Hi Paul, Here is how an amateur statistician deals with this problem when analyzing spike trains from simultaneously recorded neurons.
Start by estimating the "hazard function" h(t) of your several point processes (if you have a copy of MASS, check out the chapter 13, If you have a copy of Jim Lindsey, "The Statistical Analysis of Stochastic Processes in Time", check out chap 3 & 4; the hazard function is also called the "conditional intensity" or the "stochastic intensity"). In practice if you have a renewal process, meaning that the successive intervals between your events times are independent, you can first estimate the "Inter Event Interval" pdf, f(t), and its cumulative distribution function F(t). h(t) is then given by: h(t) = f(t) / (1-F(t)), where the quantity S(t) = 1-F(t) is often called the survivor function. Fine, now if your processes are well approximated by renewal processes, you can look for the distribution of "time to next event" (TTN) and "time to former event" (TTF). By that I mean that for each of the black events of your figure, you must get the interval separating it from the last red event preceding it (the time to former) and the next red event following it (the time to next). Under the null hypothesis of no correlation these to random variables have the same pdf given by: TTN(i) = S(i) / <IEI>, where S(i) in that case is the survivor function of the red (test) process and <IEI> is its inter event interval expected value. Using this approach I typically estimate the TTN and TTF pdfs with histograms and compare these histograms to their expected values under the null hypothesis. A warning though, I have most of the time much more events than you seem to have on your figure. Let me know if any of this makes sense. Christophe. paul sorenson wrote: >I have some time stamped events that are supposed to be unrelated. > >I have plotted them and that assumption does not appear to be valid. >http://metrak.com/tmp/sevents.png is a plot showing three sets of events >over time. For the purpose of this exercise, the Y value is irrelevant. > The series are not sampled at the same time and are not equispaced >(just events in a log file). > >The plot is already pretty convincing but requires a human-in-the-loop >to zoom in on "hot" areas and then visually interpret the result. I >want to calculate some index of the events' temporal relationship. > >I think the question I am trying to ask is something like: "If event B >occurs, how likely is it that an event A occurred at almost the same time?". > >Can anyone suggest an established approach that could provide some >further insight into this relationship? I can think of a fairly basic >approach where I start out with the ecdf of the time differences but I >am guessing I would be reinventing some wheel. > >Any tips would be most appreciated. > >cheers > >______________________________________________ >[email protected] mailing list >https://stat.ethz.ch/mailman/listinfo/r-help >PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html > > > -- A Master Carpenter has many tools and is expert with most of them.If you only know how to use a hammer, every problem starts to look like a nail. Stay away from that trap. Richard B Johnson. -- Christophe Pouzat Laboratoire de Physiologie Cerebrale CNRS UMR 8118 UFR biomedicale de l'Universite Paris V 45, rue des Saints Peres 75006 PARIS France tel: +33 (0)1 42 86 38 28 fax: +33 (0)1 42 86 38 30 web: www.biomedicale.univ-paris5.fr/physcerv/C_Pouzat.html ______________________________________________ [email protected] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
