Computer problem

Simulate the activity of 64 neurons with Von Mises tuning curves to orientation evenly distributed along a circle.

Use A=90, b=10 and K=5. Make sure to express s in radians.   Assume that the noise is independent across neurons and follows a Gaussian distribution with fixed variance (s²=25).

1- Simulate 10000 trials for an orientation of 0 rad. On each trial, read out the encoded direction using population vector and maximum likelihood. Compute the bias and variance of both estimators.

2- Derive the Cramer-Rao bound for this population code using the formula:

Compare the variance predicted by the CR bound to the ones obtained in the simulations for s=0 rad.

3- Select the 64 preferred directions randomly and compute the bias and variance for population vector and maximum likelihood, using 10000 trials for an orientation of 0 rad. Which method is the most robust to this manipulation?