Re: [gmx-users] What is the autocorrelation time
Hi Patrick, There is a fast decay of the hbond acf for liquid water on a 100-200 fs timescale that traditionally is associated with the librational motion of water molecules. There's a good paper by Omer Markovich and Noam Agmon in J. Chem. Phys. 129 084505 2008 where this effect is discussed, although it's not the main focus of that paper. Then, after 10 ps or so, there's a regime where the acf falls of as a power law. As a consequence the correlation time is not really derived from a purely exponential acf and the interpretation might be misleading to some extent if you imply exponential behaviour. Best, Erik 21 maj 2012 kl. 14.07 skrev Patrick Fuchs: Hi Erik, your examples on H-bond acfs are interesting. I'm wondering about the distinct features which are non-exponential in your examples. What do you mean exactly? Could these features be due to rare (H-bonding) events, or in other words to poor sampling? Intuitively, I'd say that the interpretation of the acf (at least for the decay and the decorelation) is always valid unless maybe if you have very poor statistics. Ciao, Patrick Le 20/05/2012 16:12, Erik Marklund a écrit : Dear Chris, As I see it there one can interpret the acf and correlatation time further for certain types of data. I'll use the h-bond autocorrelation function as an example. Here the data is time series of logical true and false, represented as ones and zeros. This type of acf can be direcly interpreted as a probablity, and some quantities derived from the acf can bear further meaning because of this. I also thought that the nature of the data may be such there is a non-exponential part, which makes the autocorreltaion time less valid, or less connected to other intuitive concepts. Again, the h-bond acf has distinct features which are non-exponential and the autocorreltaion time derived from such acfs may in fact be misleading when the h-bond kinetics is to be determined. Hope that makes sense. I's be happy to hear from you if you disagree. Best, Erik 19 maj 2012 kl. 04.01 skrev Christopher Neale: Dear Erik: I thought about your comment for a while and I have come to understand that you are correct. The exponential (or integral) autocorrelation time is a mathematical construct and is defined as such. What I was looking for was an interpretation of the autocorrelation time in terms of the time required to decorrelate the sampling. As to whether or not this will depend on the nature of the data, I don't really understand your conjecture. If the interpretation of the autocorrelation time depends on the nature of the data, then that implies to me that a single scalar value is useless in this case. I don't understand how it could be useful to represent the autocorrelation time by a single number if that number does not mean anything on its own. If you have time, I would appreciate if you could elaborate on this point. Thank you, Chris. -- original message -- Aren't you looking for an interpretation rather than a definition? And will this not depend on the nature of the data? Best, Erik -- gmx-users mailing list gmx-users@gromacs.org mailto:gmx-users@gromacs.org http://lists.gromacs.org/mailman/listinfo/gmx-users Please search the archive at http://www.gromacs.org/Support/Mailing_Lists/Search before posting! Please don't post (un)subscribe requests to the list. Use the www interface or send it to gmx-users-requ...@gromacs.org. Can't post? Read http://www.gromacs.org/Support/Mailing_Lists --- Erik Marklund, PhD Dept. of Cell and Molecular Biology, Uppsala University. Husargatan 3, Box 596, 75124 Uppsala, Sweden phone: +46 18 471 6688 fax: +46 18 511 755 er...@xray.bmc.uu.se mailto:er...@xray.bmc.uu.se http://www2.icm.uu.se/molbio/elflab/index.html -- ___ Patrick FUCHS Dynamique des Structures et Interactions des Macromolécules Biologiques INTS, INSERM UMR-S665, Université Paris Diderot, 6 rue Alexandre Cabanel, 75015 Paris Tel : +33 (0)1-44-49-30-57 - Fax : +33 (0)1-43-06-50-19 E-mail address: patrick.fu...@univ-paris-diderot.fr Web Site: http://www.dsimb.inserm.fr/~fuchs -- gmx-users mailing listgmx-users@gromacs.org http://lists.gromacs.org/mailman/listinfo/gmx-users Please search the archive at http://www.gromacs.org/Support/Mailing_Lists/Search before posting! Please don't post (un)subscribe requests to the list. Use the www interface or send it to gmx-users-requ...@gromacs.org. Can't post? Read http://www.gromacs.org/Support/Mailing_Lists --- Erik Marklund, PhD Dept. of Cell and Molecular Biology, Uppsala University. Husargatan 3, Box 596,75124 Uppsala, Sweden phone:+46 18 471 6688fax: +46 18 511 755 er...@xray.bmc.uu.se http://www2.icm.uu.se/molbio/elflab/index.html
Re: [gmx-users] What is the autocorrelation time
Hi Erik, your examples on H-bond acfs are interesting. I'm wondering about the distinct features which are non-exponential in your examples. What do you mean exactly? Could these features be due to rare (H-bonding) events, or in other words to poor sampling? Intuitively, I'd say that the interpretation of the acf (at least for the decay and the decorelation) is always valid unless maybe if you have very poor statistics. Ciao, Patrick Le 20/05/2012 16:12, Erik Marklund a écrit : Dear Chris, As I see it there one can interpret the acf and correlatation time further for certain types of data. I'll use the h-bond autocorrelation function as an example. Here the data is time series of logical true and false, represented as ones and zeros. This type of acf can be direcly interpreted as a probablity, and some quantities derived from the acf can bear further meaning because of this. I also thought that the nature of the data may be such there is a non-exponential part, which makes the autocorreltaion time less valid, or less connected to other intuitive concepts. Again, the h-bond acf has distinct features which are non-exponential and the autocorreltaion time derived from such acfs may in fact be misleading when the h-bond kinetics is to be determined. Hope that makes sense. I's be happy to hear from you if you disagree. Best, Erik 19 maj 2012 kl. 04.01 skrev Christopher Neale: Dear Erik: I thought about your comment for a while and I have come to understand that you are correct. The exponential (or integral) autocorrelation time is a mathematical construct and is defined as such. What I was looking for was an interpretation of the autocorrelation time in terms of the time required to decorrelate the sampling. As to whether or not this will depend on the nature of the data, I don't really understand your conjecture. If the interpretation of the autocorrelation time depends on the nature of the data, then that implies to me that a single scalar value is useless in this case. I don't understand how it could be useful to represent the autocorrelation time by a single number if that number does not mean anything on its own. If you have time, I would appreciate if you could elaborate on this point. Thank you, Chris. -- original message -- Aren't you looking for an interpretation rather than a definition? And will this not depend on the nature of the data? Best, Erik -- gmx-users mailing list gmx-users@gromacs.org mailto:gmx-users@gromacs.org http://lists.gromacs.org/mailman/listinfo/gmx-users Please search the archive at http://www.gromacs.org/Support/Mailing_Lists/Search before posting! Please don't post (un)subscribe requests to the list. Use the www interface or send it to gmx-users-requ...@gromacs.org. Can't post? Read http://www.gromacs.org/Support/Mailing_Lists --- Erik Marklund, PhD Dept. of Cell and Molecular Biology, Uppsala University. Husargatan 3, Box 596, 75124 Uppsala, Sweden phone: +46 18 471 6688 fax: +46 18 511 755 er...@xray.bmc.uu.se mailto:er...@xray.bmc.uu.se http://www2.icm.uu.se/molbio/elflab/index.html -- ___ Patrick FUCHS Dynamique des Structures et Interactions des Macromolécules Biologiques INTS, INSERM UMR-S665, Université Paris Diderot, 6 rue Alexandre Cabanel, 75015 Paris Tel : +33 (0)1-44-49-30-57 - Fax : +33 (0)1-43-06-50-19 E-mail address: patrick.fu...@univ-paris-diderot.fr Web Site: http://www.dsimb.inserm.fr/~fuchs -- gmx-users mailing listgmx-users@gromacs.org http://lists.gromacs.org/mailman/listinfo/gmx-users Please search the archive at http://www.gromacs.org/Support/Mailing_Lists/Search before posting! Please don't post (un)subscribe requests to the list. Use the www interface or send it to gmx-users-requ...@gromacs.org. Can't post? Read http://www.gromacs.org/Support/Mailing_Lists
Re: [gmx-users] What is the autocorrelation time
Hi Chris, I understand your question, this autocorrelation time puzzled me for a long time as well. Not far from the interpretation you give, Scott Feller defines it (http://dx.doi.org/10.1007/978-1-59745-519-0_7) as the time a given observable takes to lose the memory of its previous state, or in other words the time it takes to relax (that's why it's sometimes called relaxation time). He also discusses it as a tool to choose the block size for calculating an error estimate of an observable (one single simulation can be used as independant samples if each block size is autocorrelation time). We also had a nice discussion some years ago on the mailing list on free energy calculation and error estimate: http://lists.gromacs.org/pipermail/gmx-users/2007-May/027281.html. John Chodera pointed me to a useful article from Wolfhard Janke (the link in the discussion is broken, here's the new one: http://www2.fz-juelich.de/nic-series/volume10/janke2.pdf). There you'll find a rigorous mathematical definition of autocorrelation time. Quoting this paper This shows more clearly that only every 2 tau_int iterations the measurements are approximately uncorrelated and gives a better idea of the relevant effective size of the statistical sample (tau_int is the integrated autocorrelation time; as you said the autocorrelation function is usually a single exponential, but sometimes it's more complex and one needs to evaluate it by integration of the autocorrelation function). After all these considerations, the autocorrelation time can be seen as a tool to assess the time that is needed to have a good estimate of an observable: the simulation must be many many times longer than the autocorrelation time. And sometimes it's directly related to experimental observables (i.e. NMR relaxation experiments). Hope it's useful, Patrick Le 16/05/2012 23:39, Christopher Neale a écrit : Thank you Stephane. Unfortunately, neither of those links contains the information that I am seeking. Those links contain some example plots of autocorrelation functions including a discussion of time-spans over which the example time-series is autocorrelated and when it is not, but neither link defines the (exponential or integral) autocorrelation time except to show a plot and indicate when it is non-zero and when it fluctuates about zero. For example, I already know that the autocorrelation time describes the exponential decay of the correlation and that two values drawn from the same simulation are statistically independent if they are separated by a sufficient number of (accurate) autocorrelation times, but this information is not exactly a definition of the autocorrelation time. I am hoping to find a definition of the autocorrelation time in terms of the probability of drawing uncorrelated samples, although any complete definition will do. If anybody else has the time, I would appreciate it. Thank you, Chris. -- original message -- Probably these links give you simple and clear response for your question http://idlastro.gsfc.nasa.gov/idl_html_help/Time-Series_Analysis.html and http://www.statsoft.com/textbook/time-series-analysis/ HTH Stephane -- ___ Patrick FUCHS Dynamique des Structures et Interactions des Macromolécules Biologiques INTS, INSERM UMR-S665, Université Paris Diderot, 6 rue Alexandre Cabanel, 75015 Paris Tel : +33 (0)1-44-49-30-57 - Fax : +33 (0)1-43-06-50-19 E-mail address: patrick.fu...@univ-paris-diderot.fr Web Site: http://www.dsimb.inserm.fr/~fuchs -- gmx-users mailing listgmx-users@gromacs.org http://lists.gromacs.org/mailman/listinfo/gmx-users Please search the archive at http://www.gromacs.org/Support/Mailing_Lists/Search before posting! Please don't post (un)subscribe requests to the list. Use the www interface or send it to gmx-users-requ...@gromacs.org. Can't post? Read http://www.gromacs.org/Support/Mailing_Lists
[gmx-users] What is the autocorrelation time
Thank you very much Patrick. This is exactly what I was looking for. Based on what you sent, I'm going to go with the following text in my work: The value of tau_int is approximately half of the amount of time required, on average, to obtain a statistically independent (decorrelated) sample [ref Janke]. I really appreciate it! Thank you for your help. Chris. -- original message -- Hi Chris,I understand your question, this autocorrelation time puzzled me for a long time as well. Not far from the interpretation you give, Scott Feller defines it (http://dx.doi.org/10.1007/978-1-59745-519-0_7) as the time a given observable takes to lose the memory of its previous state, or in other words the time it takes to relax (that's why it's sometimes called relaxation time). He also discusses it as a tool to choose the block size for calculating an error estimate of an observable (one single simulation can be used as independant samples if each block size is autocorrelation time). We also had a nice discussion some years ago on the mailing list on free energy calculation and error estimate: http://lists.gromacs.org/pipermail/gmx-users/2007-May/027281.html. John Chodera pointed me to a useful article from Wolfhard Janke (the link in the discussion is broken, here's the new one: http://www2.fz-juelich.de/nic-series/volume10/janke2.pdf). There you'll find a rigorous mathematical definition of autocorrelation time. Quoting this paper This shows more clearly that only every 2 tau_int iterations the measurements are approximately uncorrelated and gives a better idea of the relevant effective size of the statistical sample (tau_int is the integrated autocorrelation time; as you said the autocorrelation function is usually a single exponential, but sometimes it's more complex and one needs to evaluate it by integration of the autocorrelation function). After all these considerations, the autocorrelation time can be seen as a tool to assess the time that is needed to have a good estimate of an observable: the simulation must be many many times longer than the autocorrelation time. And sometimes it's directly related to experimental observables (i.e. NMR relaxation experiments). Hope it's useful, Patrick Le 16/05/2012 23:39, Christopher Neale a écrit : Thank you Stephane. Unfortunately, neither of those links contains the information that I am seeking. Those links contain some example plots of autocorrelation functions including a discussion of time-spans over which the example time-series is autocorrelated and when it is not, but neither link defines the (exponential or integral) autocorrelation time except to show a plot and indicate when it is non-zero and when it fluctuates about zero. For example, I already know that the autocorrelation time describes the exponential decay of the correlation and that two values drawn from the same simulation are statistically independent if they are separated by a sufficient number of (accurate) autocorrelation times, but this information is not exactly a definition of the autocorrelation time. I am hoping to find a definition of the autocorrelation time in terms of the probability of drawing uncorrelated samples, although any complete definition will do. If anybody else has the time, I would appreciate it. Thank you, Chris. -- original message -- Probably these links give you simple and clear response for your question http://idlastro.gsfc.nasa.gov/idl_html_help/Time-Series_Analysis.html and http://www.statsoft.com/textbook/time-series-analysis/ HTH Stephane -- -- gmx-users mailing listgmx-users@gromacs.org http://lists.gromacs.org/mailman/listinfo/gmx-users Please search the archive at http://www.gromacs.org/Support/Mailing_Lists/Search before posting! Please don't post (un)subscribe requests to the list. Use the www interface or send it to gmx-users-requ...@gromacs.org. Can't post? Read http://www.gromacs.org/Support/Mailing_Lists
[gmx-users] What is the autocorrelation time
Dear Erik: I thought about your comment for a while and I have come to understand that you are correct. The exponential (or integral) autocorrelation time is a mathematical construct and is defined as such. What I was looking for was an interpretation of the autocorrelation time in terms of the time required to decorrelate the sampling. As to whether or not this will depend on the nature of the data, I don't really understand your conjecture. If the interpretation of the autocorrelation time depends on the nature of the data, then that implies to me that a single scalar value is useless in this case. I don't understand how it could be useful to represent the autocorrelation time by a single number if that number does not mean anything on its own. If you have time, I would appreciate if you could elaborate on this point. Thank you, Chris. -- original message -- Aren't you looking for an interpretation rather than a definition? And will this not depend on the nature of the data? Best, Erik -- gmx-users mailing listgmx-users@gromacs.org http://lists.gromacs.org/mailman/listinfo/gmx-users Please search the archive at http://www.gromacs.org/Support/Mailing_Lists/Search before posting! Please don't post (un)subscribe requests to the list. Use the www interface or send it to gmx-users-requ...@gromacs.org. Can't post? Read http://www.gromacs.org/Support/Mailing_Lists
Re: [gmx-users] What is the autocorrelation time
16 maj 2012 kl. 23.39 skrev Christopher Neale: Thank you Stephane. Unfortunately, neither of those links contains the information that I am seeking. Those links contain some example plots of autocorrelation functions including a discussion of time-spans over which the example time-series is autocorrelated and when it is not, but neither link defines the (exponential or integral) autocorrelation time except to show a plot and indicate when it is non-zero and when it fluctuates about zero. For example, I already know that the autocorrelation time describes the exponential decay of the correlation and that two values drawn from the same simulation are statistically independent if they are separated by a sufficient number of (accurate) autocorrelation times, but this information is not exactly a definition of the autocorrelation time. I am hoping to find a definition of the autocorrelation time in terms of the probability of drawing uncorrelated samples, although any complete definition will do. Aren't you looking for an interpretation rather than a definition? And will this not depend on the nature of the data? Best, Erik If anybody else has the time, I would appreciate it. Thank you, Chris. -- original message -- Probably these links give you simple and clear response for your question http://idlastro.gsfc.nasa.gov/idl_html_help/Time-Series_Analysis.html and http://www.statsoft.com/textbook/time-series-analysis/ HTH Stephane -- gmx-users mailing listgmx-users@gromacs.org http://lists.gromacs.org/mailman/listinfo/gmx-users Please search the archive at http://www.gromacs.org/Support/Mailing_Lists/Search before posting! Please don't post (un)subscribe requests to the list. Use the www interface or send it to gmx-users-requ...@gromacs.org. Can't post? Read http://www.gromacs.org/Support/Mailing_Lists --- Erik Marklund, PhD Dept. of Cell and Molecular Biology, Uppsala University. Husargatan 3, Box 596,75124 Uppsala, Sweden phone:+46 18 471 6688fax: +46 18 511 755 er...@xray.bmc.uu.se http://www2.icm.uu.se/molbio/elflab/index.html -- gmx-users mailing listgmx-users@gromacs.org http://lists.gromacs.org/mailman/listinfo/gmx-users Please search the archive at http://www.gromacs.org/Support/Mailing_Lists/Search before posting! Please don't post (un)subscribe requests to the list. Use the www interface or send it to gmx-users-requ...@gromacs.org. Can't post? Read http://www.gromacs.org/Support/Mailing_Lists
[gmx-users] What is the autocorrelation time
Dear users: Let us say that I used g_analyze -g -fitfn exp and obtained the exponential autocorrelation time of a dataset. What does the exponential autocorrelation time represent? I imagine that it might be the time required to, on average, obtain a statistically independent sample, or perhaps the time required to obtain a 50% chance of the next sample being statistically independent. I've looked around the web and while I can find lots of information about how to obtain the exponential autocorrelation time, I am still unsure exactly what it represents. Thank you, Chris. -- gmx-users mailing listgmx-users@gromacs.org http://lists.gromacs.org/mailman/listinfo/gmx-users Please search the archive at http://www.gromacs.org/Support/Mailing_Lists/Search before posting! Please don't post (un)subscribe requests to the list. Use the www interface or send it to gmx-users-requ...@gromacs.org. Can't post? Read http://www.gromacs.org/Support/Mailing_Lists
[gmx-users] What is the autocorrelation time
Hi Chris, Probably these links give you simple and clear response for your question http://idlastro.gsfc.nasa.gov/idl_html_help/Time-Series_Analysis.html and http://www.statsoft.com/textbook/time-series-analysis/ HTH Stephane -- gmx-users mailing listgmx-users@gromacs.org http://lists.gromacs.org/mailman/listinfo/gmx-users Please search the archive at http://www.gromacs.org/Support/Mailing_Lists/Search before posting! Please don't post (un)subscribe requests to the list. Use the www interface or send it to gmx-users-requ...@gromacs.org. Can't post? Read http://www.gromacs.org/Support/Mailing_Lists
[gmx-users] What is the autocorrelation time
Thank you Stephane. Unfortunately, neither of those links contains the information that I am seeking. Those links contain some example plots of autocorrelation functions including a discussion of time-spans over which the example time-series is autocorrelated and when it is not, but neither link defines the (exponential or integral) autocorrelation time except to show a plot and indicate when it is non-zero and when it fluctuates about zero. For example, I already know that the autocorrelation time describes the exponential decay of the correlation and that two values drawn from the same simulation are statistically independent if they are separated by a sufficient number of (accurate) autocorrelation times, but this information is not exactly a definition of the autocorrelation time. I am hoping to find a definition of the autocorrelation time in terms of the probability of drawing uncorrelated samples, although any complete definition will do. If anybody else has the time, I would appreciate it. Thank you, Chris. -- original message -- Probably these links give you simple and clear response for your question http://idlastro.gsfc.nasa.gov/idl_html_help/Time-Series_Analysis.html and http://www.statsoft.com/textbook/time-series-analysis/ HTH Stephane -- gmx-users mailing listgmx-users@gromacs.org http://lists.gromacs.org/mailman/listinfo/gmx-users Please search the archive at http://www.gromacs.org/Support/Mailing_Lists/Search before posting! Please don't post (un)subscribe requests to the list. Use the www interface or send it to gmx-users-requ...@gromacs.org. Can't post? Read http://www.gromacs.org/Support/Mailing_Lists
