When using a Gaussian kernel to smooth neuronal firing rates, the choice of σ (sigma) determines the spatial extent of the smoothing. A larger value of σ results in a wider Gaussian kernel and a smoother firing rate estimate, while a smaller value of σ results in a narrower Gaussian kernel and a more localized estimate.

The choice of σ depends on several factors, including the desired level of smoothing, the noise level in the data, and the spatial scale of the phenomena being studied. In general, there is no one "correct" value of σ that works best for all cases, and it is often necessary to choose a value that balances the need for smoothing with the desire to preserve important features in the data.

One approach to choosing σ is to perform a sensitivity analysis in which different values of σ are tested and the results are compared. For example, one could plot the smoothed firing rate estimates for a range of σ values and visually inspect the results to determine the level of smoothing that best preserves the relevant features of the data.

Another approach is to use cross-validation, in which the data is divided into training and testing sets and different σ values are tested on the training set to determine the value that produces the best predictive performance on the testing set.

Ultimately, the choice of σ will depend on the specific data being analyzed and the goals of the analysis. It is important to consider the potential trade-offs between smoothing and preserving important features in the data, and to choose a value of σ that produces a balance between these factors.