Frequentist properties of Bayesian inequality tests
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arXiv
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| Format: | Preprint |
| Published: |
2016
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| _version_ | 1866910510281129984 |
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| author | Kaplan, David M. Zhuo, Longhao |
| author_facet | Kaplan, David M. Zhuo, Longhao |
| contents | Bayesian and frequentist criteria fundamentally differ, but often posterior and sampling distributions agree asymptotically (e.g., Gaussian with same covariance). For the corresponding single-draw experiment, we characterize the frequentist size of a certain Bayesian hypothesis test of (possibly nonlinear) inequalities. If the null hypothesis is that the (possibly infinite-dimensional) parameter lies in a certain half-space, then the Bayesian test's size is $α$; if the null hypothesis is a subset of a half-space, then size is above $α$; and in other cases, size may be above, below, or equal to $α$. Rejection probabilities at certain points in the parameter space are also characterized. Two examples illustrate our results: translog cost function curvature and ordinal distribution relationships. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1607_00393 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Frequentist properties of Bayesian inequality tests Kaplan, David M. Zhuo, Longhao Statistics Theory Econometrics Methodology Bayesian and frequentist criteria fundamentally differ, but often posterior and sampling distributions agree asymptotically (e.g., Gaussian with same covariance). For the corresponding single-draw experiment, we characterize the frequentist size of a certain Bayesian hypothesis test of (possibly nonlinear) inequalities. If the null hypothesis is that the (possibly infinite-dimensional) parameter lies in a certain half-space, then the Bayesian test's size is $α$; if the null hypothesis is a subset of a half-space, then size is above $α$; and in other cases, size may be above, below, or equal to $α$. Rejection probabilities at certain points in the parameter space are also characterized. Two examples illustrate our results: translog cost function curvature and ordinal distribution relationships. |
| title | Frequentist properties of Bayesian inequality tests |
| topic | Statistics Theory Econometrics Methodology |
| url | https://arxiv.org/abs/1607.00393 |