| Bayes' t. |
a theorem used to interconvert conditional probabilities: P ( B | A ) = P(A|B) P(B)P(A|B) P(B) + P(A|not B) P(not B) where P(A) and P(B) are the probabilities of two events, A and B, and P(A|B) and P(B|A) are the conditional probabilities of A given B and of B given A. For example, if A denotes a positive laboratory test result and B denotes the actual presence of disease in a tested patient, then P (A|B) is the “diagnostic sensitivity” of the test (true positive rate) and P (B) is the prevalence of the disease (P(A) is the frequency of positive test results). P(B|A) is the “predictive value of a positive test,” the probability that a patient testing positive will actually have the disease. The denominator of the equation, representing the sum of the true positives and false positives, is sometimes simplified to the equivalent function P(A), representing all those with positive results, both true and false.
출처: www.mercksource.com/pp/us/cns/cns_health_library.j...
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| bayesian s. |
a somewhat controversial statistical methodology that, unlike conventional statistics, which treats population parameters as fixed (though unknown) values, treats parameters as random variables with a specified probability distribution, termed the prior (or a priori) distribution. Bayes' theorem is then used to convert the probability distribution of an observable statistic (treated as a conditional probability for a given parameter value) to a conditional probability distribution of the parameter values for a given value of the observable statistic. This distribution is termed the posterior (or a posteriori) distribution because it assigns a probability to each parameter value that depends on the observed data. The controversial point is the prior distribution, which represents a subjective opinion of the experimenter as to the a priori credibility of the various parameter values; for example, in estimating the probability of the presence of a particular disease given a positive test result, the prior distribution represents the experimenter's judgment of the prevalence of the disease in the population under study.
출처: www.mercksource.com/pp/us/cns/cns_health_library.j...
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| Bayes' theorem |
A means to update the model parameter probability distributions based on data. Since p(MD) = p(M|D) p(D) = p(M) p(D|M), p(M|D) = p(M) p(D|M) / p(D). This is Bayes' Theorem. Usually, M represents the model parameters, D represents the data, and the | symbol indicates a statement of conditional probability. Here, p(M) are the a priori probabilities on the model parameters, p(D|M) is the likelihood, and p(D) is a normalizing factor.
출처: hea-www.harvard.edu/AstroStat/statjargon.html
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| bayesian statistics |
Statistics which incorporate prior knowledge and accumulated experience into probability calculations.
출처: www.dmdsurveys.com/dmd_site3/terminology_pages/ter...
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