WinBUGS – A Bayesian modelling framework: Concepts, structure, and extensibility
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...of such a package is BUGS (Lunn et al. 2000), which stands for “Bayesian updating using Gibbs Sampling”....
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...13MCMC simulations for random-slopes and more complex mixed-effects models can be run with general-purpose graphical models software such as WinBUGS (Lunn et al., 2000), JAGS (Plummer, 2003), or MCMCglmm (Hadfield, 2010)....
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...13 MCMC simulations for random-slopes and more complex mixed-effects models can be run with general-purpose graphical models software such as WinBUGS (Lunn, Thomas, Best, & Spiegelhalter, 2000), JAGS (Plummer, 2003), or MCMCglmm (Hadfield, 2010)....
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"WinBUGS – A Bayesian modelling fram..." refers methods in this paper
...... combine with the normal likelihood to give a gamma full conditional for? . (See Spiegelhalter et al. 1996b, pp. 17, 21, for tables of distributions and their so-called conjugate priors.) If for any node the full conditional distribution is not available in closed form then samples may be obtained by using (2) within a more general sampling method, such as adaptive rejection sampling (Gilks and Wild 1992) or a Metropolis-Hastings algorithm ......
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...Discrete Inversion of cumulative distribution function (trivial) Closed form (conjugate) Direct sampling using standard algorithms Log-concave Derivative-free adaptive rejection sampling (Gilks 1992) Restricted range Slice sampling (Neal 1997) Unrestricted range Metropolis-Hastings ( Metropolis et al. 1953, Hastings 1970)...
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...If for any node the full conditional distribution is not available in closed form then samples may be obtained by using (2) within a more general sampling method, such as adaptive rejection sampling (Gilks and Wild 1992) or a Metropolis-Hastings algorithm (Metropolis et al. 1953, Hastings 1970)....
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18,761 citations
"WinBUGS – A Bayesian modelling fram..." refers methods in this paper
...The primary technique is Gibbs sampling (Geman and Geman 1984), in which at each iteration a new value for each unobserved stochastic node is sampled from the corresponding parameter’s full conditional distribution, i....
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...The primary technique is Gibbs sampling (Geman and Geman 1984), in which at each iteration a new value for each unobserved stochastic node is sampled from the corresponding parameter’s full conditional distribution, i.e. its distribution conditional upon all other model parameters and the data....
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...Various algorithms exist for carrying out the required simulations, including Gibbs sampling (Geman and Geman 1984, Gelfand and Smith 1990), which is particularly useful for exploiting conditional independence assumptions (see Section 2.1)....
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14,965 citations
"WinBUGS – A Bayesian modelling fram..." refers methods in this paper
...If for any node the full conditional distribution is not available in closed form then samples may be obtained by using (2) within a more general sampling method, such as adaptive rejection sampling (Gilks and Wild 1992) or a Metropolis-Hastings algorithm (Metropolis et al. 1953, Hastings 1970)....
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7,399 citations