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- What is the difference between likelihood and probability?
The wikipedia page claims that likelihood and probability are distinct concepts In non-technical parlance, "likelihood" is usually a synonym for "probability," but in statistical usage there is a clear distinction in perspective: the number that is the probability of some observed outcomes given a set of parameter values is regarded as the likelihood of the set of parameter values given the
- Confusion about concept of likelihood vs. probability
Likelihood is a measure of the extent to which a sample provides support for particular values of a parameter in a parametric model In the rain and umbrella example, this would mean that, on a scale from 0 to 10, the fact that Graham is using an umbrella provides about 2 units of support for the hypothesis that it is raining
- How to derive the likelihood function for binomial distribution for . . .
This is due to the asymptotic theory of likelihood ratios (which are asymptotically chi-square -- subject to certain regularity conditions that are often appropriate) Likelihood ratio tests are favored due to the Neyman-Pearson Lemma Therefore, when we attempt to test two simple hypotheses, we will take the ratio and the common leading factor
- estimation - Likelihood vs quasi-likelihood vs pseudo-likelihood and . . .
The concept of likelihood can help estimate the value of the mean and standard deviation that would most likely produce these observations We can also use this for estimating the beta coefficient of a regression model I am having a bit of difficulty understanding the quasi likelihood and the restricted likelihood
- Why is everything based on likelihoods even though likelihoods are so . . .
Likelihood — The likelihood that any parameter (or set of parameters) should have any assigned value (or set of values) is proportional to the probability that if this were so, the totality of observations should be that observed Distribution of likelihood
- bayesian - What is Likelihood Principle? - Cross Validated
The likelihood principle: a review, generalizations, and statistical implications by James O Berger and Robert L Wolpert is available for free on Project Euclid and provides an in-depth study of the principle You can also check the discussion paper by science philosopher Deborah Mayo On the Birnbaum Argument for the Strong Likelihood Principle
- How to calculate the likelihood function - Cross Validated
Admittedly though, looking at the likelihood like this, may make more clear the fact that what matters here for inference (for the specific distributional assumption), is the sum of the realizations, and not their individual values: the above likelihood is not "sample-specific" but rather "sum-of-realizations-specific": if we are given any
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