## Mail Stop 10-R

### BibTeX

@MISC{Sinharay_mailstop,

author = {Sandip Sinharay and Hal S. Stern},

title = {Mail Stop 10-R},

year = {}

}

### OpenURL

### Abstract

ETS research prior to publication. They are available without charge from: Research Publications Office

### Citations

2570 | Density Estimation for Statistics and Data Analysis - Silverman - 1986 |

1461 | Bayesian Data Analysis - Gelman, Carlin, et al. - 1995 |

1144 | Bayes factors - Kass, Raftery - 1995 |

921 | Reversible jump Markov chain Monte Carlo computation and Bayesian model determination - Green - 1995 |

563 | Theory of Probability - Jeffreys - 1948 |

441 |
Modern applied statistics with S-Plus
- Venables, Ripley
- 1997
(Show Context)
Citation Context ...del. The posterior mode is taken to be the fixed point required in this method. Verdinelli-Wasserman. The Savage density ratio, given by (8), is applicable here. We use the S-PLUS function “density” (=-=Venables & Ripley, 1998-=-) for estimating the posterior density from a posterior sample. The function implements a kernel-density estimation with normal density function as the default choice of kernel. Our work uses the kern... |

376 | Marginal likelihood from the gibbs output
- Chib
- 1995
(Show Context)
Citation Context ... set that we have found most applicable to GLMMs. Other methods for computing Bayes factors appropriate in the GLMM context include bridge sampling (Meng & Wong, 1996), product space search (Carlin & =-=Chib, 1995-=-), Metropolized product space search (Dellaportas, Forster, & Ntzoufras, 2002), and reversible jump using partial analytic structure (Godsill, 2001). Parameterization A number of the methods for compu... |

267 |
Bayesian image restoration with two applications in spatial statistics
- BESAG, YORK, et al.
- 1991
(Show Context)
Citation Context ...nal matrix D having dii = E −1 i and a variance parameter σ2 . In practice, it appears often to be the case that either η or ψ dominates the other, but which one will not usually be known in advance (=-=Besag et al., 1991-=-). The model above contains 3 variance parameters (τ 2 , σ 2 , and φ) and as many as 112 random effects parameters, making it a more challenging data set to handle computationally 19than the turtle d... |

225 |
Accurate approximations for posterior moments and marginal densities JASA
- TIERNEY, KADANE
- 1986
(Show Context)
Citation Context ...) The integral is analytically intractable except for normal linear models, making computations with GLMMs difficult. Numerical integration techniques (e.g., Simpson’s rule) or Laplace approximation (=-=Tierney & Kadane, 1986-=-) may be used to approximate the GLMM likelihood. However, each of these two approaches is problematic and is not generally recommended (see, for example, Sinharay, 2001, and the references therein). ... |

222 | Constrained Monte Carlo maximum likelihood for dependent data - Geyer, Thompson - 1992 |

173 |
Bayesian model choice via Markov chain Monte Carlo methods
- Carlin, Chib
- 1995
(Show Context)
Citation Context ...esent the set that we have found most applicable to GLMMs. Other methods for computing Bayes factors appropriate in the GLMM context include bridge sampling (Meng & Wong, 1996), product space search (=-=Carlin & Chib, 1995-=-), Metropolized product space search (Dellaportas, Forster, & Ntzoufras, 2002), and reversible jump using partial analytic structure (Godsill, 2001). Parameterization A number of the methods for compu... |

160 |
Empirical Bayes estimates of age-standardized relative risks for use in disease mapping
- CLAYTON, KALDOR
- 1987
(Show Context)
Citation Context ...e variance component. The computations become much more difficult and time-consuming for such models. 17Description of the Data Set Table 2 shows a part of a frequently-analyzed data set (see, e.g., =-=Clayton & Kaldor, 1987-=-) regarding lip cancer data from the 56 administrative districts in Scotland. The objective of the study was to find out any pattern of regional variation in the disease incidence of lip cancer. The d... |

124 |
Marginal Likelihood from the MetropolisHastings
- Chib, Jeliazkov
- 2001
(Show Context)
Citation Context ...the Chib’s method and its run time may be reduced by reducing the autocorrelation of the generated parameter values in the MCMC 23algorithm, for example, by the use of the tailored proposal density (=-=Chib & Jeliazkov, 2001-=-). MCMC implementation is more complex for GLMMs than for the models used by Han and Carlin. 6. Discussion and Recommendations GLMMs are applied extensively and their use is likely to increase with th... |

119 | Simulating Ratios of Normalizing Constants via a Simple Identity
- Meng, Wong
- 1996
(Show Context)
Citation Context .... The methods summarized in this work represent the set that we have found most applicable to GLMMs. Other methods for computing Bayes factors appropriate in the GLMM context include bridge sampling (=-=Meng & Wong, 1996-=-), product space search (Carlin & Chib, 1995), Metropolized product space search (Dellaportas, Forster, & Ntzoufras, 2002), and reversible jump using partial analytic structure (Godsill, 2001). Parame... |

98 | Approximate Bayesian Inference by the Weighted Likelihood Bootstrap (with Discussion - Newton, Raftery - 1994 |

72 | Computing Bayes factors by combining simulation and asymptotic approximations - DiCiccio, Kass, et al. - 1997 |

56 | Bayesian model and variable selection using MCMC
- Dellaportas, Forster, et al.
- 2002
(Show Context)
Citation Context .... Other methods for computing Bayes factors appropriate in the GLMM context include bridge sampling (Meng & Wong, 1996), product space search (Carlin & Chib, 1995), Metropolized product space search (=-=Dellaportas, Forster, & Ntzoufras, 2002-=-), and reversible jump using partial analytic structure (Godsill, 2001). Parameterization A number of the methods for computing Bayes factors require computing the marginal likelihood p(y|ω, M) for on... |

40 |
Markov chain Monte Carlo methods for computing bayes factors: A comparative review
- Han, Carlin
- 2001
(Show Context)
Citation Context ... the best method to use for computation of the Bayes factor estimate for this data set. This is a noteworthy finding in that it runs counter to the conclusions of Han and Carlin (2001). They comment (=-=Han & Carlin, 2001-=-, p. 1131) that we are inclined to conclude that the marginal likelihood methods (Chib’s) appear to offer a better and safer approach to recommend to practitioners seeking to choose amongst a collecti... |

32 | On the relationship between Markov chain Monte Carlo for model uncertainty
- Godsill
- 2001
(Show Context)
Citation Context ...ing (Meng & Wong, 1996), product space search (Carlin & Chib, 1995), Metropolized product space search (Dellaportas, Forster, & Ntzoufras, 2002), and reversible jump using partial analytic structure (=-=Godsill, 2001-=-). Parameterization A number of the methods for computing Bayes factors require computing the marginal likelihood p(y|ω, M) for one or more values of ω. If the accurate computation of p(y|ω, M), which... |

19 | Bayesian tests and model diagnostics in conditionally independent hierarchical models - Albert - 1997 |

18 | Maximum-likelihood estimation for constrained- or missing- data models - Gelfand, Carlin - 1993 |

14 | A prior for the variance in hierarchical models
- Daniels
- 1999
(Show Context)
Citation Context ...ection 3 that application of the Verdinelli-Wasserman method requires that the prior distribution for σ 2 be finite and non-zero at σ 2 = 0. Our work uses the shrinkage prior distribution (see, e.g., =-=Daniels, 1999-=-) for the variance components, p(σ 2 ) = c (c+σ2) 2 , where c is a fixed constant denoting the median of p(σ2 ). We fix c at 1 and use this prior distribution for all the methods. A proper vague prior... |

13 |
Variance component testing in generalized linear models with random eects
- Lin
- 1997
(Show Context)
Citation Context ...whether a particular variance component is zero. The classical approaches for testing in this context are the likelihood ratio test (LRT) using a simulation-based null distribution or the score test (=-=Lin, 1997-=-). Our study concentrates on the Bayes factor, a Bayesian tool to perform hypothesis testing or model selection. 3. Bayes Factors Introduction The Bayesian approach to test a hypothesis about the vari... |

9 | 2000b) Experimental analysis of an early life-history stage: avian predation selects for larger body size of hatchling turtles
- Janzen, Tucker, et al.
(Show Context)
Citation Context ...one or more variance components in a GLMM are zero. Section 4 describes an application of a simple GLMM, a probit regression model with random effects, to the data set from a natural selection study (=-=Janzen, Tucker, & Paukstis, 2000-=-). The Bayes factor (comparing the models with and without the variance component) is estimated using the different approaches discussed in Section 3 and the performance of the approaches compared. Se... |

6 | Bayes factors for variance component models - Pauler, Wakefield, et al. - 1999 |

5 | Bayes Factors for Variance Component Testing in Generalized Linear Mixed Models,” Doctoral dissertation
- Sinharay
- 2001
(Show Context)
Citation Context ...Laplace approximation (Tierney & Kadane, 1986) may be used to approximate the GLMM likelihood. However, each of these two approaches is problematic and is not generally recommended (see, for example, =-=Sinharay, 2001-=-, and the references therein). Geyer and Thompson (1992) and Gelfand and Carlin (1993) suggest the use of importance sampling to estimate the value of the likelihood function. Starting from (1), for a... |

4 | Easy Estimation of Normalizing Constants and Bayes Factors from Posterior Simulation: Stabilizing the Harmonic Mean Estimator - Satagopan, Newton, et al. - 2000 |

3 | Mapping Rates Associated with Polygons - Cressie, Stern, et al. - 2000 |

3 | On the Sensitivity of Bayes Factors to the Prior Distribution - Sinharay, Stern - 2002 |

2 | Bayesian and constrained Bayesian inference for extremes in epidemiology - Stern, Cressie - 1995 |