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Bayesian inference (/ ˈ b eɪ z i ə n / BAY-zee-ən or / ˈ b eɪ ʒ ən / BAY-zhən) [1] is a method of statistical inference in which Bayes' theorem is used to calculate a probability of a hypothesis, given prior evidence, and update it as more information becomes available.
Bayesian statistics (/ ˈ b eɪ z i ə n / BAY-zee-ən or / ˈ b eɪ ʒ ən / BAY-zhən) [1] is a theory in the field of statistics based on the Bayesian interpretation of probability, where probability expresses a degree of belief in an event. The degree of belief may be based on prior knowledge about the event, such as the results of previous ...
Credible intervals are a Bayesian analog to confidence intervals in frequentist statistics. [2] The two concepts arise from different philosophies: [ 3 ] Bayesian intervals treat their bounds as fixed and the estimated parameter as a random variable, whereas frequentist confidence intervals treat their bounds as random variables and the ...
In Bayesian statistics, one can compute (Bayesian) prediction intervals from the posterior probability of the random variable, as a credible interval. In theoretical work, credible intervals are not often calculated for the prediction of future events, but for inference of parameters – i.e., credible intervals of a parameter, not for the ...
The Bayes factor is a ratio of two competing statistical models represented by their evidence, and is used to quantify the support for one model over the other. [1] The models in question can have a common set of parameters, such as a null hypothesis and an alternative, but this is not necessary; for instance, it could also be a non-linear model compared to its linear approximation.
The likelihood ratio is central to likelihoodist statistics: the law of likelihood states that the degree to which data (considered as evidence) supports one parameter value versus another is measured by the likelihood ratio. In frequentist inference, the likelihood ratio is the basis for a test statistic, the so-called likelihood-ratio test.
In particular, the bootstrap is useful when there is no analytical form or an asymptotic theory (e.g., an applicable central limit theorem) to help estimate the distribution of the statistics of interest. This is because bootstrap methods can apply to most random quantities, e.g., the ratio of variance and mean.
The base rate is an important concept in statistical inference, particularly in Bayesian statistics. [2] In Bayesian analysis, the base rate is combined with the observed data to update our belief about the probability of the characteristic or trait of interest.