The multi-neuron response to the direction of stimulation is modelled as follows. Suppose that the conditional firing rate per neuron is expressed as follows:

Where a=1... N is the number of the neuron, s is the direction Angle of the external stimulus ([0,180]), s_a is the preferred direction of neuron a, and _a>0 is the parameter of the neuron tuning function. Assume that:

1. The neuronal action potential emission was statistically independent.

2. Neuronal action potential emission is a Poisson process.

Suppose that the Bayesian loss is the square variance:

S_hat is the estimated direction angle.

Through the action potential firing time points of these N neurons, establish an unbiased (MVUB) estimate of the minimum variance of the external stimulus direction s is and calculate its squared error.

fa(s)=exp(2a2(ssa)2) loss=(ss^)2