Results obtained with the following hypotheses: A Bayesian estimator finds the probability that there is something interesting at one side, based on how many fishes have gone that way. This estimator has 3 parameters: Probabilities of true positive and true negative for the other fishes, and absolute probability that something interesting is at that side. We have two of these estimators, one for each side. Then, the fish decides to go to the side with highest probability of being interesting, but we add a random number from a normal distribution to one of the probabilities to introduce stochasticity. The variance of this random number is the fourth parameter of the model.
I fit the four parameters for best comparison with the results presented by Ward et al. (2008) Quorum decision-making facilitates… PNAS, in their Figure 2.
>> params=fitparametros_bayes(hist_wardetal,1000);
>> params
params =
0.5271 0.9003 0.4316 0.5311
I only run 10 iterations for the fitting. Also, I think that the lines in the graph above should not cross, and also should decrease monotonically. So the fit must be improved.
However, I would say the results are good. Bars are experimental data from Ward et al. 2008, lines are model predictions. Compare with Figure 2 of Ward et al. 2008:
All these results are without replica predator. I will introduce the predator tomorrow.
Lab book for Zebrafish experiments 
Amazing. Good trick adding the gaussian.
Can we use the exps they do to fix parameters?
Comment by gonzalopolavieja — October 27, 2009 @ 8:55 pm
My first guess is that they are not comparable enough to fix our parameters. But I will check tomorrow.
Comment by alperezescudero — October 27, 2009 @ 9:33 pm
Reviewing the paper, I see that they have in fact 4 parameters:
1.- l:r, preference for one side for an individual fish (only different from 0.5:0.5 when there is a replica predator). They perform an experiment to fix it.
2.- m, which is the maximum probability for going to either side.
3.- a, which is the spontaneous accept rate.
4.- k, which is the stepness.
5.- T, which is the number of time steps that affect the probability.
They fit the last three parameters by crapy optimization. They independently fix m to 0.45, but it is also sort of a fitting to get the properties they expect. So in the end I would say they fit 4 parameters.
And we have also 4 parameters, so we are OK.
Comment by alperezescudero — October 28, 2009 @ 12:59 pm
The results of the model are extremely similar to Ward et al. What is the reason for the extreme similarity given that the theories are in principle very dissimilar? Do they collapse into the same maths for the parameters that fit teh experiment?
Comment by gonzalopolavieja — October 30, 2009 @ 11:24 am