First passage time of an Ehrenfest process

Modeling
1

Hello all, I have a question regarding modelling first-passage time of an Ehrenfest urn process.

I know stan supports a first passage time Wiener process using the x ~ wiener(...) sampling statement. I should be clear that my understanding of the differences are limited but I believe that an Ehrenfest process FPT distribution has quite different properties - has anyone implemented something like this in the past or would have any idea how to do it?

I don’t have any code, but the data could be as simple as a single set of observations of times in seconds:

x: 2.35, 2.1, 1.7, ...

I’d like to be able to specify a number of particles for the process, and model e.g. thresholds, drift rate, noise rate, and starting point, similar to how stan models the Wiener diffusion model.

Any pointers would be super helpful!

2

I’m not familiar with the Ehrenfest urn process, so unfortunately I can’t directly address your question. But regarding the Wiener process - just in case you’re not aware - the distribution functions have recently been extended to additionally enable specifying inter-trial variabilities in the drift rate, non-decision time, and relative starting point (that is, 7 parameters in total). So perhaps that’s also of interest.

Also, if you just have simple response time data (i.e., no choice aspect), you could also consider a much simpler model like the Wald (a.k.a. inverse Gaussian) distribution, which can be parameterised in terms of a drift coefficient, diffusion coefficient, and threshold (and obviously non-decision time by shifting the lower bound). I have some Stan code and resources on that here.

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Thank you - that’s great. I have in the past used the Wiener process and my first instinct was to do so again this time. The thing that gave me pause was this paper, in which experiments very similar to mine seem to not be modelled well with a Wiener process (due to an incorrect coefficient of variation and mismatching skewness).

I think in the absence of an efficient implementation of the Ehrenfest process I will just use the Wiener and mention caveats, but was curious if anyone had done this before.

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