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I have a bunch of point processes that are generated by some unknown model. There is a marked pause that seems to begin and end at the same time in each process. I would like to measure this pause.

I have fruitlessly tried fitting the waiting times from the processes to standard distributions. The point processes represent the spiking activity of a neuron which is probably generated by a very complicated, currently unknown mechanism. Is there a largely nonparametric method for detecting changepoints for this data?

My original method was to use something like edge detection, though I'd like a more statistical method. Any help is appreciated and please let me know if this question is unclear or if anyone would like more detail.

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Although the approach is parametric, try looking at Bayesian Changepoint Detection, especially papers by Adams, R. P. & MacKay (see https://arxiv.org/abs/0710.3742), and Fearnhead, P. & Liu (see http://onlinelibrary.wiley.com/doi/10.1111/j.1467-9868.2007.00601.x/abstract). For point processes in particular, have a look at: http://mlg.eng.cam.ac.uk/pub/pdf/SaaTurRas10.pdf.

The approach is that you partition your data into disjoint segments (that are ordered in time). According to the product partition model (See Barry and Hartigan,1992) each segment is independently modelled by a given probability distribution (i.e. model). As you are going to see in these papers you maintain a run-length distribution (distribution of possible segment lengths). Conditioning on that distribution you can try to model the data generating process by assigning a model/distribution to your data (say the multivariate normal) and a prior to the parameters of that model. As you get more and more data, you update your prior beliefs into posterior ones and predict whether a CP has occurred.

Hope that will get you going...

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