## Estimating Bayes Factors via Posterior Simulation with the Laplace-Metropolis Estimator (1994)

Venue: | Journal of the American Statistical Association |

Citations: | 38 - 11 self |

### BibTeX

@ARTICLE{Lewis94estimatingbayes,

author = {Steven M. Lewis and Adrian E. Raftery},

title = {Estimating Bayes Factors via Posterior Simulation with the Laplace-Metropolis Estimator},

journal = {Journal of the American Statistical Association},

year = {1994},

volume = {92},

pages = {648--655}

}

### OpenURL

### Abstract

The key quantity needed for Bayesian hypothesis testing and model selection is the marginal likelihood for a model, also known as the integrated likelihood, or the marginal probability of the data. In this paper we describe a way to use posterior simulation output to estimate marginal likelihoods. We describe the basic LaplaceMetropolis estimator for models without random effects. For models with random effects the compound Laplace-Metropolis estimator is introduced. This estimator is applied to data from the World Fertility Survey and shown to give accurate results. Batching of simulation output is used to assess the uncertainty involved in using the compound Laplace-Metropolis estimator. The method allows us to test for the effects of independent variables in a random effects model, and also to test for the presence of the random effects. KEY WORDS: Laplace-Metropolis estimator; Random effects models; Marginal likelihoods; Posterior simulation; World Fertility Survey. 1 Introduction...

### Citations

1336 | Monte Carlo sampling methods using Markov chains and their applications - Hastings - 1970 |

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(Show Context)
Citation Context ...ayes factor for comparing the model with random effects to the model without random effects. The marginal likelihood for the model without random effects can be approximated using the Laplace method (=-=Raftery 1993-=-). For the 4 fixed effects model this was \Gamma222:15. Hence the Bayes factor for comparing the model with random effects against the model without random effects is exp f\Gamma220:5 \Gamma (\Gamma22... |

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40 |
Applications of a method for the efficient computation of posterior distributions
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- 1982
(Show Context)
Citation Context ...has been done by taking advantage of conjugacy or by assuming approximate posterior normality. In other cases the requisite integrals have been approximated using such methods as Gaussian quadrature (=-=Naylor and Smith 1982-=-), the Laplace approximation (de Bruijn 1970; Tierney and Kadane 1986) or Monte Carlo methods. With the availability of increasing computer power, Markov chain Monte Carlo (MCMC) has become a reasonab... |

25 | Hypothesis testing and model selection via posterior simulation - Raftery - 1996 |

21 | Educational applications of hierarchical linear models: A review - Raudenbush - 1988 |

14 | Demand or ideation? Evidence from the Iranian marital fertility decline. Unpublished paper - Raftery, Lewis, et al. - 1993 |

10 | The World Fertility Survey: An Assessment - Cleland, Scott - 1987 |

5 | Event history modeling of World Fertility Survey data." Working Paper No - Raftery, Lewis, et al. - 1993 |

4 |
Multilevel Modeling of Discrete Event History Data Using Markov Chain Monte Carlo Methods," unpublished
- Lewis
- 1994
(Show Context)
Citation Context ...kelihood; the predominant contribution of the maximized log-likelihood is apparent. The mean of the 15 within batch estimates is \Gamma220:5 and their standard deviation is 0:7. It can be argued (see =-=Lewis 1994-=-) that the compound Laplace-Metropolis estimator will have an approximate t-distribution with (B \Gamma 1) degrees of freedom. Using this approximation, a 95% highest posterior density interval for th... |

3 |
Contribution to the Discussion of three papers on Gibbs sampling and related Markov chain Monte Carlo methods
- Lewis
- 1993
(Show Context)
Citation Context ...n the sample. We implemented a Metropolis algorithm for estimating the parameters of a mixed logistic model, equation (8), in a Fortran program written specifically to handle event history data sets (=-=Lewis 1993, 1994; Ra-=-ftery, Lewis and Aghajanian 1994). We obtained the results shown in Table 1. Metropolis was run for a total of 5; 500 iterations of which the first 500 were discarded for "burn-in". Table 1:... |