تقرير
Decision Theory and Large Deviations for Dynamical Hypotheses Tests: Neyman-Pearson, Min-Max and Bayesian Tests
| العنوان: | Decision Theory and Large Deviations for Dynamical Hypotheses Tests: Neyman-Pearson, Min-Max and Bayesian Tests |
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| المؤلفون: | Ferreira, Hermes H., Lopes, Artur O., Lopes, Silvia R. C. |
| سنة النشر: | 2021 |
| المجموعة: | Mathematics Condensed Matter Mathematical Physics Statistics |
| مصطلحات موضوعية: | Mathematics - Statistics Theory, Condensed Matter - Statistical Mechanics, Mathematical Physics, Mathematics - Dynamical Systems, Mathematics - Probability, 37D35, 62C20, 62C10 |
| الوصف: | We analyze hypotheses tests using classical results on large deviations to compare two models, each one described by a different H\"older Gibbs probability measure. One main difference to the classical hypothesis tests in Decision Theory is that here the two measures are singular with respect to each other. Among other objectives, we are interested in the decay rate of the wrong decisions probability, when the sample size $n$ goes to infinity. We show a dynamical version of the Neyman-Pearson Lemma displaying the ideal test within a certain class of similar tests. This test becomes exponentially better, compared to other alternative tests, when the sample size goes to infinity. We are able to present the explicit exponential decay rate. We also consider both, the Min-Max and a certain type of Bayesian hypotheses tests. We shall consider these tests in the log likelihood framework by using several tools of Thermodynamic Formalism. Versions of the Stein's Lemma and Chernoff's information are also presented. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2101.08227 |
| رقم الأكسشن: | edsarx.2101.08227 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |