Demonstrating similarity of two time series

Hello! I’m new to Bayesian techniques and brms, so I’m wondering if anyone might have some experience/advice on the following.

I am trying to compare two eye-tracking trajectories of two different conditions to show their similarity without it showing as a null effect (i.e., wanting to quantify their large amount of overlap). I’m aware of Kruschke’s BEST method as a way of accepting the null value; my current idea is to apply BEST to each time point (total 30 time points). But, I’m wondering if anyone might have any other ideas. I’ve read through many other posts, but haven’t been able to find one that is seeking to demonstrate similarity and accept this null value.

Thank you in advance, I appreciate your help and input!

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With 30 time points, it’d be tractable to use a Gaussian Process. I’d parameterize things such that there’s an intercept GP and a GP that encodes the difference between conditions, where null in the latter will yield a ribbon centered on zero.