Dictionary of Evidence-based Medicine.pdf

10 Dictionary of Evidence-based Medicine
where P(A|B) = conditional probability of event A given that event B has
occurred and P(B|A) the conditional probability of B given A.
In diagnostic testing the theorem can be expressed as:
where D = disease, +T = positive test, P(D) = probability of no disease and
P(D|+T) = probability of disease given that (or conditional on) the test is
positive; P(+T|D) = probability of positive test given the presence of the
disease; P(+T|D) = probability of positive test given that the disease is
absent.
The theorem can be generalized to:
where E v E 2 ,...,E n are mutually exclusive and exhaustive events and A is
ny other event in the same domain.
Bayes' theorem can also be expressed in terms of odds, as follows:
The equation states that the posterior odds m)in favour of A is the
P(B|A) ^ ' ' P(A)
product of the Bayes' factor ( -=^) and the prior odds ( ,-) in
F
y
F
P(B|A)
P(A)
favour of A. The Bayes' factor is hence the ratio of the likelihood of event
A for observation B (P(B|A)) and the likelihood of event not A for observation
B (P(B|A)). The likelihood of a model can be defined as the probability
of the observations given that model (Figure 2).
Bayesian inference
Bayesian inference uses Bayes' theorem as a basis for making inference.
Central to Bayesian inference is the concept of conditional probability.
Unlike classic statistical inference, parameters are considered as random
variables with their own statistical distributions rather than as fixed
entities. In Bayesian statistical inference the observations are considered
fixed while the parameters are not. In contrast, in classic statistical inference,
the parameters are considered as fixed but the observations are not,
although they are known.