: DOI Link
Roberts, Gareth O.; Rosenthal, Jeffrey S.; Segers, Johan; Sousa, Bruno Erratum to: Extremal indices, geometric ergodicity of Markov chains, and MCMC. (English) Zbl 1226.65006 Extremes 13, No. 3, 373-374 (2010). MSC: 65C40 60G70 60J22 65C05 PDFBibTeX XMLCite \textit{G. O. Roberts} et al., Extremes 13, No. 3, 373--374 (2010; Zbl 1226.65006) Full Text: DOI
Roberts, Gareth O.; Rosenthal, Jeffrey S. Variance bounding Markov chains. (English) Zbl 1142.60047 Ann. Appl. Probab. 18, No. 3, 1201-1214 (2008). MSC: 60J10 65C40 47A10 60J22 PDFBibTeX XMLCite \textit{G. O. Roberts} and \textit{J. S. Rosenthal}, Ann. Appl. Probab. 18, No. 3, 1201--1214 (2008; Zbl 1142.60047) Full Text: DOI arXiv
Roberts, Gareth O.; Rosenthal, Jeffrey S. Coupling and ergodicity of adaptive Markov chain Monte Carlo algorithms. (English) Zbl 1137.62015 J. Appl. Probab. 44, No. 2, 458-475 (2007). Reviewer: Gheorghe Oprişan (Bucureşti) MSC: 62F15 65C40 65C05 60J10 PDFBibTeX XMLCite \textit{G. O. Roberts} and \textit{J. S. Rosenthal}, J. Appl. Probab. 44, No. 2, 458--475 (2007; Zbl 1137.62015) Full Text: DOI
Roberts, Gareth O.; Rosenthal, Jeffrey S.; Segers, Johan; Sousa, Bruno Extremal indices, geometric ergodicity of Markov chains and MCMC. (English) Zbl 1142.65011 Extremes 9, No. 3-4, 213-229 (2006); erratum ibid. 13, No. 3, 373-374 (2010). Reviewer: R. E. Maiboroda (Kyïv) MSC: 65C40 60G70 60J22 65C05 PDFBibTeX XMLCite \textit{G. O. Roberts} et al., Extremes 9, No. 3--4, 213--229 (2006; Zbl 1142.65011) Full Text: DOI
Roberts, Gareth O.; Rosenthal, Jeffrey S. Harris recurrence of Metropolis-within-Gibbs and trans-dimensional Markov chains. (English) Zbl 1121.60076 Ann. Appl. Probab. 16, No. 4, 2123-2139 (2006). MSC: 60J05 65C05 60J22 62F15 PDFBibTeX XMLCite \textit{G. O. Roberts} and \textit{J. S. Rosenthal}, Ann. Appl. Probab. 16, No. 4, 2123--2139 (2006; Zbl 1121.60076) Full Text: DOI arXiv
Christensen, Ole F.; Roberts, Gareth O.; Rosenthal, Jeffrey S. Scaling limits for the transient phase of local Metropolis-Hastings algorithms. (English) Zbl 1075.65012 J. R. Stat. Soc., Ser. B, Stat. Methodol. 67, No. 2, 253-268 (2005). MSC: 65C40 65C05 60J22 62D05 PDFBibTeX XMLCite \textit{O. F. Christensen} et al., J. R. Stat. Soc., Ser. B, Stat. Methodol. 67, No. 2, 253--268 (2005; Zbl 1075.65012) Full Text: DOI
Roberts, Gareth O.; Rosenthal, Jeffrey S. General state space Markov chains and MCMC algorithms. (English) Zbl 1189.60131 Probab. Surv. 1, 20-71 (2004). MSC: 60J05 62F10 65C05 60-02 PDFBibTeX XMLCite \textit{G. O. Roberts} and \textit{J. S. Rosenthal}, Probab. Surv. 1, 20--71 (2004; Zbl 1189.60131) Full Text: DOI arXiv EuDML
Roberts, Gareth O.; Rosenthal, Jeffrey S. Combinatorial identities associated with CFTP. (English) Zbl 1092.60028 Far East J. Math. Sci. (FJMS) 13, No. 3, 391-404 (2004). MSC: 60J10 05A19 PDFBibTeX XMLCite \textit{G. O. Roberts} and \textit{J. S. Rosenthal}, Far East J. Math. Sci. (FJMS) 13, No. 3, 391--404 (2004; Zbl 1092.60028)
Roberts, Gareth O.; Rosenthal, Jeffrey S. Downweighting tightly knit communities in World Wide Web rankings. (English) Zbl 1089.68667 Adv. Appl. Stat. 3, No. 3, 199-216 (2003). MSC: 68W20 68U35 62C12 PDFBibTeX XMLCite \textit{G. O. Roberts} and \textit{J. S. Rosenthal}, Adv. Appl. Stat. 3, No. 3, 199--216 (2003; Zbl 1089.68667)
Fort, G.; Moulines, E.; Roberts, G. O.; Rosenthal, J. S. On the geometric ergodicity of hybrid samplers. (English) Zbl 1028.65002 J. Appl. Probab. 40, No. 1, 123-146 (2003). Reviewer: Silvia Curteanu (Iaşi) MSC: 65C05 60J10 65C40 PDFBibTeX XMLCite \textit{G. Fort} et al., J. Appl. Probab. 40, No. 1, 123--146 (2003; Zbl 1028.65002) Full Text: DOI Link
Roberts, Gareth O.; Rosenthal, Jeffrey S. One-shot coupling for certain stochastic recursive sequences. (English) Zbl 1058.60058 Stochastic Processes Appl. 99, No. 2, 195-208 (2002). MSC: 60J05 65C40 60J22 PDFBibTeX XMLCite \textit{G. O. Roberts} and \textit{J. S. Rosenthal}, Stochastic Processes Appl. 99, No. 2, 195--208 (2002; Zbl 1058.60058) Full Text: DOI
Roberts, Gareth O.; Rosenthal, Jeffrey S. The polar slice sampler. (English) Zbl 1006.65004 Stoch. Models 18, No. 2, 257-280 (2002). Reviewer: Jaromir Antoch (Praha) MSC: 65C40 PDFBibTeX XMLCite \textit{G. O. Roberts} and \textit{J. S. Rosenthal}, Stoch. Models 18, No. 2, 257--280 (2002; Zbl 1006.65004) Full Text: DOI
Roberts, Gareth O.; Rosenthal, Jeffrey S. Optimal scaling for various Metropolis-Hastings algorithms. (English) Zbl 1127.65305 Stat. Sci. 16, No. 4, 351-367 (2001). MSC: 65C05 60J05 PDFBibTeX XMLCite \textit{G. O. Roberts} and \textit{J. S. Rosenthal}, Stat. Sci. 16, No. 4, 351--367 (2001; Zbl 1127.65305) Full Text: DOI
Roberts, Gareth O.; Rosenthal, Jeffrey S. Markov chains and de-initializing processes. (English) Zbl 0985.60067 Scand. J. Stat. 28, No. 3, 489-501 (2001). Reviewer: R.E.Maiboroda (Kyïv) MSC: 60J05 60F05 PDFBibTeX XMLCite \textit{G. O. Roberts} and \textit{J. S. Rosenthal}, Scand. J. Stat. 28, No. 3, 489--501 (2001; Zbl 0985.60067) Full Text: DOI
Breyer, Laird; Roberts, Gareth O.; Rosenthal, Jeffrey S. A note on geometric ergodicity and floating-point roundoff error. (English) Zbl 0991.60064 Stat. Probab. Lett. 53, No. 2, 123-127 (2001). MSC: 60J27 65C50 PDFBibTeX XMLCite \textit{L. Breyer} et al., Stat. Probab. Lett. 53, No. 2, 123--127 (2001; Zbl 0991.60064) Full Text: DOI
Roberts, Gareth O.; Rosenthal, Jeffrey S. Infinite hierarchies and prior distributions. (English) Zbl 1006.62017 Bernoulli 7, No. 3, 453-471 (2001). MSC: 62F15 62A01 PDFBibTeX XMLCite \textit{G. O. Roberts} and \textit{J. S. Rosenthal}, Bernoulli 7, No. 3, 453--471 (2001; Zbl 1006.62017) Full Text: DOI Link
Roberts, Gareth O.; Rosenthal, Jeffrey S. Small and pseudo-small sets for Markov chains. (English) Zbl 0981.60068 Stoch. Models 17, No. 2, 121-145 (2001). MSC: 60J27 PDFBibTeX XMLCite \textit{G. O. Roberts} and \textit{J. S. Rosenthal}, Stoch. Models 17, No. 2, 121--145 (2001; Zbl 0981.60068) Full Text: DOI
Roberts, Gareth O.; Rosenthal, Jeffrey S. Recent progress on computable bounds and the simple slice sampler. (English) Zbl 0966.65007 Madras, Neal (ed.), Monte Carlo methods. Proceedings of the workshop, Toronto, Ontario, Canada, October 25-29, 1998. Providence, RI: AMS, American Mathematical Society. Fields Inst. Commun. 26, 123-130 (2000). MSC: 65C40 65C05 60J22 PDFBibTeX XMLCite \textit{G. O. Roberts} and \textit{J. S. Rosenthal}, Fields Inst. Commun. 26, 123--130 (2000; Zbl 0966.65007)
Cowles, Mary Kathryn; Roberts, Gareth O.; Rosenthal, Jeffrey S. Possible biases induced by MCMC convergence diagnostics. (English) Zbl 1156.62315 J. Stat. Comput. Simulation 64, No. 1, 87-104 (1999). MSC: 62F15 65C60 PDFBibTeX XMLCite \textit{M. K. Cowles} et al., J. Stat. Comput. Simulation 64, No. 1, 87--104 (1999; Zbl 1156.62315) Full Text: DOI
Roberts, Gareth O.; Rosenthal, Jeffrey S. Convergence of slice sampler Markov chains. (English) Zbl 0929.62098 J. R. Stat. Soc., Ser. B, Stat. Methodol. 61, No. 3, 643-660 (1999). MSC: 62M99 65C60 65C40 PDFBibTeX XMLCite \textit{G. O. Roberts} and \textit{J. S. Rosenthal}, J. R. Stat. Soc., Ser. B, Stat. Methodol. 61, No. 3, 643--660 (1999; Zbl 0929.62098) Full Text: DOI
Roberts, Gareth O.; Rosenthal, Jeffrey S. Two convergence properties of hybrid samplers. (English) Zbl 0938.60055 Ann. Appl. Probab. 8, No. 2, 397-407 (1998). Reviewer: G.G.Vrănceanu (Bucureşti) MSC: 60J05 62F99 62M05 PDFBibTeX XMLCite \textit{G. O. Roberts} and \textit{J. S. Rosenthal}, Ann. Appl. Probab. 8, No. 2, 397--407 (1998; Zbl 0938.60055) Full Text: DOI
Roberts, Gareth O.; Rosenthal, Jeffrey S. On convergence rates of Gibbs samplers for uniform distributions. (English) Zbl 0935.60054 Ann. Appl. Probab. 8, No. 4, 1291-1302 (1998). Reviewer: Joseph Melamed (Los Angeles) MSC: 60J05 62M05 PDFBibTeX XMLCite \textit{G. O. Roberts} and \textit{J. S. Rosenthal}, Ann. Appl. Probab. 8, No. 4, 1291--1302 (1998; Zbl 0935.60054) Full Text: DOI
Roberts, Gareth O.; Rosenthal, Jeffrey S. Optimal scaling of discrete approximations to Langevin diffusions. (English) Zbl 0913.60060 J. R. Stat. Soc., Ser. B, Stat. Methodol. 60, No. 1, 255-268 (1998). MSC: 60J20 65C05 PDFBibTeX XMLCite \textit{G. O. Roberts} and \textit{J. S. Rosenthal}, J. R. Stat. Soc., Ser. B, Stat. Methodol. 60, No. 1, 255--268 (1998; Zbl 0913.60060) Full Text: DOI Link
Roberts, Gareth O.; Rosenthal, Jeffrey S. Markov-chain Monte Carlo: Some practical implications of theoretical results (With discussions and rejoinder). (English) Zbl 0920.62105 Can. J. Stat. 26, No. 1, 5-31 (1998). Reviewer: W.Schlee (München) MSC: 62M05 60J05 65C05 65C20 PDFBibTeX XMLCite \textit{G. O. Roberts} and \textit{J. S. Rosenthal}, Can. J. Stat. 26, No. 1, 5--31 (1998; Zbl 0920.62105) Full Text: DOI
Roberts, Gareth O.; Rosenthal, Jeffrey S.; Schwartz, Peter O. Convergence properties of perturbed Markov chains. (English) Zbl 0909.60049 J. Appl. Probab. 35, No. 1, 1-11 (1998). Reviewer: E.Kazarovitsky (Kyïv) MSC: 60J05 62F99 62M05 PDFBibTeX XMLCite \textit{G. O. Roberts} et al., J. Appl. Probab. 35, No. 1, 1--11 (1998; Zbl 0909.60049) Full Text: DOI Link
Roberts, Gareth O.; Rosenthal, Jeffrey S. Geometric ergodicity and hybrid Markov chains. (English) Zbl 0890.60061 Electron. Commun. Probab. 2, 13-25 (1997). MSC: 60J10 60J35 PDFBibTeX XMLCite \textit{G. O. Roberts} and \textit{J. S. Rosenthal}, Electron. Commun. Probab. 2, 13--25 (1997; Zbl 0890.60061) Full Text: DOI EuDML EMIS
Roberts, Gareth O.; Rosenthal, Jeffrey S. Shift-coupling and convergence rates of ergodic averages. (English) Zbl 0871.60046 Commun. Stat., Stochastic Models 13, No. 1, 147-165 (1997). MSC: 60J10 60F05 PDFBibTeX XMLCite \textit{G. O. Roberts} and \textit{J. S. Rosenthal}, Commun. Stat., Stochastic Models 13, No. 1, 147--165 (1997; Zbl 0871.60046) Full Text: DOI
Roberts, Gareth O.; Rosenthal, Jeffrey S. Quantitative bounds for convergence rates of continuous time Markov processes. (English) Zbl 0891.60068 Electron. J. Probab. 1, No. 9, 1-21 (1996). MSC: 60J25 PDFBibTeX XMLCite \textit{G. O. Roberts} and \textit{J. S. Rosenthal}, Electron. J. Probab. 1, No. 9, 1--21 (1996; Zbl 0891.60068) Full Text: DOI EuDML EMIS