arXiv 10 Feb 2022 · Econometrics · 2 citations (OpenAlex)
arXiv:2202.05192 · PDF · DOI · OpenAlex · Extracted main text
The von Mises-Fisher family is a parametric family of distributions on the surface of the unit ball, summarised by a concentration parameter and a mean direction. As a quasi-Bayesian prior, the von Mises-Fisher distribution is a convenient and parsimonious choice when parameter spaces are isomorphic to the hypersphere (e.g., maximum score estimation in semi-parametric discrete choice, estimation of single-index treatment assignment rules via empirical welfare maximisation, under-identifying linear simultaneous equation models). Despite a long history of application, measures of statistical divergence have not been analytically characterised for von Mises-Fisher distributions. This paper provides analytical expressions for the $f$-divergence of a von Mises-Fisher distribution from another, distinct, von Mises-Fisher distribution in $\mathbb{R}^p$ and the uniform distribution over the hypersphere. This paper also collect several other results pertaining to the von Mises-Fisher family of distributions, and characterises the limiting behaviour of the measures of divergence that we consider.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Amos, D. E (1974) Computation of modified Bessel functions and their ratios | 1.000 | 7 | 3 | 100% |
| 2 | Mardia, K. V. and P. E. Jupp (2009) Directional statistics | 1.000 | 6 | 3 | 100% |
| 3 | Kitagawa, T., H. Lopez, and J. Rowley (2022) Stochastic Treatment Choice with Empirical Welfare Updating self | 1.000 | 5 | 3 | 100% |
| 4 | Hornik, K. and B. Grün (2013) On conjugate families and Jeffreys priors for von Mises–Fisher distributions | 0.874 | 7 | 2 | 100% |
| 5 | NIST (2021) Digital Library of Mathematical Functions, Release 1.1.1 of 2021-03-15, F. W. J | 0.874 | 6 | 2 | 100% |
| 6 | van Erven, T. and P. Harremoës (2014) Rényi divergence and Kullback-Leibler divergence | 0.693 | 5 | 1 | 100% |
| 7 | Dhillon, I. S. and S. Sra (2003) Modeling data using directional distributions, Tech | 0.644 | 2 | 2 | 100% |
| 8 | Diethe, T (2015) A Note on the Kullback-Leibler Divergence for the von Mises-Fisher distribution | 0.511 | 2 | 1 | 100% |
| 9 | Hillen, T., K. J. Painter, A. C. Swan, and A. D. Murtha (2017) Moments of von Mises and Fisher distributions and applications | 0.511 | 2 | 1 | 100% |
| 10 | Lattimore, T. and C. Szepesvári (2020) Bandit algorithms | 0.511 | 2 | 1 | 100% |
Showing the top 10 of 38 scored citations.