
doi: 10.2307/2951572
An elicitation diagnostic forms a question that compares the information in the prior distribution with the information in the given sample. This paper presents one elicitation diagnostic which identifies a family of prior distributions that are practically equivalent to the completely diffuse prior. Another diagnostic identifies priors that concentrate enough mass in the neighborhood of zero. Both diagnostics depend on sample size. For determining the sample size the diagnostic compares the sample information with the prior information. The formal treatment of elicitation diagnostics for normal linear regression models is considered in section 2. The question of a dogmatic or diffuse distribution as an adequate approximation to the prior distribution is comprehensively discussed. The multidimensional case is treated in section 3. Using the sample covariance matrix, diagnostics show themselves invariant to linear transformations of the model. The traditional misspecification tests play an important role in determining the values of the elicitation diagnostics. The results show the diagnostics that indicate a) families of priors which are equivalent to the dogmatic prior, b) the range of priors equivalent to the diffuse prior. For illustrating the formal parts of the paper, an example is discussed in the last section. Due to the important scientific results the paper is recommended to both theoretical and applied statisticians and econometricians which do research in Bayesian statistics.
dogmatic prior, elicitation diagnostics, missspecification tests, Bayesian inference, completely diffuse prior, prior distributions, normal linear regression models, Diagnostics, and linear inference and regression, approximations to prior distributions, sample covariance matrix, Applications of statistics to economics, prior elicitation
dogmatic prior, elicitation diagnostics, missspecification tests, Bayesian inference, completely diffuse prior, prior distributions, normal linear regression models, Diagnostics, and linear inference and regression, approximations to prior distributions, sample covariance matrix, Applications of statistics to economics, prior elicitation
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