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Bayesian inference computes the posterior probability according to Bayes' theorem: – the posterior probability of a hypothesis is proportional to its prior probability (its inherent likeliness) and the newly acquired likelihood (its compatibility with the new observed evidence). If the evidence does not match up with a hypothesis, one should reject the hypothesis.

But if a hypothesis is extremely unlikely a priori, one should also reject it, even if the evidence does appear to match up.

A prior can be elicited from the purely subjective assessment of an experienced expert.

An uninformative prior can be created to reflect a balance among outcomes when no information is available.

For more information see the Knowledge Base article on the maximum size for distribution lists.

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After the group has been created, you can send e-mail messages to the distribution list and all of the members will receive the message.

You can also set up a distribution list of phone numbers in the Messages app for sending text messages to a group of people. Tap "Save" in the upper-right corner of the screen to add the email distribution list to your contacts data.

Bayes' theorem calculates the renormalized pointwise product of the prior and the likelihood function, to produce the posterior probability distribution, which is the conditional distribution of the uncertain quantity given the data.

Similarly, the prior probability of a random event or an uncertain proposition is the unconditional probability that is assigned before any relevant evidence is taken into account. A prior can be determined from past information, such as previous experiments.

In the philosophy of decision theory, Bayesian inference is closely related to subjective probability, often called "Bayesian probability". In the table, the values w, x, y and z give the relative weights of each corresponding condition and case.

The figures denote the cells of the table involved in each metric, the probability being the fraction of each figure that is shaded. P(A|B) = Bayesian inference derives the posterior probability as a consequence of two antecedents, a prior probability and a "likelihood function" derived from a statistical model for the observed data.

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