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Practical bounds on the error of Bayesian posterior approximations: A nonasymptotic approach [article]

Jonathan H. Huggins, Trevor Campbell, Mikołaj Kasprzak, Tamara Broderick
<span title="2018-10-01">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We demonstrate the usefulness of our Fisher distance approach by deriving bounds on the Wasserstein error of the Laplace approximation and Hilbert coresets.  ...  In this work, we develop a flexible new approach to bounding the error of mean and uncertainty estimates of scalable inference algorithms.  ...  A natural approach is to start by bounding a statistical divergence between the exact and approximate posterior distributions, then use this bound to in turn bound the error in approximate posterior functionals  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1809.09505v2">arXiv:1809.09505v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/75egtih6ezb4zpmr4eeic2trum">fatcat:75egtih6ezb4zpmr4eeic2trum</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20191021191648/https://arxiv.org/pdf/1809.09505v2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/17/9e/179efe0e5945a553bbbf66499b05c7e2783580e5.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1809.09505v2" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Error bounds for some approximate posterior measures in Bayesian inference [article]

Han Cheng Lie, T. J. Sullivan, Aretha Teckentrup
<span title="2020-04-22">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In certain applications involving the solution of a Bayesian inverse problem, it may not be possible or desirable to evaluate the full posterior, e.g. due to the high computational cost of doing so.  ...  We review some error bounds for random and deterministic approximate posteriors that arise when the approximate data misfits and approximate forward models are random.  ...  The work of TJS has been partially supported by the Freie Universität Berlin within the Excellence Initiative of the German Research Foundation (DFG).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1911.05669v2">arXiv:1911.05669v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2who56vjprgntkfueuqywpctm4">fatcat:2who56vjprgntkfueuqywpctm4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200502182435/https://arxiv.org/pdf/1911.05669v2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1911.05669v2" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Nonasymptotic Gaussian Approximation for Inference with Stable Noise [article]

Marina Riabiz, Tohid Ardeshiri, Ioannis Kontoyiannis, Simon Godsill
<span title="2020-01-01">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In addition to the asymptotic normality of the tail of this series, we establish explicit, nonasymptotic bounds on the approximation error.  ...  A major component of our approach is the approximation of the tail of this series by a Gaussian random variable.  ...  This method also produces an approximate upper bound on the absolute error |Ī(Z (c,∞) , Z) − Q(Z (c,∞) , Z)|, which can be used to construct approximate error bands.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1802.10065v4">arXiv:1802.10065v4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/tuxl3q5sgneedk2pxwv7eag2qu">fatcat:tuxl3q5sgneedk2pxwv7eag2qu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200823201702/https://arxiv.org/pdf/1802.10065v4.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/45/d8/45d8a9c2dc1b927f07e03440febece205d9ac7e2.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1802.10065v4" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Theoretical guarantees for approximate sampling from smooth and log-concave densities [article]

Arnak S. Dalalyan
<span title="2016-12-03">2016</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We establish nonasymptotic bounds for the error of approximating the target distribution by the one obtained by the Langevin Monte Carlo method and its variants.  ...  In many situations, the exact sampling from a given distribution is impossible or computationally expensive and, therefore, one needs to resort to approximate sampling strategies.  ...  Acknowledgments The work of the author was partially supported by the grant Investissements d'Avenir (ANR-11-IDEX-0003/Labex Ecodec/ANR-11-LABX-0047).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1412.7392v6">arXiv:1412.7392v6</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4lu5gmzhtzds3cbbuqrpkryaam">fatcat:4lu5gmzhtzds3cbbuqrpkryaam</a> </span>
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Theoretical guarantees for approximate sampling from smooth and log-concave densities

Arnak S. Dalalyan
<span title="2016-04-23">2016</span> <i title="Wiley"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/gylnzjdvwjfivc5jachjxgaqoi" style="color: black;">Journal of The Royal Statistical Society Series B-statistical Methodology</a> </i> &nbsp;
We establish nonasymptotic bounds for the error of approximating the true distribution by the one obtained by the Langevin Monte Carlo method and its variants.  ...  In many situations, the exact sampling from a given distribution is impossible or computationally expensive and, therefore, one needs to resort to approximate sampling strategies.  ...  Acknowledgments The work of the author was partially supported by the grant Investissements d'Avenir (ANR-11-IDEX-0003/Labex Ecodec/ANR-11-LABX-0047).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1111/rssb.12183">doi:10.1111/rssb.12183</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/fo4xz6irzjbrbn3sepb7vcf66q">fatcat:fo4xz6irzjbrbn3sepb7vcf66q</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190428204023/http://crest.science/RePEc/wpstorage/2014-45.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/36/b0/36b026411a9bcd550c3e1ae594d2906950aa710a.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1111/rssb.12183"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Probably approximate Bayesian computation: nonasymptotic convergence of ABC under misspecification [article]

James Ridgway
<span title="2019-01-01">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Approximate Bayesian computation (ABC) is a widely used inference method in Bayesian statistics to bypass the point-wise computation of the likelihood.  ...  The bounds are given in the form of oracle inequalities for a finite sample size. The dependence on the dimension of the parameter space and the number of statistics is made explicit.  ...  Acknowledgments I would like to warmly thank Pierre Alquier and Nicolas Chopin for the helpful discussions and comments.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1707.05987v2">arXiv:1707.05987v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ccpci5ufo5hfhlpzaoozhz2e2m">fatcat:ccpci5ufo5hfhlpzaoozhz2e2m</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200826174734/https://arxiv.org/pdf/1707.05987v2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/16/3b/163b5c6dae3b78c53c0e4955b295c6c78fb510af.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1707.05987v2" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Approximating Bayes in the 21st Century [article]

Gael M. Martin, David T. Frazier, Christian P. Robert
<span title="2021-12-20">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The 21st century has seen an enormous growth in the development and use of approximate Bayesian methods.  ...  The aim is to help new researchers in particular -- and more generally those interested in adopting a Bayesian approach to empirical work -- distinguish between different approximate techniques; understand  ...  Simulation-based approaches Approximate Bayesian computation (ABC) From its initial beginnings as a practical approach for inference in population genetics models with computationally expensive likelihoods  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2112.10342v1">arXiv:2112.10342v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/225euaxkqrcjzals2jluqrocbu">fatcat:225euaxkqrcjzals2jluqrocbu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20211223064128/https://arxiv.org/pdf/2112.10342v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/93/c5/93c5083c0823f760bd1582132b02c99a33889b05.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2112.10342v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Accuracy of Gaussian approximation in nonparametric Bernstein – von Mises Theorem [article]

Vladimir Spokoiny, Maxim Panov
<span title="2020-06-01">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
First we derive tight finite sample bounds on posterior contraction in terms of the so called effective dimension of the parameter space.  ...  This paper offers another non-asymptotic approach to studying the behavior of the posterior for a special but rather popular and useful class of statistical models and for Gaussian priors.  ...  In particular, we establish a nonasymptotic upper bound on concentration and on the error of Gaussian approximation for the posterior in total variation distance in terms of efficient dimension of the  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1910.06028v5">arXiv:1910.06028v5</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/kc27ni5w5fdvdd2nfk5fpchi5a">fatcat:kc27ni5w5fdvdd2nfk5fpchi5a</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200610053719/https://arxiv.org/pdf/1910.06028v5.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1910.06028v5" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Convergence Speed and Approximation Accuracy of Numerical MCMC [article]

Tiangang Cui, Jing Dong, Ajay Jasra, Xin T. Tong
<span title="2022-03-07">2022</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Our results can be easily extended to obtain non-asymptotic error bounds for MCMC estimators.  ...  Our results show that when the original Markov chain converges to stationarity fast enough and the perturbed transition kernel is a good approximation to the original transition kernel, the corresponding  ...  Nonasymptotic error bounds are more useful in practice [16] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2203.03104v1">arXiv:2203.03104v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/e4firz7ffvgkhaegoo4o2lvvcy">fatcat:e4firz7ffvgkhaegoo4o2lvvcy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20220310160301/https://arxiv.org/pdf/2203.03104v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/d6/35/d635432b3369ccab08a391eb7132ae573d1db56d.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2203.03104v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Deep Nonparametric Regression on Approximately Low-dimensional Manifolds [article]

Yuling Jiao, Guohao Shen, Yuanyuan Lin, Jian Huang
<span title="2022-03-07">2022</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
To establish these results, we derive a novel approximation error bound for the H\"older smooth functions with a positive smoothness index using ReLU activated neural networks, which may be of independent  ...  Our error bounds achieve minimax optimal rate and significantly improve over the existing ones in the sense that they depend polynomially on the dimension of the predictor, instead of exponentially on  ...  (ii) We establish nonasymptotic bounds on the prediction error of nonparametric regression using deep neural networks.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2104.06708v4">arXiv:2104.06708v4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/y675xtkeyndhlk6ww3jlawqfra">fatcat:y675xtkeyndhlk6ww3jlawqfra</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20220309113551/https://arxiv.org/pdf/2104.06708v4.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/d7/b8/d7b8740dd880b1e08c20c51d335eb294788e3ed7.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2104.06708v4" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Diffusion Approximations for a Class of Sequential Testing Problems [article]

Victor F. Araman, Rene Caldentey
<span title="2021-06-21">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Under such regime, we derive a diffusion approximation for the sequential experimentation problem, which provides a number of important insights about the nature of the problem and its solution.  ...  Motivated by emerging practices in e-commerce, we assume that the seller is able to use a crowdvoting system to learn these preferences before a final assortment decision is made.  ...  The second author thank the University of Chicago Booth School of Business for financial support.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2102.07030v3">arXiv:2102.07030v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/r7aqzi6pvrgmrdtemxxohiqfji">fatcat:r7aqzi6pvrgmrdtemxxohiqfji</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20210623062034/https://arxiv.org/pdf/2102.07030v3.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/dc/6d/dc6d4c27e08bedc71e496d35c07d3303dcdfea79.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2102.07030v3" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Nonasymptotic bounds on the estimation error of MCMC algorithms

Krzysztof Łatuszyński, Błażej Miasojedow, Wojciech Niemiro
<span title="">2013</span> <i title="Bernoulli Society for Mathematical Statistics and Probability"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ir6muuxg4rbafminkxdo54uzh4" style="color: black;">Bernoulli</a> </i> &nbsp;
We address the problem of upper bounding the mean square error of MCMC estimators. Our analysis is nonasymptotic.  ...  As a corollary, we provide results on confidence estimation.  ...  We also gratefully acknowledge the help of Agnieszka Perduta and comments of three referees and an Associate Editor that helped improve the paper.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3150/12-bej442">doi:10.3150/12-bej442</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/x66midsjhrhg5cybo7iphtfely">fatcat:x66midsjhrhg5cybo7iphtfely</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170814161508/http://www2.warwick.ac.uk/fac/sci/statistics/staff/academic-research/latuszynski/bej442.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/89/15/8915eb355c1a3f8b2870b01ef2d0ce43234a0824.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3150/12-bej442"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Estimation in the partially observed stochastic Morris–Lecar neuronal model with particle filter and stochastic approximation methods

Susanne Ditlevsen, Adeline Samson
<span title="">2014</span> <i title="Institute of Mathematical Statistics"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/3ug7ktuisbglri55pm3ycqp46u" style="color: black;">Annals of Applied Statistics</a> </i> &nbsp;
The main contributions of this paper are an approach to estimate in this ill-posed situation and nonasymptotic convergence results for the method.  ...  An experimental data set of intracellular recordings of the membrane potential of a spinal motoneuron of a red-eared turtle is analyzed, and the performance is further evaluated in a simulation study.  ...  The authors are grateful to Rune W. Berg for  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1214/14-aoas729">doi:10.1214/14-aoas729</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xbv562275rhnbnhu6y6r6j2ab4">fatcat:xbv562275rhnbnhu6y6r6j2ab4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190318064831/https://core.ac.uk/download/pdf/52194218.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/57/aa/57aafbdd04d4f8786214d3cd8c2bb4c94d7c592d.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1214/14-aoas729"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Importance Sampling: Intrinsic Dimension and Computational Cost

S. Agapiou, O. Papaspiliopoulos, D. Sanz-Alonso, A. M. Stuart
<span title="">2017</span> <i title="Institute of Mathematical Statistics"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/d3twmsnkvjdlhnnpijld3rlsum" style="color: black;">Statistical Science</a> </i> &nbsp;
A general theory is presented, with a focus on the use of importance sampling in Bayesian inverse problems and filtering.  ...  The basic idea of importance sampling is to use independent samples from a proposal measure in order to approximate expectations with respect to a target measure.  ...  The Supplementary Material contains the proofs of all our results.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1214/17-sts611">doi:10.1214/17-sts611</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xk3uf2vql5hz7aebvekbs4g5ka">fatcat:xk3uf2vql5hz7aebvekbs4g5ka</a> </span>
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Nonasymptotic bounds on the estimation error for regenerative MCMC algorithms [article]

Krzysztof Latuszynski, Blazej Miasojedow, Wojciech Niemiro
<span title="2009-07-28">2009</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We consider a regenerative setting and Monte Carlo estimators based on i.i.d. blocks of a Markov chain trajectory. The main result is an inequality for the mean square error.  ...  MCMC methods are used in Bayesian statistics not only to sample from posterior distributions but also to estimate expectations.  ...  Acknowledgements Discussions with Jacek Weso lowski helped prepare an early version of this paper. The authors are also grateful to the anonymous referee for his/her constructive comments.  ... 
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