What is the meaning of conditional independence?

In probability theory, conditional independence describes situations wherein an observation is irrelevant or redundant when evaluating the certainty of a hypothesis.

What are the conditions of independence?

Two events are independent, statistically independent, or stochastically independent if the occurrence of one does not affect the probability of occurrence of the other (equivalently, does not affect the odds).

What is conditional probability and independence?

A conditional probability can always be computed using the formula in the definition. Sometimes it can be computed by discarding part of the sample space. Two events A and B are independent if the probability P(A∩B) of their intersection A∩B is equal to the product P(A)⋅P(B) of their individual probabilities.

What is conditional independence in research?

X and Y are conditionally independent given Z, denoted by X ⊥ Y | Z, if and only if P(X, Y | Z) = P(X | Z) P(Y | Z). It reflects the fact that given the values of Z, further knowing the values of X does not provide any additional information about Y.

Does independence mean conditional independence?

Let C be a third random variable defined as C=A+B. Now, A and B are not conditionally independent given C. This is because if C is given then knowing either A or B gives perfect information about the other. Independence does not imply conditional independence.

What is meant by conditional independence between two events?

Definition. Two events A and B are conditionally independent given an event C with P(C)>0 if P(A∩B|C)=P(A|C)P(B|C)(1.8) Recall that from the definition of conditional probability, P(A|B)=P(A∩B)P(B), if P(B)>0.

What is meant by conditional independence between two events describe it in the context of a real time scenario?

Remember that two events A and B are independent if P(A∩B)=P(A)P(B),or equivalently, P(A|B)=P(A). We can extend this concept to conditionally independent events. In particular, Definition. Two events A and B are conditionally independent given an event C with P(C)>0 if P(A∩B|C)=P(A|C)P(B|C)(1.8)

What is the difference between dependent and independent probability?

Dependent events influence the probability of other events – or their probability of occurring is affected by other events. Independent events do not affect one another and do not increase or decrease the probability of another event happening.

What is the main difference between conditional probability and mutually exclusive events?

Conditional Probability for Mutually Exclusive Events The simplest example of mutually exclusive are events that cannot occur simultaneously. In other words, if one event has already occurred, another can event cannot occur. Thus, the conditional probability of mutually exclusive events is always zero.

What are conditional independence relations in Bayesian network?

A. Conditional Independence in Bayesian Network (aka Graphical Models) A Bayesian network represents a joint distribution using a graph. Specifically, it is a directed acyclic graph in which each edge is a conditional dependency, and each node is a distinctive random variable.

What is conditional independence in naive Bayes?

Naive Bayes classifier assume that the effect of the value of a predictor (x) on a given class (c) is independent of the values of other predictors. This assumption is called class conditional independence. P(x|c) is the likelihood which is the probability of predictor given class.