Make the conditioning event the new space
For an event with , conditioning uses the probability measure . Restrict each event to its part inside and ignore outcomes outside it.
Probability & statistics / English
Conditional Independence
Elliot Nicholson · YouTube · 4:22
YouTube · Elliot NicholsonOriginal video
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The explanation, unpacked.
Reviewed learning material · Video analysis · English01 02 03
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Conditional independence is independence after restricting the probability space to a conditioning event. The lesson defines it and explains why it must be distinguished from ordinary independence in the original space.
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Chapters
0:40Make the conditioning event the new space1:30The defining product equation3:13Neither kind of independence implies the otherLearning script
Generated from the video's visuals and explanation; not verbatim speech.
For an event with , conditioning uses the probability measure . Restrict each event to its part inside and ignore outcomes outside it.
Events and are conditionally independent given when . This is the usual independence relation evaluated in the conditioned space.
Independence before conditioning need not survive conditioning. Conversely, conditional independence for a particular does not imply independence in the original space. This introductory video states the distinction without developing a numerical counterexample.
Knowledge cards
The defining product equation
Events and are conditionally independent given when . This is the usual independence relation evaluated in the conditioned space.
Neither kind of independence implies the other
Independence before conditioning need not survive conditioning. Conversely, conditional independence for a particular does not imply independence in the original space. This introductory video states the distinction without developing a numerical counterexample.
Explore the knowledge in this video
- Independence ExplanationAt 0:40
Why this connection?
For an event with , conditioning uses the probability measure . Restrict each event to its part inside and ignore outcomes outside it. Events and are conditionally independent given when . This is the usual independence relation evaluated in the conditioned space. Independence before conditioning need not survive conditioning. Conversely, conditional independence for a particular does not imply independence in the original space. This introductory video states the distinction without developing a numerical counterexample.
- Independence ExplanationAt 0:40
Why this connection?
For an event with , conditioning uses the probability measure . Restrict each event to its part inside and ignore outcomes outside it. Events and are conditionally independent given when . This is the usual independence relation evaluated in the conditioned space. Independence before conditioning need not survive conditioning. Conversely, conditional independence for a particular does not imply independence in the original space. This introductory video states the distinction without developing a numerical counterexample.
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