Definition:Bayesian Inference
Definition
Bayesian inference is a method of statistical inference based on Bayes' Theorem.
The unknowns to be estimated are assumed to have a prior probability distribution.
Using Bayes' Theorem, this is combined with the information from observed data expressed in terms of the likelihood of forming a posterior probability distribution for the unknowns.
As and when further data become available, the posterior distribution may be used as a prior distribution for further analysis.
Belief-Based
Belief-based Bayesian inference is a method of Bayesian inference in which the prior distribution is based on a personal belief about how it is likely to be.
The precise nature of this prior probability distribution influences the posterior distribution.
Noncommittal Approach
Noncommittal Bayesian inference is a method of Bayesian inference in which there is a noncommittal attitude towards what the prior distribution is likely to be.
Under such an approach, the prior distribution is typically taken to be a uniform distribution over a plausible range of values.
Also see
- Definition:Conjugate Prior Distribution
- Definition:Gibbs Sampler
- Definition:Markov Chain Monte Carlo Simulation
- Definition:Bayes' Factor
- Results about Bayesian inference can be found here.
Source of Name
This entry was named for Thomas Bayes.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Bayesian inference
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Bayesian inference