This can happen easily in Bayesian hierarchical models, where there is a hyperparameter that controls the variance of many lower-level parameters. When the variance is small, the probability density for these parameters is high (their distribution is sharply peaked), when the variance is large, the density is smaller (maybe many, many orders of magnitude smaller). So the mode will be where the variance is small, even if the data make this a much less probable region of the parameter space. (Note: the probability of a region is the product of its volume and its probability density - the total probability can be low even if the density is extremely high.)
You'll also typically get an unrepresentative mode for a neural network or other ML-type model, since the mode will be a highly-overfitted point.
You'll also typically get an unrepresentative mode for a neural network or other ML-type model, since the mode will be a highly-overfitted point.