Jabarkan L(b2)/L(b1), dari Likelihood dalam bahasa sunda

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Likelihood nyaéta istilah nu dipaké keur fungsi likelihood.  Dina basa nu ilahat dipaké sapopoe, "likelihood" nyaéta salah sahiji harti nu sarua keur istilah "probability", tapi dina artikel ieu bakal ngagunakeun dina harti sacara téhnik.

In a sense, likelihood works backwards from probability: given B, we use the conditional probability P(A | B) to réason about A, and, given A, we use the likelihood function P(A | B) to réason about B.

This mode of réasoning is formalized in Bayes' theorem;

note the appéarance of a likelihood function for B given A in:

since, as functions of B, both P(A|B) and P(A|B)/P(A) are likelihood functions for B given A.

For more about making inferences via likelihood functions, see also

the method of maximum likelihood, and likelihood-ratio testing.

Likelihood function of a parametrized model

Among many applications, we consider here one of broad théoretical and practical importance.

Given a parametrized family of probability density functions

where θ is the paraméter (in the case of discrete distributions, the probability density functions are probability "mass" functions) the likelihood function is

where x is the observed outcome of an experiment.  In other words, when f(x | θ) is viewed as a function of x with θ fixed, it is a probability density function, and when viewed as a function of θ with x fixed, it is a likelihood function.

Note: This is not the same as the probability that those paraméters are the right ones, given the observed sample. Attempting to interpret the likelihood of a hypothesis given observed evidence as the probability of the hypothesis is a common error, with potentially disastrous réal-world consequences in medicine, engineering or jurisprudence. See prosecutor's fallacy for an example of this.