The center of a normal distribution has high likelihood (e.g. 1000000) if the standard deviation is small or low likelihood if the standard deviation is large (e.g. 1/1000000.)
This effect is amplified when you are working with products of likelihoods. They can be infinitesimal or astronomical.
Giant likelihoods really surprised me the first time I experienced them but they’re not uncommon when you work with synthetic test data in high dimensions and/or small scales.
They still integrate to the same magnitude because the higher likelihood values are spread over shorter spans.
The center of a normal distribution has high likelihood (e.g. 1000000) if the standard deviation is small or low likelihood if the standard deviation is large (e.g. 1/1000000.)
This effect is amplified when you are working with products of likelihoods. They can be infinitesimal or astronomical.
Giant likelihoods really surprised me the first time I experienced them but they’re not uncommon when you work with synthetic test data in high dimensions and/or small scales.
They still integrate to the same magnitude because the higher likelihood values are spread over shorter spans.