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We study convergence properties of pseudo-marginal Markov chain Monte Carlo algorithms (Andrieu and Roberts [Ann.
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Jarner, Søren F.S. F. andRoberts, Gareth O.G. O. (2002). Polynomial convergence rates of Markov chains. Ann. Appl. Probab. 12 224–247
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Douc, RandalR., Fort, GersendeG., Moulines, EricE. andSoulier, PhilippeP. (2004). Practical drift conditions for subgeometric rates of convergence. Ann. Appl. Probab. 14 1353–1377
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Andrieu, ChristopheC. andFort, GersendeG. (2005). Explicit control of subgeometric ergodicity. Research Report No. 05:17, Univ. Bristol
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Andrieu, ChristopheC., Doucet, ArnaudA. andHolenstein, RomanR. (2010). Particle Markov chain Monte Carlo methods. J. R. Stat. Soc. Ser. B Stat. Methodol. 72 269–342
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Saksman, EeroE. andVihola, MattiM. (2010). On the ergodicity of the adaptive Metropolis algorithm on unbounded domains. Ann. Appl. Probab. 20 2178–2203
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Lee, AnthonyA., Andrieu, ChristopheC. andDoucet, ArnaudA. (2012). Discussion of “Constructing summary statistics for approximate Bayesian computation: semi-automatic approximate Bayesian computation” by Fearnhead and Prangle. J. R. Stat. Soc. Ser. B Stat. Methodol. 74 449–450
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2012
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Beskos, AlexandrosA., Papaspiliopoulos, OmirosO., Roberts, Gareth O.G. O. andFearnhead, PaulP. (2006). Exact and computationally efficient likelihood-based estimation for discretely observed diffusion processes. J. R. Stat. Soc. Ser. B Stat. Methodol. 68 333–382
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Gåsemyr, JørundJ. (2006). The spectrum of the independent Metropolis–Hastings algorithm. J. Theoret. Probab. 19 152–165
2006
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Douc, RandalR., Moulines, EricE. andSoulier, PhilippeP. (2007). Computable convergence rates for sub-geometric ergodic Markov chains. Bernoulli 13 831–848
2007
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Roberts, Gareth O.G. O. andRosenthal, Jeffrey S.J. S. (2008). Variance bounding Markov chains. Ann. Appl. Probab. 18 1201–1214
2008
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Andrieu, ChristopheC. andRoberts, Gareth O.G. O. (2009). The pseudo-marginal approach for efficient Monte Carlo computations. Ann. Statist. 37 697–725
2009
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Meyn, SeanS. andTweedie, Richard L.R. L. (2009). Markov Chains and Stochastic Stability, 2nd ed. Cambridge Univ. Press, Cambridge
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2012
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Karagiannis, GeorgiosG. andAndrieu, ChristopheC. (2013). Annealed importance sampling reversible jump MCMC algorithms. J. Comput. Graph. Statist. 22 623–648
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Andrieu, ChristopheC. andVihola, MattiM. (2014). Markovian stochastic approximation with expanding projections. Bernoulli 20 545–585
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Łatuszyński, KrzysztofK., Miasojedow, BłażejB. andNiemiro, WojciechW. (2013). Nonasymptotic bounds on the estimation error of MCMC algorithms. Bernoulli 19 2033–2066
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