Likelihood (5752 bytes)
1: In [[statistics]], a '''likelihood function''' is
7: That is, the likelihood function for ''B'' is the [[equivalence class]] o...
16: ...hood function'''''. In the colloquial language, "likelihood" is one of several informal synonyms for "probabi...
18: ... reason about ''A'', and, given ''A'', we use the likelihood function P(''A'' | ''B'') to reason about ''B''.
20: note the appearance of a likelihood function for ''B'' given ''A'' in:

Maximum likelihood (3333 bytes)
1: ...e parameter space that maximizes the [[likelihood|likelihood function]].
2: ... a function of ''p'' with ''x'' held fixed is the likelihood function
6: ... of those ''n'' voters will vote "yes". Then the likelihood function is
10: ...it is much less work to take the logarithm of the likelihood function before finding the root of the derivativ...
14: ...ihood is commonplace among statisticians. The log-likelihood is closely related to [[information entropy]].

Likelihood principle (11671 bytes)
2: ...pling (statistics)|sample]] is contained in the [[likelihood function]].
4: A [[likelihood function]] is a [[conditional probability|conditi...
5: ... a scalar multiple of the other; according to the likelihood principle, all information from the data relevant...
14: Then the observation that ''X'' = 3 induces the likelihood function
18: and the observation that ''Y'' = 12 induces the likelihood function

Marginal likelihood (2763 bytes)
1: ...t this usage is somewhat idiosyncratic. "Marginal likelihood" is the most commonly-used of these three terms.
3: ... function ''p''(''x''|''a'', ''b''), the marginal likelihood of ''b'' is
7: ...ution of ''a'' conditional on ''b''. The marginal likelihood of ''a'' is computed in an analogous way, by exch...
9: ...ng θ for the model parameters, the marginal likelihood for the model ''M'' is
13: ...el ''M''₂ involves a ratio of marginal likelihoods, the so-called [[Bayes factor]]:

Likelihood-ratio test (4970 bytes)
1: ...e test]] and the [[G-test]] can be phrased as log-likelihood ratios or approximations thereof.
5: ...at was actually observed, i.e., the data. The '''likelihood ratio''' is
9: ... ''x'', and is therefore a [[statistic]]. The '''likelihood-ratio test''' rejects the null hypothesis if the ...
31: ... so that they satisfy the constraints for the log-likelihood ratio to have the desired nice distribution. Sin...
33: ...e general contingency table, we can write the log-likelihood ratio statistic as

Chi-square test (979 bytes)
4: ...s in the analysis of variance and ''t''-tests are likelihood-ratio tests, but the test statistic does not have...

Posterior probability (1331 bytes)
4: ...s' theorem]] from the prior probability and the [[likelihood]].
6: ...g the [[prior probability distribution]] by the [[likelihood function]], and then dividing by the [[normalizin...
12: ...L_{X\mid Y=y}(x) = f_{Y\mid X=x}(y)</math> is the likelihood function as a function of ''x'',

Type II error (616 bytes)
3: ...as the likelihood of Type II error decreases, the likelihood of Type I error increases.

PRML (759 bytes)
1: In [[data storage]], '''Partial Response Maximum Likelihood''' (PRML) is a method for converting the weak ana...
6: * [[maximum likelihood]]

Expectation-maximization algorithm (3869 bytes)
1: ...maximization (M) step, which computes the maximum likelihood estimates of the parameters given the data and se...
7: ... (M) the expectation (E) of the complete data log-likelihood with respect to the conditional distribution of t...
13: ... EM iteration does not decrease the observed data likelihood function,
14: ...on are the stationary points of the observed data likelihood function.
16: ...verge to a [[local maximum]] of the observed data likelihood function.

G-test (2406 bytes)
1: ...lihood ratio test|likelihood-ratio]] or [[maximum likelihood]] [[statistical significance]] tests that are inc...
3: ...the time it was unduly laborious to calculate log-likelihood ratios. With the advent of electronic calculator...

Valence effect (1016 bytes)
1: ...he tendency for people to simply overestimate the likelihood of good things happening rather than bad things. ...
5: ...tional bias|attribution]] when we overpredict the likelihood of positive events happening to ''ourselves'' rel...

Effective Cycling (1183 bytes)
3: ... that these self-defeating behaviors increase the likelihood of a collision with another vehicle instead of mi...
5: ...bicycle lanes", which are claimed to increase the likelihood of collisions because they encourage overtaking '...

List of digital estimation techniques (796 bytes)
6: ****[[Maximum likelihood]]
23: ***[[Maximum likelihood]]

MLE (201 bytes)
3: *In [[statistics]], [[maximum likelihood]] estimator.

V-trend (1172 bytes)
5: ... in the same direction as their market index. The likelihood for an individual stock historically is its v-tre...

MPC-MLQ (191 bytes)
1: MPC-MLQ Multipulse LPC with Maximum Likelihood Quantization is a speech coding algorithm used fo...

Conjugate prior (2642 bytes)
3: ...alculated from the prior ''p''(&theta;) and the [[likelihood function]] ''p''(''x''|&theta;) as
8: ... the likelihood function be considered fixed; the likelihood function is usually well-determined from a statem...

Bayes factor (3630 bytes)
7: ...d-ratio test]], but instead of ''maximisimg'' the likelihood Bayesians ''average'' it over the parameters. Gen...
35: ...f 200, and find 115 success and 85 failures. The likelihood is
44: ... ratio test, which would have found the [[maximum likelihood]] estimate for ''q'', namely ¹¹⁵&#8260...

Estimation of covariance matrices (5441 bytes)
1: ...the [[probability distribution]] of the [[maximum likelihood]] [[estimator]] of the [[covariance matrix]] of a...
11: ==Maximum-likelihood estimation==
17: ...adily shown that the [[maximum likelihood|maximum-likelihood]] estimate of the expected value &mu; is the "sam...
23: ...'V'', we can just substitute it for &mu; in the [[likelihood function]]
87: is the maximum-likelihood estimator of the "population covariance matrix" '...

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