Bayesian Hierarchical Modeling Algorithm
A Bayesian Hierarchical Modeling Algorithm is a statistical modeling algorithm that ...
- See: Bayesian Inference, Bayesian Hierarchical Clustering, Robust Statistics, Statistical Model, Parameters, Posterior Probability, Bayes’ Theorem, Prior Distribution.
References
2015
- (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/Bayesian_hierarchical_modeling Retrieved:2015-10-1.
- Bayesian hierarchical modeling is a statistical model written in multiple levels (hierarchical form) that estimates the parameters of the posterior distribution using the Bayesian method.[1] The sub-models combine to form the hierarchical model, and the Bayes’ theorem is used to integrate them with the observed data, and account for all the uncertainty that is present. The result of this integration is the posterior distribution, also known as the updated probability estimate, as additional evidence on the prior distribution is acquired.
Frequentist statistics, the more popular foundation of statistics, has been known to contradict Bayesian statistics due to its treatment of the parameters as a random variable, and its use of subjective information in establishing assumptions on these parameters. However, Bayesians argue that relevant information regarding decision making and updating beliefs cannot be ignored and that hierarchical modeling has the potential to overrule classical methods in applications where respondents give multiple observational data. Moreover, the model has proven to be robust, with the posterior distribution less sensitive to the more flexible hierarchical priors. Hierarchical modeling is used when information is available on several different levels of observational units. The hierarchical form of analysis and organization helps in the understanding of multiparameter problems and also plays an important role in developing computational strategies.
- Bayesian hierarchical modeling is a statistical model written in multiple levels (hierarchical form) that estimates the parameters of the posterior distribution using the Bayesian method.[1] The sub-models combine to form the hierarchical model, and the Bayes’ theorem is used to integrate them with the observed data, and account for all the uncertainty that is present. The result of this integration is the posterior distribution, also known as the updated probability estimate, as additional evidence on the prior distribution is acquired.
- ↑ Allenby, Rossi, McCulloch (January 2005). “Hierarchical Bayes Model: A Practitioner’s Guide”. Journal of Bayesian Applications in Marketing, pp. 1–4. Retrieved 26 April 2014, p. 3
2005
- (Fei & Perona, 2005) ⇒ Li Fei-Fei, and Pietro Perona. (2005). “A Bayesian Hierarchical Model for Learning Natural Scene Categories.” In: Computer Vision and Pattern Recognition,