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Likelihoods aren’t fundamentally small. The center of a normal distribution has high likelihood (e.g. 1000000) if the standard deviation is small or low likeli
by lukego 3y ago
Likelihoods aren’t fundamentally small.
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.
- jdhwosnhw 3y agoAnother issue is that likelihoods associated with continuous distributions very often have units. You can’t meaningfully assign “magnitude” to a quantity with units. You can always change your unit system to make the likelihood of, say, a particular height in a population of humans to be arbitrarily large.