Bayesian robustness on constrained density band classes
An interesting class in Bayesian robustness is a ‘band’ of priors: its flexibility allows for different tail behaviours while excluding point masses. In this paper, we consider density band classes of priors with additional constraints modelling different available prior information: quantiles, moments, constraints derived from the probability of observables or from the dependence structure in a multidimensional setting. The proposed techniques allow us to obtain the range of quantities of interest that are not linear or ratio linear functionals. Numerical examples are provided.
KeywordsBayesian robustness Density band class Neyman and pearson lemma Linear constrained optimization Fractional optimization
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- Perone Pacifico, M. (1995).Metodologie per la Robustezza Bayesiana: Un Approccio Unificante. Ph.D. Thesis, Univ. ‘La Sapienza’, Roma.Google Scholar
- Perone Pacifico, M., Salinetti, G. and Tardella, L. (1994). Bayesian robustness in the density bounded class through the Neyman and Pearson Lemma.Tech. Rep. A14, di Statistica, Univ. ‘La Sapienza’, Roma.Google Scholar
- Salinetti, G. (1994). Discussion to “An overview of robust Bayesian analysis”,Test 3, 109–115.Google Scholar
- Schaible, S. (1981). A survey of fractional programming.Generalized concavity in Optimization and Economics (S. Schaible and W. T. Ziemba eds.) New York: Academic Press, 417–440.Google Scholar
- Wasserman, L. (1992). Recent Methodological advances in robust Bayesian inference.Bayesian Statistics 4 (J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, eds.) Oxford: University Press, 483–502, (with discussion).Google Scholar