| Carota, C., Parmigiani, G., and Polson, N. G. (1996). Diagnostic measures for model criticism. Journal of the American Statistical Association 91, 753--762. |
....could replace the entire probability model, or some level of a hierarchical model. Speci cally, we de ne nonparametric extensions of a parametric probability model using Dirichlet process (DP) priors. Similar approaches have been used in the literature to implement formal model t diagnostics (Carota, Parmigiani and Polson, 1996). In this paper we discuss at an operational level how such extensions can be implemented. Assuming that inference in the original parametric model is implemented by Markov chain Monte Carlo (MCMC) simulation, we show how minimal additional code can turn the same program into an ....
....we have introduced practically feasible approaches to implement such model extensions with at least in principle minimal additional e ort. Considering nonparametric extensions can also be used for formal robustness measures in the form of model diagnostics. Such approaches are considered in Carota, Parmigiani and Polson (1996) and Florens, Richard and Rolin (1996) using DP priors, in Berger and Guglielmi (1999) using Polya tree priors, and in Verdinelli and Wasserman (1998) using Gaussian processes. The beauty of the nonparametric Bayesian sensitivity analysis model elaboration is that it plays this dual role. As a ....
Carota, C., Parmigiani, G. and Polson, N. G. (1996), \Diagnostic measures for model criticism," Journal of the American Statistical Association, 91, 753 { 762.
....Outlier detection then consists of parametric inference based on the extended model. For example, using variance inflation and or location shift extensions of normal linear models, this approach is applied in Pettit and Smith (1985) Sharples (1990) and Verdinelli and Wasserman (1991) Recently, Carota et. al (1996) provide a comprehensive account of related model elaboration methodology. Model extension techniques follow Principle D2 of Weisberg (1983) by turning a problem of null model criticism into one of parametric inference. However, because they use more complex models, Bayesian outlier diagnostics ....
Carota, C., Parmigiani, G., and Polson, N. G. (1996), "Diagnostic Measures for Model Criticism, " Journal of the American Statistical Association, 91, 753--762.
....controls the extent to which the model is allowed to adapt non parametrically to the data. In discrete models, the data can provide substantial information about the dispersion parameter. This fact has been used to develop goodness of fit diagnostics for discrete distributions (Carota, 1994; Carota et al. 1996) and to formulate adaptive semi parametric extensions of GLM s (Carota and Parmigiani, 1997) In this paper we pursue this approach in the context of developmental toxicology studies. A simple approach to the analysis of dose response data in toxicology studies is the logistic regression model ....
Carota, C., Parmigiani, G., and Polson, N. G. (1996). Diagnostic measures for model criticism. Journal of the American Statistical Association 91, 753--762.
....and illustrate its use in an application to biomedical data. Keywords: Bayesian model criticism, binomial data, logarithmic divergence, chi square statistics. Running Title: Binomial Goodness of Fit 1 Introduction Diagnostic measures are often used to assess the validity of a model. Recently, in Carota Parmigiani and Polson (1996), we proposed an approach to developing diagnostic measures that compromises between a fully coherent, utility based assessment of modelling alternatives and the exploratory character of much diagnostic and model building work. In summary, we suggested to approach model criticism by: 1) ....
....3) measuring the value of elaborating. In this paper we use this approach in the context of assessing the adequacy of the binomial model. Our approach builds on the extensive literature on model criticism. For brevity, we refer the reader to the references in Bernardo and Bayarri (1985) and Carota Parmigiani and Polson (1996). Likewise, for the literature on goodness of fit statistics for discrete data we refer to Read and Cressie (1988) and Lambert and Roeder (1995) The diagnostic measure investigated here uses a model elaboration based on the Dirichlet process, and uses the Kullback Leibler divergence between the ....
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Carota, C. Parmigiani, G. and Polson, N.G. (1996) Diagnostic Measures for Model Criticism.
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C. Carota, G. Parmigian & N. G. Polson (1996). Diagnostic measures for model criticism. Journal of the American Statistical Association, 91, 753--762.
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Carota, C., Parmigiani, G. and Polson, N. G. (1996). Diagnostic measures for model criticism. J. Amer. Statist. Assoc., 91, 753--762.
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Carota, C., Parmigiani, G. and Polson, N.G. (1993). "Diagnostic measures for model criticism", Technical Report #93-A20, ISDS, Duke University, Durham.
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Carota, C., Parmigiani, G. and Polson, N.G. (1993). "Diagnostic measures for model criticism", Technical Report #93-A20, ISDS, Duke University, Durham.
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