What is Log-likelihood?
An example would be great.
A:
Log-likelihood ratio
A likelihood-ratio test is a statistical test relying on a test statistic computed by taking the ratio of the maximum value of the likelihood function under the constraint of the null hypothesis to the maximum with that constraint relaxed. If that ratio is Λ and the null hypothesis holds, then for commonly occurring families of probability distributions, −2 log Λ has a particularly handy asymptotic distribution. Many common test statistics such as the Z-test, the F-test and Pearson's chi-square test can be phrased as log-likelihood ratios or approximations thereof.
http://www.knowledgerush.com/kr/encyclopedia/Log-likelihood_ratio/
Bruno Rothgiesser
2010-02-26 16:32:47
+2
A:
The only reason to use the log-likelihood instead of the plain old likelihood is mathematical convenience, because it lets you turn multiplication into addition. The plain old likelihood is P(parameters | data), i.e. assuming your data is fixed and you vary the parameters of your model. Maximizing this is one way to do parameter estimation and is known as maximum likelihood.
dsimcha
2010-02-26 16:36:07
I agree that this is probably what the question is about. On notation: the likelihood is typically denoted p(data|params) or L(params|data). The object p(params|data) is the posterior.
Tristan
2010-02-26 21:53:24