The CoM method is specifically designed for problems where the field and hyperparameters follow Gaussian distributions. When dealing with non-Gaussian random fields or non-Gaussian observation noise models, the performance of the CoM method may be affected.
For non-Gaussian random fields, the assumption of Gaussianity in the CoM method may lead to inaccuracies in representing the field distribution. Non-Gaussian fields may have heavier tails or skewness that cannot be captured effectively by a Gaussian distribution. This could result in biased estimates and unreliable inference results.
Similarly, non-Gaussian observation noise models can introduce complexities in the likelihood function. If the noise is not normally distributed, the likelihood calculation in the CoM method may not accurately capture the true data generation process. This can lead to incorrect posterior distributions and inference outcomes.
In such cases, modifications to the CoM method would be necessary to accommodate non-Gaussianity in both the field and observation noise models. This could involve using alternative probabilistic models or sampling techniques that are more suitable for non-Gaussian data.