Abstract
In conventional information geometry, the deep relationship between differential geometrical structures such as the Fisher metric and \( \alpha \)-connections and statistical theory has been investigated for statistical models satisfying regularity conditions. However, the study of information geometry on non-regular statistical models has not been fully investigated. A one-sided truncated exponential family (oTEF) is a typical example. In this study, we define the Riemannian metric on the oTEF model not in a formal way but in the way compatible with the asymptotic properties of MLE in statistical theory. Then, we define alpha-parallel priors and show that the one-parallel prior exists on the oTEF model.
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Acknowledgements
This work was supported by JSPS KAKENHI Grant Number 19K11860 and JST SPRING Grant Number JPMJSP2138. This work was also supported by the Research Institute for Mathematical Sciences, an International Joint Usage/Research Center located in Kyoto University.
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Yoshioka, M., Tanaka, F. (2023). Alpha-parallel Priors on a One-Sided Truncated Exponential Family. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2023. Lecture Notes in Computer Science, vol 14071. Springer, Cham. https://doi.org/10.1007/978-3-031-38271-0_23
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DOI: https://doi.org/10.1007/978-3-031-38271-0_23
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