Likelihood function | Wikipedia audio article

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00:00:21 1 Definition
00:00:43 1.1 Discrete probability distribution
00:01:05 1.1.1 Example
00:01:27 1.2 Continuous probability distribution
00:02:11 1.3 In general
00:02:32 1.4 Likelihood function of a parameterized model
00:02:54 1.4.1 Likelihoods for continuous distributions
00:03:27 1.5 Likelihoods for mixed continuous–discrete distributions
00:05:16 1.6 Regularity conditions
00:05:49 2 Likelihood ratio and relative likelihood
00:07:27 2.1 Likelihood ratio
00:07:38 2.1.1 Distinction to odds ratio
00:08:11 2.2 Relative likelihood function
00:08:55 2.3 Likelihood region
00:09:16 3 Likelihoods that eliminate nuisance parameters
00:09:38 3.1 Profile likelihood
00:10:00 3.2 Conditional likelihood
00:11:17 3.3 Marginal likelihood
00:11:38 3.4 Partial likelihood
00:12:00 4 Products of likelihoods
00:12:22 5 Log-likelihood
00:12:44 5.1 Likelihood equations
00:13:17 5.2 Exponential families
00:14:00 5.2.1 Example: the gamma distribution
00:14:33 6 Background and interpretation
00:15:39 6.1 Historical remarks
00:15:50 6.2 Interpretations under different foundations
00:16:11 6.2.1 Frequentist interpretation
00:16:33 6.2.2 Bayesian interpretation
00:16:44 6.2.3 Likelihoodist interpretation
00:17:06 6.2.4 AIC-based interpretation
00:17:28 7 See also
00:17:50 8 Notes






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SUMMARY

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In statistics, the likelihood function (often simply called the likelihood) expresses the plausibilities of different parameter values for a given sample of data. While not to be interpreted as a probability, it is equal to the joint probability distribution of a random sample. However, whereas the latter is a density function defined on the sample space for a particular choice of parameter values, the likelihood function is defined on the parameter space while the random variable is fixed at the given observations.The likelihood function describes a hypersurface whose peak, if it exists, represents the combination of model parameter values that maximize the probability of drawing the sample actually obtained. The procedure for obtaining these arguments of the maximum of the likelihood function is known as maximum likelihood estimation, which for computational convenience is usually done using the natural logarithm of the likelihood, known as the log-likelihood function. Additionally, the shape and curvature of the likelihood surface represent information about the stability of the estimates, which is why the likelihood function is often plotted as part of a statistical analysis.The case for using likelihood was first made by R. A. Fisher, who believed it to be a self-contained framework for statistical modelling and inference. Later, Barnard and Birnbaum led a school of thought that advocated the likelihood principle, postulating that all relevant information for inference is contained in the likelihood function. But even in frequentist and Bayesian statistics, the likelihood function plays a fundamental role.

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