Exponential families! The secret magic at the heart of traditional statistics.
Exponential families are (sorta) probability distributions that just work, in the sense that and the things you would hope you can do with them, you can.
Noted here so I have somewhere to dump notes, but not something I am going to go into right now.
Most interesting models are not exponential families. There are curved exponential families which generalise exponential families in some way that I have not looked into.
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