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Title: D-Guaranteed Discrimination of Statistical Hypotheses: a Review of Results and Unsolved Problems

Abstract

We compare two sequential d-guaranteed tests and an optimal d-guaranteed test based on a fixed number of observations with respect to the average number of observations within the most accepted practical applications of Bayesian probabilistic models. We consider the sequential “first skipping” test, the sequential locally efficient test based on the score statistic, and the test based on a fixed number of observations that minimizes the necessary sample size. We study various characteristics of these tests connected with the number of observations within three probabilistic models, namely, the normal (ϑ, σ{sup 2}) distribution of the observed random variable and the normal a priori distribution of ϑ with fixed σ{sup 2}; the exponential distribution with the intensity parameter ϑ and the a priori gamma distribution of ϑ; and the Bernoulli sampling with the success probability ϑ and the a priori beta distribution of ϑ. We discuss the connection of the d-posterior approach with the compound decision problem as applied to the analysis of data provided by microchips (when the false discovery rate, or FDR, for short, is treated as the d-risk of the first kind). We present the vast data on characteristics of the mentioned tests obtained by the method ofmore » mathematical modeling in several tables. We discuss unsolved problems of the d-guaranteed discrimination of hypotheses with the minimal number of observations and approaches to their solution.« less

Authors:
; ;  [1]
  1. Kazan State University (Russian Federation)
Publication Date:
OSTI Identifier:
22771592
Resource Type:
Journal Article
Journal Name:
Journal of Mathematical Sciences
Additional Journal Information:
Journal Volume: 228; Journal Issue: 5; Conference: International seminar on stability problems for stochastic models, Zakopane (Poland), 31 May - 5 Jun 2009; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1072-3374
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; DATA ANALYSIS; HYPOTHESIS; MATHEMATICAL MODELS; MATHEMATICAL SOLUTIONS; PROBABILISTIC ESTIMATION; PROBABILITY; RANDOMNESS; SAMPLING; STATISTICS

Citation Formats

Simushkin, D. S., Simushkin, S. V., E-mail: smshkn@gmail.com, and Volodin, I. N. D-Guaranteed Discrimination of Statistical Hypotheses: a Review of Results and Unsolved Problems. United States: N. p., 2018. Web. doi:10.1007/S10958-017-3643-6.
Simushkin, D. S., Simushkin, S. V., E-mail: smshkn@gmail.com, & Volodin, I. N. D-Guaranteed Discrimination of Statistical Hypotheses: a Review of Results and Unsolved Problems. United States. doi:10.1007/S10958-017-3643-6.
Simushkin, D. S., Simushkin, S. V., E-mail: smshkn@gmail.com, and Volodin, I. N. Thu . "D-Guaranteed Discrimination of Statistical Hypotheses: a Review of Results and Unsolved Problems". United States. doi:10.1007/S10958-017-3643-6.
@article{osti_22771592,
title = {D-Guaranteed Discrimination of Statistical Hypotheses: a Review of Results and Unsolved Problems},
author = {Simushkin, D. S. and Simushkin, S. V., E-mail: smshkn@gmail.com and Volodin, I. N.},
abstractNote = {We compare two sequential d-guaranteed tests and an optimal d-guaranteed test based on a fixed number of observations with respect to the average number of observations within the most accepted practical applications of Bayesian probabilistic models. We consider the sequential “first skipping” test, the sequential locally efficient test based on the score statistic, and the test based on a fixed number of observations that minimizes the necessary sample size. We study various characteristics of these tests connected with the number of observations within three probabilistic models, namely, the normal (ϑ, σ{sup 2}) distribution of the observed random variable and the normal a priori distribution of ϑ with fixed σ{sup 2}; the exponential distribution with the intensity parameter ϑ and the a priori gamma distribution of ϑ; and the Bernoulli sampling with the success probability ϑ and the a priori beta distribution of ϑ. We discuss the connection of the d-posterior approach with the compound decision problem as applied to the analysis of data provided by microchips (when the false discovery rate, or FDR, for short, is treated as the d-risk of the first kind). We present the vast data on characteristics of the mentioned tests obtained by the method of mathematical modeling in several tables. We discuss unsolved problems of the d-guaranteed discrimination of hypotheses with the minimal number of observations and approaches to their solution.},
doi = {10.1007/S10958-017-3643-6},
journal = {Journal of Mathematical Sciences},
issn = {1072-3374},
number = 5,
volume = 228,
place = {United States},
year = {2018},
month = {2}
}