Biometrika 86, 710-717 Clyde, M. A. (1999), Bayesian Model Averaging and Model Search Strategies. In J. M.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....each model, the weights being determined from the posterior probabilities of each model. This is known as Bayesian model averaging, and is widely used today as the basic methodology of accounting for model uncertainty. See Geisser (1993) Draper (1995) Raftery, Madigan and Hoeting (1997) and Clyde (1999) for discussion and references. Although keeping all models in the analysis is an ideal, this can be cumbersome for communication and descriptive purposes. If only one or two models receive substantial posterior probability, it would not be an egregious sin to eliminate the other models from ....

....be enormous, especially in model selection problems such as variable selection. We do not address computational issues here; some recent papers on the subject are Carlin and Chib (1995) Green (1995) Kass and Raftery (1995) Verdinelli and Wasserman (1995) Raftery, Madigan and Hoeting (1997) and Clyde (1999). 7 Diculty 2. When the models have parameter spaces of di ering dimensions, use of improper noninformative priors yields indeterminate answers. To see this, suppose that improper noninformative priors N i and N j are entertained for models M i and M j , respectively. The formal Bayes ....

Clyde, M. (1999), \Bayesian Model Averaging and Model Search Strategies," In Bayesian Statistics 6, J.M. Bernardo, A.P. Dawid, J.O. Berger, and A.F.M. Smith eds., Oxford University Press, pp. 157-185.

....(y) Indeed, the m i are often presented as the default posterior model probabilities. Whether one wants to simply select the model with the largest posterior probability, nd the best single predictive model (Barbieri Berger, 2000) or engage in Bayesian model averaging (Raftery et al. 1997; Clyde, 1999), it is necessary to compute the Bayes factors or the m i (y) or, at least, to be able to sample from the latter) 1 2 Challenges in Bayesian model selection The attractive features of the Bayesian approach to model selection are discussed, for instance, in Kass Raftery (1995) Berger ....

Clyde, M. (1999). Bayesian model averaging and model search strategies. In Bernardo, J. M., Dawid, A. P., Berger, J. O., & Smith, A. F. M., editors, Bayesian Statistics 6, pages 157-185. Oxford University Press.

....lattice field; indeed our approach may also be viewed as a process convolution model. Nonspatial Bayesian Poisson models using the identity link function and individual covariates, differing from those of Equations (2) and (3) in their use of truncated normal prior distributions, are studied by Clyde (1998). 6. SUMMARY AND FUTURE WORK In this paper we extend the class of spatial hierarchical mixture models introduced by Wolpert and Ickstadt (1998a) to allow for individual level attributes and for spatially varying covariates, by treating event locations as a marked point process in a generalized ....

Clyde, M. A. (1998). Bayesian model averaging and model search strategies. (this volume).

....model averaging also 3 produces smooth mean regression surfaces from the prior model space of non smooth piecewise surfaces. Bayesian model averaging is known to counter the inevitable model misspeci cation associated with a single model approach (Draper 1994, Raftery, Madigan and Hoeting 1997, Clyde 1999). Treating the location and number of splines as random makes the model spatially and data adaptive and in a sense automatically determines a bandwidth at each design point. We show that the complexity of the model, in terms of the number of splines used, adapts to the problem at hand. In high ....

Clyde, M. A. (1999). Bayesian model averaging and model search stratergies (with discussion), in J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. Smith (eds), Bayesian statistics VI, Oxford: Clarendon Press.

....paradigm 4 can easily incorporate model uncertainty by simultaneously considering entire families of models and obtaining estimates of the corresponding posterior model probabilities. Various computational techniques have been proposed for estimating the posterior model probabilities, see Clyde (1999) and Gamerman (1997) for example. In particular, the reversible jump MCMC (RJMCMC) algorithm proposed by Green (1995) is ideally suited to deal with Bayesian model determination problems. Given a set of models M 1 ; M k say, which a priori we are willing to consider as realistic ....

Clyde, M. A. (1999). Bayesian model averaging and model search strategies. In Bernardo, J. M., Smith, A. F. M., Dawid, A. P. and Berger, J. O., editors, Bayesian Statistics 6. Oxford University Press. In press.

....approximation to the true distribution which searches over models of high probability. In such problems, visiting the tails of the distribution may not be useful and better results, in terms of out of sample prediction can be obtained by Bayesian model averaging only over high probability models (Clyde, 1999). Thus, a search over good models is useful as demonstrated in Denison et al. 1998a) and Chipman et al. 1998) 4 Examples 4.1 First Stage Model: Wolf s sunspots example For illustration we present an analysis of Wolf s sunspots dataset using the Bayesian ASTAR model. The dataset consists of ....

Clyde, M. (1999) Bayesian model averaging and model search strategies. In Bayesian Statistics VI (Eds. J.M. Bernardo, J.O. Berger, A.P. Dawid and A.F.M. Smith). Oxford: Oxford University Press.

....and interactions in these variables. Because of the large number of possible models, we use Stochastic Search Variable Selection (SSVS) George and McCulloch 1993, 1997, Smith and Kohn 1996) to identify important models, and use Bayesian Model Averaging (BMA) Raftery, Madigan, and Hoeting 1997, Clyde 1999) to incorporate uncertainty about which predictor variables should be incorporated into the model. Rather than selecting a single model to make predictions, as is common practice, predictions under BMA are based on a weighted average of several models, where weights are based on the degree to ....

....expectations of quantities of interest. We can approximate BMA by estimating the posterior model probabilities by using a sample of models. Markov Chain Monte Carlo (MCMC) methods are one popular way of stochastically searching the model space to identify models that are used in model averaging (Clyde 1999) and lead to simulation consistent estimates of posterior means. In this problem, we will use the Stochastic Search Variable Selection algorithm of George and McCulloch (1997) which is a Gibbs sampler 8 Lamon and Clyde (Gelfand and Smith 1990) to sample models according to their posterior ....

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Clyde, M. (1999), \Bayesian Model Averaging and Model Search Strategies," In Bayesian Statistics 6, eds. Bernardo, J. M., Berger, J. O., Dawid, A. P. and Smith, A. F. M. Oxford University Press, pages 157-185.

....that the observations Y = Y 1 ; Y 2 ; Y n ) 0 are independent Poisson random variables with means = 1 ; n ) 0 and that the means are related to the covariates via a link function g, g( Xfi and use the canonical log link function. For approaches using an identity link see Clyde (1999). In the present context of variable selection, models correspond to different probability specifications for the data, so that under the m th model (Mm ) Mm : Y Poisson( log( Xm fi m 8 where Xm is the design matrix under model Mm and fi m is the vector of regression coefficients for ....

....information ensures that the prior distribution automatically takes into account the link function, so that the priors can be used with the canonical log link or the identity link. The latter may be preferable when spatial variation of covariates is an issue and data have been spatially aggregated (Clyde 1999). For the Poisson regression model with the log link the observed Fisher information is I( fi m ) X 0 m V ( fi m )Xm (9) where V (fi m ) is the covariance matrix for Y with elements exp(Xm fi m ) on the diagonal and 0 elsewhere. For the canonical link, the observed and expected Fisher ....

[Article contains additional citation context not shown here]

Clyde, M. (1999). "Bayesian model averaging and model search strategies". In Bayesian Statistics 6 J.M. Bernardo, A.P. Dawid, J.O. Berger, and A.F.M. Smith eds. Oxford University Press. pages 157-185.

No context found.

Biometrika 86, 710-717 Clyde, M. A. (1999), Bayesian Model Averaging and Model Search Strategies. In J. M.

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Clyde, M.A. (1999), \Bayesian model averaging and model search strategies," in Bayesian Statistics 6, eds. J.M. Bernardo, et. al., Oxford: Oxford University Press, pp. 23-42.

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Clyde, M.A. (1998). Bayesian Model Averaging and Model Search Strategies Bayesian Statistics 6, to appear.

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