�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��$��00N�� �[�U y�� The latter also proves a weak version of Talagrand’s suprema of empirical processes inequality. H(�m��;u��1�9#L̝��V:��������x)r�� L����KE��4�KET�2�k�j�. %�쏢 << /Names 357 0 R /OpenAction 391 0 R /Outlines 328 0 R /PageMode /UseOutlines /Pages 327 0 R /Type /Catalog >> We show that Markov couplings can be used to improve the accuracy of Markov chain Monte Carlo calculations in some situations where the steady-state probability distribution is not explicitly known. x��XKs�8��W�`���E ���3�'.G�S[�=@$�L�*����[�)���\D��h���FCt�[�ŧw�o����� Copyright © 2020 Elsevier B.V. or its licensors or contributors. 160 0 obj << /Linearized 1 /L 399192 /H [ 2714 469 ] /O 164 /E 110168 /N 27 /T 397962 >> 162 0 obj %PDF-1.5 endobj << /Filter /FlateDecode /S 396 /O 468 /Length 381 >> 161 0 obj %PDF-1.4 Coupling of Markov chains can be described as follows. US$ 39.95. �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 <> We show that Markov couplings can be used to improve the accuracy of Markov chain Monte Carlo calculations in some situations where the steady-state probability distribution is not explicitly known. x��\Yw�q��#~��S���z_��$2�H�����| b�@ "A*������C�z������>p0�Kuu�_W��7l��������>��n.��Yo.��?���&�w�z��14f#�����lv�W���bs��h:y�׫��q��l����f���������h���)��j{�G�>>�#�g&��v\+�.R�7Vl�� N�|��v'f/����v�gg5��;|4�;�����͎{㧫�xS\�`������v'g�7�+��sn�t�m���L��[�XY?�շo�`R��|+�,�������̬ << /Annots [ 392 0 R 393 0 R 394 0 R 395 0 R 396 0 R 397 0 R 398 0 R 399 0 R 400 0 R 401 0 R 402 0 R 403 0 R 404 0 R 405 0 R 406 0 R ] /Contents 165 0 R /MediaBox [ 0 0 612 792 ] /Parent 287 0 R /Resources 407 0 R /Type /Page >> chain. 2 R.L.I.M.S. << /Type /XRef /Length 97 /Filter /FlateDecode /DecodeParms << /Columns 5 /Predictor 12 >> /W [ 1 3 1 ] /Index [ 160 292 ] /Info 72 0 R /Root 162 0 R /Size 452 /Prev 397963 /ID [<1016f13ab44511ea1033cfe685f636c6>] >> Talagrand’s convex distance inequality, for a larger class of random processes, was indepen- dently proven in Marton (1998b) and Samson (2000). �f�L&L����E7|K�@�� sN��]��,4��[`����]��LM�mA�w��3�ޘ�}f���3 �����ˍ�o�Q*����M��g�QϏ��`b�Srv��3����'�i����d� 163 0 obj ���Jq�XnL�”f�ʲ`L-�������2����w��ʐ�_��>�qE�?L�/�=�z���n�{dZ��3��J���������-+��4eQV����W�1���������Y.JIn�%׏@�r!���q9U��Z�\J&�W}�l�9Y����mdYTbAq���r)(����W$��u?�uۥ՛6c�t�}�3��c۵Þ����o���o��7�ˇo�dWH�M�ֻ��a@���]�6�*��lY�u1�z�$ A,|89f���u[�H���X�����B���Z-Hl�mc��o|:�:��ۋc�m�6��︴������rM�ĭ���C�1�F 7���p�:za���l��5 3غ^��`�ص+�����C��%E��(����z`���MZiO�o��������ض���J�m�^0����_��J0�RAV��x��FY���>�6#i�x��@�l�Y#�HPA�zT� endobj As shown by the examples considered in this paper, good candidates for approximate stationary … endobj endstream 165 0 obj A maximal coupling for Markov chains. Start the Markov chain {X n} in an initial state i and allow each. 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 endstream %���� stream 476 Accesses. 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. MARKOV CHAINS AND COUPLING FROM THE PAST DYLAN CORDARO Abstract. ��^����k�J ����-��|~� �q���k���������L��CZ����a��Ck����wGǿ|>=Cf��(�� �A@a���Kk�/a�,@�d#*�M�. CS37101-1 Markov Chain Monte Carlo Methods Lecture 2: October 7, 2003 Markov Chains, Coupling, Stationary Distribution Eric Vigoda 2.1 Markov Chains In this lecture, we will introduce Markov chains and show a potential algorithmic use of Markov chains for sampling from complex distributions. This method useful in situations where the stationary distribution is not known explicitly, as in the case of nonequilibrium transport models. By continuing you agree to the use of cookies. 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). 164 0 obj We illustrate it using two models of nonequilibrium transport. We have shown that Markov couplings, when available, can be used effectively to improve the accuracy of Markov chain Monte Carlo calculations. This is a preview of subscription content, log in to check access. Access options Buy single article. Instant access to the full article PDF. 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. https://doi.org/10.1016/j.jcp.2009.03.043. << /Filter /FlateDecode /Length 2078 >> We introduce the fundamentals of probability, Markov chains, and coupling to establish a foundation for CFTP. endobj We use cookies to help provide and enhance our service and tailor content and ads. �i��� ����c��4 x�c```b`���������A� The technique generalizes the notion of control variates from classical Monte Carlo integration. Markov chain setting was further generalized to a class of random processes, for Hamming distance, in Marton (1998a). 5 0 obj stream 76 Citations. x�cbd`�g`b``8 "���F�tD2~� R$D��Hs' ɘ�b[\���@��|&��Q�`sG�Q�0ɶd��0Jf�q���a�:$ N�U Vol. stream The technique generalizes the notion of control variates from classical Monte Carlo integration. We illustrate it using two models of nonequilibrium transport. Markov chains by applying coupling techniques and methods from optimal transport in order to circumvent problems arising from the randomized setting. We then brie y study the hardcore and Ising model to gain … stream Copyright © 2009 Elsevier Inc. All rights reserved. Metrics details. rH�uu���w������{���[��m�ӯ Rk��2��u��W3A{�����נ���X�k�I�wmמz���`pi"D�J���S�҂?$R�Rrrh�6�M��Έ�����b�q�wi�&��Ӛ���G David Griffeath 1 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete volume 31, pages 95 – 106 (1975)Cite this article. Start a Markov chain {Y n}, with the same transition matrix P and state space S as for {X n}, operating under stationary conditions, so that the initial probability distribution for Y 0 is the stationary distribution {π j}.

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