Abstract
Sensitivity of a posterior quantity ρ(f, P) to the choice of the sampling distribution f and prior P is considered. Sensitivity is measured by the range of ρ(f, P) when f and P vary in nonparametric classes Γf and ΓP respectively. Direct and iterative methods are described which obtain the range of ρ(f, P) over f∈Γf when prior P is fixed, and also the overall range over f∈Γf and P∈ΓP. When multiple i.i.d. observations X 1,...,X k are observed from f, the posterior quantity ρ(f, P) is not a ratio-linear function of f. A method of steepest descent is proposed to obtain the range of ρ(f, P). Several examples illustrate applications of these methods.
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Basu, S. Posterior Sensitivity to the Sampling Distribution and the Prior: More than One Observation. Annals of the Institute of Statistical Mathematics 51, 499–513 (1999). https://doi.org/10.1023/A:1003950122133
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DOI: https://doi.org/10.1023/A:1003950122133