Another Way to Write Conditional Probability

The notation is convenient sometimes, but other times it obscures what’s going on, like in the definition of conditional independence and the law of total probability (when you fix the conditioning event).

We can rewrite as to make clear that we are deriving a new probability measure () induced from the old one () using the knowledge that occurred. Or we could shorten it even further, from to .

Conditional Independence

Conditional independence reduces to regular independence under the measure . becomes .

Total probability

, which is easier to see if we write it as .

Related Posts

Handy command line benchmarking tool

Stan Rogers

Ultimate Hot Couch Guy

Quote on Java Generics

The Programmer Tendency

Figure out undocumented JSON with gron

Mental Model of Dental Hygiene

Book Review: Swastika Night

Is there a name for this construction?

Fun with negation and idioms