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  2. Posterior predictive distribution - Wikipedia

    en.wikipedia.org/wiki/Posterior_predictive...

    In Bayesian statistics, the posterior predictive distribution is the distribution of possible unobserved values conditional on the observed values. [1] [2]Given a set of N i.i.d. observations = {, …,}, a new value ~ will be drawn from a distribution that depends on a parameter , where is the parameter space.

  3. Posterior probability - Wikipedia

    en.wikipedia.org/wiki/Posterior_probability

    In the context of Bayesian statistics, the posterior probability distribution usually describes the epistemic uncertainty about statistical parameters conditional on a collection of observed data. From a given posterior distribution, various point and interval estimates can be derived, such as the maximum a posteriori (MAP) or the highest ...

  4. Bayesian linear regression - Wikipedia

    en.wikipedia.org/wiki/Bayesian_linear_regression

    Bayesian linear regression is a type of conditional modeling in which the mean of one variable is described by a linear combination of other variables, with the goal of obtaining the posterior probability of the regression coefficients (as well as other parameters describing the distribution of the regressand) and ultimately allowing the out-of-sample prediction of the regressand (often ...

  5. Approximate Bayesian computation - Wikipedia

    en.wikipedia.org/wiki/Approximate_Bayesian...

    Step 5: The posterior distribution is approximated with the accepted parameter points. The posterior distribution should have a non-negligible probability for parameter values in a region around the true value of in the system if the data are sufficiently informative. In this example, the posterior probability mass is evenly split between the ...

  6. Bayesian statistics - Wikipedia

    en.wikipedia.org/wiki/Bayesian_statistics

    The inference process generates a posterior distribution, which has a central role in Bayesian statistics, together with other distributions like the posterior predictive distribution and the prior predictive distribution. The correct visualization, analysis, and interpretation of these distributions is key to properly answer the questions that ...

  7. Predictive probability of success - Wikipedia

    en.wikipedia.org/wiki/Predictive_probability_of...

    Predictive power addresses this issue assuming the parameter has a specific distribution. Predictive power is a Bayesian power. A parameter in Bayesian setting is a random variable. Predictive power is a function of a parameter(s), therefore predictive power is also a variable.

  8. Bayesian hierarchical modeling - Wikipedia

    en.wikipedia.org/wiki/Bayesian_hierarchical_modeling

    Bayesian-specific workflow comprises three sub-steps: (b)–(i) formalizing prior distributions based on background knowledge and prior elicitation; (b)–(ii) determining the likelihood function based on a nonlinear function ; and (b)–(iii) making a posterior inference. The resulting posterior inference can be used to start a new research cycle.

  9. Conjugate prior - Wikipedia

    en.wikipedia.org/wiki/Conjugate_prior

    In Bayesian probability theory, if, given a likelihood function (), the posterior distribution is in the same probability distribution family as the prior probability distribution (), the prior and posterior are then called conjugate distributions with respect to that likelihood function and the prior is called a conjugate prior for the likelihood function ().