# Thread: Marble-bag Memory Model in Behaviour Science

1. ## Marble-bag Memory Model in Behaviour Science

I hope this is an acceptable forum for this.

I have searched back to 2010 on the term 'geometric' without an answer.

I'm trying to assist a Masters student in (Animal) Behaviour with my 25yo rusty Math Stats degree.

They have a memory model for animals in an N-arm radial maze that can be analogised to drawing marbles from a bag, with replacement and a colour-swap on success.

Start of 'trial'...
[Draw from the bag until drawing a black marble.
[Record # of draws.
[Replace with a white marble.
... repeat N times.

For the "zero-bit" "non-memory" model, the expectation of number of "draws" before success (given t) can be modelled as a Geometric RV with p= (N+1-t)/N ... with dependent variable t = 1 + the number of explored arms of the maze = 1+ number of white marbles.

That much is fine and can be modelled by a GLM.
Models of non-"zero bit" memory are ok too.

Memory allows an integer number of arms of the maze to be remembered and not attempted again.
Equivalently, you keep an integer number of white marbles out of the bag, if you have them.

With memory of "C bits", the Geom distn has p = (N+1-t) / (N-C) for C < t <= N and can be analysed in the same way.

This all depends on C as a constant over all trials ... but the data departs from that for some animals.
They perform better with more trials.

What I'd like to do is incorporate a predetermined very simple function C(t) instead, with parameters to be determined in the analysis.

I'm wondering if it would require an EM-algorithm like I think takes place in the R command glm.nb in determining theta.

Each trial can be simply modelled as a small Markov chain ... I haven't explored that route yet.

I'd be happy to provide more detail, but I thought I should just gauge the interest level first.

Hopefully some of that is clear

Cheers,
Paul McGee

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