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I am showing participants a scatter plot of x and y and then asking them to guess the correlation. I am trying to model how they arrive at their estimates. For simplicity, our baseline model assumes uncertainty in the perception component only (there is no parameter estimation uncertainty), assuming that observers compute a noisy representation of points’ positions in the two-dimensional scene.

So, given data = (user_estimated_correlation,x,y) where x,y are the actual data points and user_estimated_correlation is the participants guess of the correlation, I would like to infer the noise level added by the uncertainty in the perception.

def perception_model(data):
    user_estimated_correlation,x,y=data

    noise_in_x = pm.Normal('mu_x', 0,x.max()-x.min(), size=x.shape[0])
    noise_in_y = pm.Normal('mu_y', 0,y.max()-y.min(), size=y.shape[0])

    @pm.deterministic
    def add_noise(sigma=sigma,guess=guess):
        noisy_x = x+noise_in_x
        noisy_y = y+noise_in
        return noisy_x,noisy_y

   noisy_guess=np.corrcoef(add_noise(x,y))

   ##how do I do this line? I want to infer the visual noise parameters for the user .. or the actual noisy dataset they observed (i.e., noisy_x, noisy_y)
   observe(user_estimated_correlation ==  noisy_guess) 
   return locals()
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  • $\begingroup$ It's not clear to me what you're trying to model. Any papers you could reference? Other implementations of something similar? $\endgroup$ – Мати Тернер Jan 11 '17 at 16:28

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