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Are nodes A and B conditionally independent given C Why or why not?
Note that A and B are NOT independent, but they are conditionally independent given C.
Are independent variables also conditionally independent?
Independence does not imply conditional independence: for instance, independent random variables are rarely independent conditionally on their sum or on their maximum.
Can be used to answer probabilistic queries conditioned on one piece of evidence?
Answer: Bayes rule can be used to answer probabilistic queries conditioned on one piece of evidence.
Which is an equivalent statement of conditional independence?
If A and B are conditionally independent given C, we obtain Thus, if A and B are conditionally independent given C, then P (A | B, C) = P (A | C) (1.9) Thus, Equations 1.8 and 1.9 are equivalent statements of the definition of conditional independence.
Can you have two independent events with conditional independence?
One important lesson here is that, generally speaking, conditional independence neither implies (nor is it implied by) independence. Thus, we can have two events that are conditionally independent but they are not unconditionally independent (such as and above). Also, we can have two events that are independent…
How is the conditional independence of a random variable determined?
Conditional independence of random variables. Two random variables X {displaystyle X} and Y {displaystyle Y} are conditionally independent given a third random variable Z {displaystyle Z} if and only if they are independent in their conditional probability distribution given Z {displaystyle Z} .
How does conditional independence reduce number of parameters?
Conditional independence between variables can greatly reduce the number of parameters. This reduces so much of the computation since we now only take into account its parent and disregard everything else. Let’s take a look at the numbers. Let’s say you have n binary variables (= n nodes).