Access options Buy single article. By continuing you agree to the use of cookies. We have shown that Markov couplings, when available, can be used effectively to improve the accuracy of Markov chain Monte Carlo calculations. << /Linearized 1 /L 399192 /H [ 2714 469 ] /O 164 /E 110168 /N 27 /T 397962 >> stream endobj 476 Accesses. Coupling of Markov chains can be described as follows. 165 0 obj David Griffeath 1 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete volume 31, pages 95 – 106 (1975)Cite this article. We introduce the fundamentals of probability, Markov chains, and coupling to establish a foundation for CFTP. ScienceDirect ® is a registered trademark of Elsevier B.V. ScienceDirect ® is a registered trademark of Elsevier B.V. Coupling control variates for Markov chain Monte Carlo. We illustrate it using two models of nonequilibrium transport. endstream We illustrate it using two models of nonequilibrium transport. This method useful in situations where the stationary distribution is not known explicitly, as in the case of nonequilibrium transport models. stream endobj �Z�u�I��Ld@��¾F_��S���M�N�(^6�e*G��,Ӭ�U-&���2�� -���8��-/ hY9Eq!�i^%\�A�`� �"�CLm�v"/Х�����9�����P�) ?|��k� ��������� {br���3���N�� � ����E�mjڽ%�j��K�W^/���ݻ��$��00N�� �[�U y�� x��\Yw�q��#~��S���z_��$2�H�����| b�@ "A*������C�z������>p0�Kuu�_W��7l��������>��n.��Yo.��?���&�w�z��14f#�����lv�W���bs��h:y�׫��q��l����f���������h���)��j{�G�>>�#�g&��v\+�.R�7Vl�� N�|��v'f/����v�gg5��;|4�;�����͎{㧫�xS\�`������v'g�7�+��sn�t�m���L��[�XY?�շo�`R��|+�,�������̬ Markov chains by applying coupling techniques and methods from optimal transport in order to circumvent problems arising from the randomized setting. << /Names 357 0 R /OpenAction 391 0 R /Outlines 328 0 R /PageMode /UseOutlines /Pages 327 0 R /Type /Catalog >> 160 0 obj chain. << /Annots [ 392 0 R 393 0 R 394 0 R 395 0 R 396 0 R 397 0 R 398 0 R 399 0 R 400 0 R 401 0 R 402 0 R 403 0 R 404 0 R 405 0 R 406 0 R ] /Contents 165 0 R /MediaBox [ 0 0 612 792 ] /Parent 287 0 R /Resources 407 0 R /Type /Page >> stream 5 0 obj H(�m��;u��1�9#L̝��V:��������x)r�� L����KE��4�KET�2�k�j�. We aim to explore Coupling from the Past (CFTP), an algorithm designed to ob-tain a perfect sampling from the stationary distribution of a Markov chain. endobj *��\В\طY�+�A�9�aA"0�Hُ����^W_e�`%6�1�\��Bn�a�f�� ��T�!��Jr��x�Ǥx)k)Q(|��],0}��@�)B=V�ɝSʂUr���PU��k����#����L��Q ��I?Vd9����&ㆄ�c�b���$c�T|(�,��D�+�2��i��=�:@ܜ>'&�,b�>1������&�9��/4��ț�Aa���\�rB���NqmxI�֩�r�����U���p�楱��q���b 163 0 obj x��XKs�8��W�`���E ���3�'.G�S[�=@$�L�*����[�)���\D��h���FCt�[�ŧw�o����� 164 0 obj 162 0 obj endobj As shown by the examples considered in this paper, good candidates for approximate stationary … 76 Citations. �lV d``i``dT�I�Z�����AY@wlj����\�_����“����0ב����2X�0�d�grUH`��n��:���l��[�{�y�5^�\���Q�ȥ��%�����r1�������K�kmV�&+�5��$��h�2�#CY %PDF-1.5 x�cbd`�g`b``8 "���F�tD2~� R$D��Hs' ɘ�b[\���@��|&��Q�`sG�Q�0ɶd��0Jf�q���a�:$ N�U x�c```b`���������A� The technique generalizes the notion of control variates from classical Monte Carlo integration. Definition 3 We define a coupling of two copies of a Markov chain on S to be a process ((Xn,Yn))n∈N0 on S ×S, with the property that both (Xn)n∈N0 and (Yn)n∈N0 are Markov chains on S with the same transition probabilities (but possibly different starting distributions). Copyright © 2009 Elsevier Inc. All rights reserved.


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