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Bayesian hierarchical modelling 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 Bayes' theorem is used to integrate them with the observed data and account for all the ...
In econometrics, a random effects model, also called a variance components model, is a statistical model where the model parameters are random variables.It is a kind of hierarchical linear model, which assumes that the data being analysed are drawn from a hierarchy of different populations whose differences relate to that hierarchy.
Regression beta coefficient estimates from the Liang-Zeger GEE are consistent, unbiased, and asymptotically normal even when the working correlation is misspecified, under mild regularity conditions. GEE is higher in efficiency than generalized linear models (GLMs) in the presence of high autocorrelation. [ 1 ]
The deviance information criterion (DIC) is a hierarchical modeling generalization of the Akaike information criterion (AIC). It is particularly useful in Bayesian model selection problems where the posterior distributions of the models have been obtained by Markov chain Monte Carlo (MCMC) simulation.
In Gaussian process regression, also known as Kriging, a Gaussian prior is assumed for the regression curve. The errors are assumed to have a multivariate normal distribution and the regression curve is estimated by its posterior mode. The Gaussian prior may depend on unknown hyperparameters, which are usually estimated via empirical Bayes. The ...
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In econometrics, the seemingly unrelated regressions (SUR) [1]: 306 [2]: 279 [3]: 332 or seemingly unrelated regression equations (SURE) [4] [5]: 2 model, proposed by Arnold Zellner in (1962), is a generalization of a linear regression model that consists of several regression equations, each having its own dependent variable and potentially ...
A draw of γ from its prior distribution is a list of the variables included in the regression. Conditional on this set of selected variables, we take a draw from the prior distribution of the regression coefficients (if γ i = 1 then β i ≠ 0 and if γ i = 0 then β i = 0). βγ denotes the subset of β for which γ i = 1.