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Correlation and causality
In the past, statisticians believe that all information contained in a system can be used statistical correlation between its variables to represent. However, the concept of cause and effect information actually beyond the statistical correlation. For example, we can compare these two sentences: "The number and amount of air pollution related to automobile" and "car cause air pollution", the previous sentence is a statistical statement after a causal statements.
In statistical statement it expressed meaning it both ways: that is, if you know there are more cars, you might conclude that air pollution is more serious; the same, if you know that air pollution is more serious, more cars can be inferred. The causal statements tell us more information: that is, if the number of cars changes can affect air pollution; but not vice-versa, other forms (such as industrial plants) caused by air pollution, does not affect the number of cars.
Reichenbach Common Cause and Effect
（Reichenbach’s common cause principle ）
Therefore, the causal relevance of information and different, because it tells us how the system will change in the intervention.
In the classical model of causality, statistics and causal information Reichenbach principle related. This principle states that, two related variables must have a common cause: one is another reason; or the presence of a third variable is both a common cause. In the latter case, if the probability common reason is conditional (conditional), the correlation disappears.
For example, the incidence of Chile tsunami and tsunami in Japan have incidence correlated statistically. On statistics, the overall probability is greater than the product of two tsunami in Chile and the tsunami in Japan probability occur independently. However, either of these events are not the cause of another event. If we are to determine the probability of seismic Pacific Basin tsunami occurred, we should find that these two events are independent: the combination of the two (condition) probability equal to the product of two independent (condition) probability. In other words, the correlation disappears.
Given our understanding of earthquake, tsunami news in Chile is not available to provide any information about our probability tsunami in Japan. Reichenbach's conditional independence suggest that the earthquake may be the common cause of the two regions of the tsunami.
In addition to providing clues about the cause and effect relationships outside the conditional independence relationships can also tell us how to update the probability of an event based on new information related to the event, which is the Bayesian inference process. Reichenbach's two core principles of causal reasoning (Bayesian and causality) associated with the model.
