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I am trying to visualise binary time series data. To do so I have a plot (see below) where I show whether a given trial was a success or a failure (red/green vertical lines at the top) and then below I plot a smoothed time series of the success probability (where I've smoothed using a gaussian kernel with some arbitrary standard deviation). The x-axis is time

What I was hoping to find is a way to put meaningful confidence intervals on the smoothed curve. I can see complicated ways of doing this using Bayesian smoothing algorithms, but am looking for a simpler alternative. I don't need the confidence intervals to be exact but they also shouldn't be entirely meaningless. Any suggestions, ideally that do not involve fitting an explicit model?

enter image description here

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    $\begingroup$ What is the x-axis? (always label your graphs). If you're trying to estimate the cumulative proportion of successes, you need a CDF curve. Or if it's just a moving proportion, I would use a GLM with smoothing splines. The CIs fall out of that one easily. $\endgroup$
    – AdamO
    Sep 12, 2019 at 14:22
  • $\begingroup$ its a moving proportion. I've never come across GLMs with smoothing splines. Any ideas for ways of estimating CIs without fitting an explicit model? $\endgroup$ Sep 12, 2019 at 14:36
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    $\begingroup$ @user3235916, you seem to calculate a moving-window average (proportion). I advise you to use the properties of binomial distribution to get the CI for the sample proportion. Are you interested in full answer? $\endgroup$ Sep 13, 2019 at 11:48
  • $\begingroup$ Yes! I was thinking of something along these lines but wasn't sure how to integrate over timepoints at different distances $\endgroup$ Sep 13, 2019 at 14:01

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