> However, the idea is that often a lot of the probability mass - an amount that is not small - will be concentrated around the maximum likelihood estimate, and so that's why it makes a good estimate, and worth using.
This may be true for low dimensions but doesn’t generalise to high dimensions. Consider a 100-dimensional standard normal distribution for example. The MLE will still be at the origin but most of the mass will live in a thin shell of distance roughly 7 units from the origin.
This may be true for low dimensions but doesn’t generalise to high dimensions. Consider a 100-dimensional standard normal distribution for example. The MLE will still be at the origin but most of the mass will live in a thin shell of distance roughly 7 units from the origin.